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<div class="headertitle"><div class="title">facility_lp_benders.cc</div></div>
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<a href="facility__lp__benders_8cc.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a id="l00001" name="l00001"></a><span class="lineno"> 1</span><span class="comment">// Copyright 2010-2021 Google LLC</span></div>
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<div class="line"><a id="l00002" name="l00002"></a><span class="lineno"> 2</span><span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
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<div class="line"><a id="l00003" name="l00003"></a><span class="lineno"> 3</span><span class="comment">// you may not use this file except in compliance with the License.</span></div>
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<div class="line"><a id="l00004" name="l00004"></a><span class="lineno"> 4</span><span class="comment">// You may obtain a copy of the License at</span></div>
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<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
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<div class="line"><a id="l00006" name="l00006"></a><span class="lineno"> 6</span><span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
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<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
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<div class="line"><a id="l00008" name="l00008"></a><span class="lineno"> 8</span><span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
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<div class="line"><a id="l00009" name="l00009"></a><span class="lineno"> 9</span><span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
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<div class="line"><a id="l00010" name="l00010"></a><span class="lineno"> 10</span><span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
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<div class="line"><a id="l00011" name="l00011"></a><span class="lineno"> 11</span><span class="comment">// See the License for the specific language governing permissions and</span></div>
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<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// limitations under the License.</span></div>
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<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
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<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment">// An advanced benders decomposition example</span></div>
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<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment">//</span></div>
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<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment">// We consider a network design problem where each location has a demand that</span></div>
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<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment">// must be met by its neighboring facilities, and each facility can control</span></div>
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<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment">// its total capacity. In this version we also require that locations cannot</span></div>
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<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="comment">// use more that a specified fraction of a facilities capacity.</span></div>
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<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="comment">//</span></div>
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<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="comment">// Problem data:</span></div>
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<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="comment">// * F: set of facilities.</span></div>
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<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="comment">// * L: set of locations.</span></div>
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<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="comment">// * E: subset of {(f,l) : f in F, l in L} that describes the network between</span></div>
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<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="comment">// facilities and locations.</span></div>
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<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="comment">// * d: demand at location (all demands are equal for simplicity).</span></div>
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<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="comment">// * c: cost per unit of capacity at a facility (all facilities are have the</span></div>
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<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="comment">// same cost for simplicity).</span></div>
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<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="comment">// * h: cost per unit transported through an edge.</span></div>
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<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="comment">// * a: fraction of a facility's capacity that can be used by each location.</span></div>
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<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="comment">//</span></div>
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<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="comment">// Decision variables:</span></div>
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<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="comment">// * z_f: capacity at facility f in F.</span></div>
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<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="comment">// * x_(f,l): flow from facility f to location l for all (f,l) in E.</span></div>
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<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="comment">//</span></div>
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<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="comment">// Formulation:</span></div>
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<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="comment">//</span></div>
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<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="comment">// min c * sum(z_f : f in F) + sum(h_e * x_e : e in E)</span></div>
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<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment">// s.t.</span></div>
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<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment">// x_(f,l) <= a * z_f for all (f,l) in E</span></div>
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<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment">// sum(x_(f,l) : l such that (f,l) in E) <= z_f for all f in F</span></div>
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<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="comment">// sum(x_(f,l) : f such that (f,l) in E) >= d for all l in L</span></div>
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<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="comment">// x_e >= 0 for all e in E</span></div>
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<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="comment">// z_f >= 0 for all f in F</span></div>
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<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="comment">//</span></div>
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<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="comment">// Below we solve this problem directly and using a benders decompostion</span></div>
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<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="comment">// approach.</span></div>
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<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span> </div>
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<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="preprocessor">#include <algorithm></span></div>
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<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="preprocessor">#include <iostream></span></div>
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<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="preprocessor">#include <limits></span></div>
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<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="preprocessor">#include <utility></span></div>
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<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="preprocessor">#include <vector></span></div>
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<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span> </div>
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<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="preprocessor">#include "absl/container/flat_hash_map.h"</span></div>
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<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="preprocessor">#include "absl/flags/flag.h"</span></div>
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<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="preprocessor">#include "absl/random/random.h"</span></div>
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<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="preprocessor">#include "absl/random/seed_sequences.h"</span></div>
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<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span><span class="preprocessor">#include "absl/random/uniform_int_distribution.h"</span></div>
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<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="preprocessor">#include "absl/status/status.h"</span></div>
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<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span><span class="preprocessor">#include "absl/status/statusor.h"</span></div>
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<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span><span class="preprocessor">#include "absl/strings/str_format.h"</span></div>
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<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span><span class="preprocessor">#include "absl/strings/string_view.h"</span></div>
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<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span><span class="preprocessor">#include "absl/time/clock.h"</span></div>
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<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span><span class="preprocessor">#include "absl/time/time.h"</span></div>
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<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span><span class="preprocessor">#include "<a class="code" href="init__google_8h.html">ortools/base/init_google.h</a>"</span></div>
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<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="preprocessor">#include "<a class="code" href="base_2logging_8h.html">ortools/base/logging.h</a>"</span></div>
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<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span><span class="preprocessor">#include "<a class="code" href="base_2status__macros_8h.html">ortools/base/status_macros.h</a>"</span></div>
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<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span><span class="preprocessor">#include "<a class="code" href="math__opt_8h.html">ortools/math_opt/cpp/math_opt.h</a>"</span></div>
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<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span><span class="preprocessor">#include "<a class="code" href="util_2status__macros_8h.html">ortools/util/status_macros.h</a>"</span></div>
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<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span> </div>
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<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"><a class="line" href="facility__lp__benders_8cc.html#ab408ded47ed4632487b6f538ae4df9d0"> 72</a></span><a class="code hl_function" href="facility__lp__benders_8cc.html#ab408ded47ed4632487b6f538ae4df9d0">ABSL_FLAG</a>(<span class="keywordtype">int</span>, num_facilities, 3000, <span class="stringliteral">"Number of facilities."</span>);</div>
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<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"><a class="line" href="facility__lp__benders_8cc.html#a187b2452ce7ffbf3dc80a9c6ccc8b4d4"> 73</a></span><a class="code hl_function" href="facility__lp__benders_8cc.html#ab408ded47ed4632487b6f538ae4df9d0">ABSL_FLAG</a>(<span class="keywordtype">int</span>, num_locations, 50, <span class="stringliteral">"Number of locations."</span>);</div>
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<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"><a class="line" href="facility__lp__benders_8cc.html#a589d83de6bdfda324029266b63574e44"> 74</a></span><a class="code hl_function" href="facility__lp__benders_8cc.html#ab408ded47ed4632487b6f538ae4df9d0">ABSL_FLAG</a>(<span class="keywordtype">double</span>, edge_probability, 0.99, <span class="stringliteral">"Edge probability."</span>);</div>
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<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"><a class="line" href="facility__lp__benders_8cc.html#ab26c80732ec6702942ce6b3d16027861"> 75</a></span><a class="code hl_function" href="facility__lp__benders_8cc.html#ab408ded47ed4632487b6f538ae4df9d0">ABSL_FLAG</a>(<span class="keywordtype">double</span>, benders_precission, 1e-9, <span class="stringliteral">"Benders target precission."</span>);</div>
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<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"><a class="line" href="facility__lp__benders_8cc.html#a3d6782a997bb7c460159f23717a3a622"> 76</a></span><a class="code hl_function" href="facility__lp__benders_8cc.html#ab408ded47ed4632487b6f538ae4df9d0">ABSL_FLAG</a>(<span class="keywordtype">double</span>, location_demand, 1, <span class="stringliteral">"Client demands."</span>);</div>
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<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"><a class="line" href="facility__lp__benders_8cc.html#a70ca27183ea1caa3da0c437d9124d7b2"> 77</a></span><a class="code hl_function" href="facility__lp__benders_8cc.html#ab408ded47ed4632487b6f538ae4df9d0">ABSL_FLAG</a>(<span class="keywordtype">double</span>, facility_cost, 100, <span class="stringliteral">"Facility capacity cost."</span>);</div>
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<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"><a class="line" href="facility__lp__benders_8cc.html#a36423080607ac8d3b16d220c1f4d0c62"> 78</a></span><a class="code hl_function" href="facility__lp__benders_8cc.html#ab408ded47ed4632487b6f538ae4df9d0">ABSL_FLAG</a>(</div>
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<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span> <span class="keywordtype">double</span>, location_fraction, 0.001,</div>
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<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span> <span class="stringliteral">"Fraction of a facility's capacity that can be used by each location."</span>);</div>
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<div class="line"><a id="l00081" name="l00081"></a><span class="lineno"><a class="line" href="facility__lp__benders_8cc.html#a8877ac7799451df01858e6a1b79a4ba3"> 81</a></span><a class="code hl_function" href="facility__lp__benders_8cc.html#ab408ded47ed4632487b6f538ae4df9d0">ABSL_FLAG</a>(<a class="code hl_enumeration" href="namespaceoperations__research_1_1math__opt.html#a8b06041d7c1fb05f379714f4312306ec">operations_research::math_opt::SolverType</a>, solver_type,</div>
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<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span> <a class="code hl_enumvalue" href="namespaceoperations__research_1_1math__opt.html#a8b06041d7c1fb05f379714f4312306eca512b5059e1ca814e697fb191d93aaf7f">operations_research::math_opt::SolverType::kGlop</a>,</div>
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<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span> <span class="stringliteral">"the LP solver to use, possible values: glop, gurobi, glpk, pdlp"</span>);</div>
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<div class="line"><a id="l00084" name="l00084"></a><span class="lineno"> 84</span> </div>
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<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span><span class="keyword">namespace </span>{</div>
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<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> </div>
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<div class="line"><a id="l00087" name="l00087"></a><span class="lineno"> 87</span><span class="keyword">namespace </span><a class="code hl_namespace" href="namespaceoperations__research_1_1math__opt.html">math_opt</a> = <a class="code hl_namespace" href="namespaceoperations__research_1_1math__opt.html">operations_research::math_opt</a>;</div>
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<div class="line"><a id="l00088" name="l00088"></a><span class="lineno"> 88</span><span class="keyword">constexpr</span> <span class="keywordtype">double</span> <a class="code hl_variable" href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">kInf</a> = std::numeric_limits<double>::infinity();</div>
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<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span><span class="keyword">constexpr</span> <span class="keywordtype">double</span> <a class="code hl_variable" href="lagrangian__relaxation_8cc.html#a6ffb9a02546adae760787b2366ae6e41">kZeroTol</a> = 1.0e-3;</div>
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<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span> </div>
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<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span><span class="comment">// Facility location instance representation and generation</span></div>
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<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span><span class="comment"></span> </div>
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<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span><span class="comment">// First element is a facility and second is a location.</span></div>
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<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span><span class="keyword">using</span> Edge = std::pair<int, int>;</div>
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<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span> </div>
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<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span><span class="comment">// A simple randomly-generated facility-location network.</span></div>
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<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span><span class="keyword">class </span>Network {</div>
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<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span> Network(<span class="keywordtype">int</span> num_facilities, <span class="keywordtype">int</span> num_locations, <span class="keywordtype">double</span> edge_probability);</div>
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<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span> </div>
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<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> <span class="keywordtype">int</span> num_facilities()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> num_facilities_; }</div>
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<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> <span class="keywordtype">int</span> num_locations()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> num_locations_; }</div>
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<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span> </div>
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<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> <span class="keyword">const</span> std::vector<Edge>& edges()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> edges_; }</div>
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<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span> </div>
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<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span> <span class="keyword">const</span> std::vector<Edge>& edges_incident_to_facility(</div>
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<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span> <span class="keyword">const</span> <span class="keywordtype">int</span> facility)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span> <span class="keywordflow">return</span> facility_edge_incidence_[facility];</div>
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<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span> }</div>
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<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span> </div>
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<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> <span class="keyword">const</span> std::vector<Edge>& edges_incident_to_location(</div>
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<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> <span class="keyword">const</span> <span class="keywordtype">int</span> location)<span class="keyword"> const </span>{</div>
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<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="keywordflow">return</span> location_edge_incidence_[location];</div>
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<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span> }</div>
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<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> </div>
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<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span> <span class="keywordtype">double</span> edge_cost(<span class="keyword">const</span> Edge& edge)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> edge_costs_.at(edge); }</div>
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<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span> </div>
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<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span> <span class="keywordtype">int</span> num_facilities_;</div>
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<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span> <span class="keywordtype">int</span> num_locations_;</div>
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<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span> <span class="comment">// No order is assumed for the following lists of edges.</span></div>
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<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> std::vector<Edge> edges_;</div>
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<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> absl::flat_hash_map<Edge, double> edge_costs_;</div>
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<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> std::vector<std::vector<Edge>> facility_edge_incidence_;</div>
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<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> std::vector<std::vector<Edge>> location_edge_incidence_;</div>
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<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</span>};</div>
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<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> </div>
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<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span>Network::Network(<span class="keyword">const</span> <span class="keywordtype">int</span> num_facilities, <span class="keyword">const</span> <span class="keywordtype">int</span> num_locations,</div>
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<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> <span class="keyword">const</span> <span class="keywordtype">double</span> edge_probability) {</div>
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<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> absl::SeedSeq seq({1, 2, 3});</div>
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<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> absl::BitGen bitgen(seq);</div>
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<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> </div>
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<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> num_facilities_ = num_facilities;</div>
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<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> num_locations_ = num_locations;</div>
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<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> facility_edge_incidence_ =</div>
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<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</span> std::vector<std::vector<std::pair<int, int>>>(num_facilities);</div>
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<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> location_edge_incidence_ = std::vector<std::vector<std::pair<int, int>>>(</div>
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<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> num_locations, std::vector<std::pair<int, int>>());</div>
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<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> facility = 0; facility < num_facilities_; ++facility) {</div>
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<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> location = 0; location < num_locations_; ++location) {</div>
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<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> <span class="keywordflow">if</span> (absl::Bernoulli(bitgen, edge_probability)) {</div>
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<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> <span class="keyword">const</span> std::pair<int, int> edge({facility, location});</div>
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<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> facility_edge_incidence_[facility].push_back(edge);</div>
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<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> location_edge_incidence_[location].push_back(edge);</div>
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<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> edges_.push_back(edge);</div>
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<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> edge_costs_.insert({edge, absl::Uniform(bitgen, 0, 1.0)});</div>
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<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> }</div>
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<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> }</div>
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<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> }</div>
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<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> <span class="comment">// Ensure every facility is connected to at least one location and every</span></div>
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<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> <span class="comment">// location is connected to at least one facility.</span></div>
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<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> facility = 0; facility < num_facilities; ++facility) {</div>
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<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span> <span class="keyword">auto</span>& locations = facility_edge_incidence_[facility];</div>
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<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> <span class="keywordflow">if</span> (locations.empty()) {</div>
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<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span> <span class="keyword">const</span> <span class="keywordtype">int</span> location =</div>
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<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span> absl::uniform_int_distribution<int>(0, num_locations - 1)(bitgen);</div>
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<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="keyword">const</span> std::pair<int, int> edge({facility, location});</div>
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<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</span> locations.push_back(edge);</div>
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<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> location_edge_incidence_[location].push_back(edge);</div>
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<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> edges_.push_back(edge);</div>
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<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> edge_costs_.insert({edge, absl::Uniform(bitgen, 0, 1.0)});</div>
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<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> }</div>
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<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> }</div>
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<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> location = 0; location < num_locations; ++location) {</div>
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<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> <span class="keyword">auto</span>& facilities = location_edge_incidence_[location];</div>
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<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> <span class="keywordflow">if</span> (facilities.empty()) {</div>
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<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> <span class="keyword">const</span> <span class="keywordtype">int</span> facility =</div>
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<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</span> absl::uniform_int_distribution<int>(0, num_facilities - 1)(bitgen);</div>
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<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> <span class="keyword">const</span> std::pair<int, int> edge({facility, location});</div>
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<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> facilities.push_back(edge);</div>
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<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> facility_edge_incidence_[facility].push_back(edge);</div>
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<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> edges_.push_back(edge);</div>
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<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> edge_costs_.insert({edge, absl::Uniform(bitgen, 0, 1.0)});</div>
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<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> }</div>
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<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> }</div>
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<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span>}</div>
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<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> </div>
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<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span><span class="keyword">struct </span>FacilityLocationInstance {</div>
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<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> Network network;</div>
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<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="keywordtype">double</span> location_demand;</div>
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<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <span class="keywordtype">double</span> facility_cost;</div>
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<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <span class="keywordtype">double</span> location_fraction;</div>
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<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span>};</div>
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<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> </div>
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<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span><span class="comment">// Direct solve</span></div>
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<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span><span class="comment"></span> </div>
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<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span><span class="comment">// See file level comment for problem description and formulation.</span></div>
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<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span>absl::Status FullProblem(<span class="keyword">const</span> FacilityLocationInstance& instance,</div>
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<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> <span class="keyword">const</span> <a class="code hl_enumeration" href="namespaceoperations__research_1_1math__opt.html#a8b06041d7c1fb05f379714f4312306ec">math_opt::SolverType</a> solver_type) {</div>
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<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_facilities = instance.network.num_facilities();</div>
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<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_locations = instance.network.num_locations();</div>
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<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> </div>
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<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_model.html">math_opt::Model</a> <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>(<span class="stringliteral">"Full network design problem"</span>);</div>
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<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> </div>
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<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> <span class="comment">// Capacity variables</span></div>
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<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> std::vector<math_opt::Variable> z;</div>
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<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < num_facilities; j++) {</div>
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<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> z.push_back(<a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.AddContinuousVariable(0.0, <a class="code hl_variable" href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">kInf</a>));</div>
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<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> }</div>
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<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> </div>
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<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> <span class="comment">// Flow variables</span></div>
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<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> absl::flat_hash_map<Edge, math_opt::Variable> x;</div>
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<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>& edge : instance.network.edges()) {</div>
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<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_variable.html">math_opt::Variable</a> x_edge = <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.AddContinuousVariable(0.0, <a class="code hl_variable" href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">kInf</a>);</div>
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<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> x.insert({edge, x_edge});</div>
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<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> }</div>
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<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> </div>
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<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> <span class="comment">// Objective Function</span></div>
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<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_linear_expression.html">math_opt::LinearExpression</a> objective_for_edges;</div>
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<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>& [edge, x_edge] : x) {</div>
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<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> objective_for_edges += instance.network.edge_cost(edge) * x_edge;</div>
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<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> }</div>
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<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</span> <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.Minimize(objective_for_edges +</div>
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<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> instance.facility_cost * <a class="code hl_function" href="namespaceoperations__research_1_1math__opt.html#a2d3e7a73de1ae32066be431b5e68f613">math_opt::Sum</a>(z));</div>
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<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> </div>
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<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> <span class="comment">// Demand constraints</span></div>
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<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> location = 0; location < num_locations; ++location) {</div>
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<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_linear_expression.html">math_opt::LinearExpression</a> incomming_supply;</div>
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<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>& edge :</div>
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<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> instance.network.edges_incident_to_location(location)) {</div>
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<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> incomming_supply += x.at(edge);</div>
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<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> }</div>
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<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.AddLinearConstraint(incomming_supply >= instance.location_demand);</div>
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<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> }</div>
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<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> </div>
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<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> <span class="comment">// Supply constraints</span></div>
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<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> facility = 0; facility < num_facilities; ++facility) {</div>
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<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_linear_expression.html">math_opt::LinearExpression</a> outgoing_supply;</div>
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<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>& edge :</div>
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<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> instance.network.edges_incident_to_facility(facility)) {</div>
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<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> outgoing_supply += x.at(edge);</div>
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<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> }</div>
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<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.AddLinearConstraint(outgoing_supply <= z[facility]);</div>
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<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> }</div>
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<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> </div>
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<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span> <span class="comment">// Arc constraints</span></div>
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<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> facility = 0; facility < num_facilities; ++facility) {</div>
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<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>& edge :</div>
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<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> instance.network.edges_incident_to_facility(facility)) {</div>
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<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.AddLinearConstraint(x.at(edge) <=</div>
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<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> instance.location_fraction * z[facility]);</div>
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<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> }</div>
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<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> }</div>
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<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> <a class="code hl_define" href="base_2status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011">ASSIGN_OR_RETURN</a>(<span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_solve_result.html">math_opt::SolveResult</a> result,</div>
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<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <a class="code hl_function" href="namespaceoperations__research_1_1math__opt.html#a5767ee23f380e72488d3c7ebf2d742b1">math_opt::Solve</a>(<a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>, solver_type));</div>
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<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> <span class="keywordflow">if</span> (result.<a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_solve_result.html#a77d1ea96211300e9417b965981953c81">termination</a>.<a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_termination.html#a36d5365d462f57468ba3a9d8ae6bbec9">reason</a> != math_opt::TerminationReason::kOptimal) {</div>
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<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceutil.html#a302ee4bfcb86ea9ed64a193ed0b14648">util::InternalErrorBuilder</a>()</div>
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<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> << <span class="stringliteral">"failed to find an optimal solution: "</span> << result.<a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_solve_result.html#a77d1ea96211300e9417b965981953c81">termination</a>;</div>
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<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> }</div>
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<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span> </div>
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<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> std::cout << <span class="stringliteral">"Full problem optimal objective: "</span></div>
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<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span> << absl::StrFormat(<span class="stringliteral">"%.9f"</span>, result.<a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_solve_result.html#a84f066c304d8bcbb9567be094feb9b08">objective_value</a>()) << std::endl;</div>
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<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> <span class="keywordflow">return</span> absl::OkStatus();</div>
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<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"> 258</span>}</div>
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<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> </div>
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<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span><span class="comment">// Benders solver</span></div>
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<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span><span class="comment"></span> </div>
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<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span><span class="comment">// Setup first stage model:</span></div>
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<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span><span class="comment">//</span></div>
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<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span><span class="comment">// min c * sum(z_f : f in F) + w</span></div>
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<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span><span class="comment">// s.t.</span></div>
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<div class="line"><a id="l00268" name="l00268"></a><span class="lineno"> 268</span><span class="comment">// z_f >= 0 for all f in F</span></div>
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<div class="line"><a id="l00269" name="l00269"></a><span class="lineno"> 269</span><span class="comment">// sum(fcut_f^i z_f) + fcut_const^i <= 0 for i = 1,...</span></div>
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<div class="line"><a id="l00270" name="l00270"></a><span class="lineno"> 270</span><span class="comment">// sum(ocut_f^j z_f) + ocut_const^j <= w for j = 1,...</span></div>
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<div class="line"><a id="l00271" name="l00271"></a><span class="lineno"> 271</span><span class="keyword">struct </span>FirstStageProblem {</div>
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<div class="line"><a id="l00272" name="l00272"></a><span class="lineno"> 272</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_model.html">math_opt::Model</a> <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>;</div>
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<div class="line"><a id="l00273" name="l00273"></a><span class="lineno"> 273</span> std::vector<math_opt::Variable> z;</div>
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<div class="line"><a id="l00274" name="l00274"></a><span class="lineno"> 274</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_variable.html">math_opt::Variable</a> w;</div>
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<div class="line"><a id="l00275" name="l00275"></a><span class="lineno"> 275</span> </div>
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<div class="line"><a id="l00276" name="l00276"></a><span class="lineno"> 276</span> FirstStageProblem(<span class="keyword">const</span> Network& network, <span class="keyword">const</span> <span class="keywordtype">double</span> facility_cost);</div>
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<div class="line"><a id="l00277" name="l00277"></a><span class="lineno"> 277</span>};</div>
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<div class="line"><a id="l00278" name="l00278"></a><span class="lineno"> 278</span> </div>
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<div class="line"><a id="l00279" name="l00279"></a><span class="lineno"> 279</span>FirstStageProblem::FirstStageProblem(<span class="keyword">const</span> Network& network,</div>
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<div class="line"><a id="l00280" name="l00280"></a><span class="lineno"> 280</span> <span class="keyword">const</span> <span class="keywordtype">double</span> facility_cost)</div>
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<div class="line"><a id="l00281" name="l00281"></a><span class="lineno"> 281</span> : <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>(<span class="stringliteral">"First stage problem"</span>), w(<a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.AddContinuousVariable(0.0, <a class="code hl_variable" href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">kInf</a>)) {</div>
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<div class="line"><a id="l00282" name="l00282"></a><span class="lineno"> 282</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_facilities = network.num_facilities();</div>
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<div class="line"><a id="l00283" name="l00283"></a><span class="lineno"> 283</span> </div>
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<div class="line"><a id="l00284" name="l00284"></a><span class="lineno"> 284</span> <span class="comment">// Capacity variables</span></div>
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<div class="line"><a id="l00285" name="l00285"></a><span class="lineno"> 285</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < num_facilities; j++) {</div>
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<div class="line"><a id="l00286" name="l00286"></a><span class="lineno"> 286</span> z.push_back(<a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.AddContinuousVariable(0.0, <a class="code hl_variable" href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">kInf</a>));</div>
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<div class="line"><a id="l00287" name="l00287"></a><span class="lineno"> 287</span> }</div>
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<div class="line"><a id="l00288" name="l00288"></a><span class="lineno"> 288</span> </div>
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<div class="line"><a id="l00289" name="l00289"></a><span class="lineno"> 289</span> <span class="comment">// First stage objective</span></div>
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<div class="line"><a id="l00290" name="l00290"></a><span class="lineno"> 290</span> <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.Minimize(w + facility_cost * <a class="code hl_function" href="namespaceoperations__research_1_1math__opt.html#a2d3e7a73de1ae32066be431b5e68f613">Sum</a>(z));</div>
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<div class="line"><a id="l00291" name="l00291"></a><span class="lineno"> 291</span>}</div>
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<div class="line"><a id="l00292" name="l00292"></a><span class="lineno"> 292</span> </div>
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<div class="line"><a id="l00293" name="l00293"></a><span class="lineno"> 293</span><span class="comment">// Represents a cut if the form:</span></div>
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<div class="line"><a id="l00294" name="l00294"></a><span class="lineno"> 294</span><span class="comment">//</span></div>
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<div class="line"><a id="l00295" name="l00295"></a><span class="lineno"> 295</span><span class="comment">// z_coefficients^T z + constant <= w_coefficient * w</span></div>
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<div class="line"><a id="l00296" name="l00296"></a><span class="lineno"> 296</span><span class="comment">//</span></div>
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<div class="line"><a id="l00297" name="l00297"></a><span class="lineno"> 297</span><span class="comment">// This will be a feasibility cut if w_coefficient = 0.0 and an optimality</span></div>
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<div class="line"><a id="l00298" name="l00298"></a><span class="lineno"> 298</span><span class="comment">// cut if w_coefficient = 1.</span></div>
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<div class="line"><a id="l00299" name="l00299"></a><span class="lineno"> 299</span><span class="keyword">struct </span>Cut {</div>
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<div class="line"><a id="l00300" name="l00300"></a><span class="lineno"> 300</span> std::vector<double> z_coefficients;</div>
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<div class="line"><a id="l00301" name="l00301"></a><span class="lineno"> 301</span> <span class="keywordtype">double</span> <a class="code hl_variable" href="variable__and__expressions_8cc.html#a98c17ae8d99a73259ea78de8c4b66254">constant</a>;</div>
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<div class="line"><a id="l00302" name="l00302"></a><span class="lineno"> 302</span> <span class="keywordtype">double</span> w_coefficient;</div>
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<div class="line"><a id="l00303" name="l00303"></a><span class="lineno"> 303</span>};</div>
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<div class="line"><a id="l00304" name="l00304"></a><span class="lineno"> 304</span> </div>
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<div class="line"><a id="l00305" name="l00305"></a><span class="lineno"> 305</span><span class="comment">// Solves the second stage model:</span></div>
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<div class="line"><a id="l00306" name="l00306"></a><span class="lineno"> 306</span><span class="comment">//</span></div>
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<div class="line"><a id="l00307" name="l00307"></a><span class="lineno"> 307</span><span class="comment">// min sum(h_e * x_e : e in E)</span></div>
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<div class="line"><a id="l00308" name="l00308"></a><span class="lineno"> 308</span><span class="comment">// s.t.</span></div>
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<div class="line"><a id="l00309" name="l00309"></a><span class="lineno"> 309</span><span class="comment">// x_(f,l) <= a * zz_f for all (f,l) in E</span></div>
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<div class="line"><a id="l00310" name="l00310"></a><span class="lineno"> 310</span><span class="comment">// sum(x_(f,l) : l such that (f,l) in E) <= zz_f for all f in F</span></div>
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<div class="line"><a id="l00311" name="l00311"></a><span class="lineno"> 311</span><span class="comment">// sum(x_(f,l) : f such that (f,l) in E) >= d for all l in L</span></div>
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<div class="line"><a id="l00312" name="l00312"></a><span class="lineno"> 312</span><span class="comment">// x_e >= 0 for all e in E</span></div>
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<div class="line"><a id="l00313" name="l00313"></a><span class="lineno"> 313</span><span class="comment">//</span></div>
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<div class="line"><a id="l00314" name="l00314"></a><span class="lineno"> 314</span><span class="comment">// where zz_f are fixed values for z_f from the first stage model, and generates</span></div>
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<div class="line"><a id="l00315" name="l00315"></a><span class="lineno"> 315</span><span class="comment">// an infeasibility or optimality cut as needed.</span></div>
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<div class="line"><a id="l00316" name="l00316"></a><span class="lineno"> 316</span><span class="keyword">class </span>SecondStageSolver {</div>
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<div class="line"><a id="l00317" name="l00317"></a><span class="lineno"> 317</span> <span class="keyword">public</span>:</div>
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<div class="line"><a id="l00318" name="l00318"></a><span class="lineno"> 318</span> <span class="keyword">static</span> absl::StatusOr<std::unique_ptr<SecondStageSolver>> New(</div>
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<div class="line"><a id="l00319" name="l00319"></a><span class="lineno"> 319</span> FacilityLocationInstance instance, <a class="code hl_enumeration" href="namespaceoperations__research_1_1math__opt.html#a8b06041d7c1fb05f379714f4312306ec">math_opt::SolverType</a> solver_type);</div>
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<div class="line"><a id="l00320" name="l00320"></a><span class="lineno"> 320</span> </div>
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<div class="line"><a id="l00321" name="l00321"></a><span class="lineno"> 321</span> absl::StatusOr<std::pair<double, Cut>> <a class="code hl_function" href="namespaceoperations__research_1_1math__opt.html#a5767ee23f380e72488d3c7ebf2d742b1">Solve</a>(</div>
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<div class="line"><a id="l00322" name="l00322"></a><span class="lineno"> 322</span> <span class="keyword">const</span> std::vector<double>& z_values, <span class="keywordtype">double</span> w_value,</div>
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<div class="line"><a id="l00323" name="l00323"></a><span class="lineno"> 323</span> <span class="keywordtype">double</span> fist_stage_objective);</div>
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<div class="line"><a id="l00324" name="l00324"></a><span class="lineno"> 324</span> </div>
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<div class="line"><a id="l00325" name="l00325"></a><span class="lineno"> 325</span> <span class="keyword">private</span>:</div>
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<div class="line"><a id="l00326" name="l00326"></a><span class="lineno"> 326</span> SecondStageSolver(FacilityLocationInstance instance,</div>
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<div class="line"><a id="l00327" name="l00327"></a><span class="lineno"> 327</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_solve_parameters.html">math_opt::SolveParameters</a> second_stage_params);</div>
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<div class="line"><a id="l00328" name="l00328"></a><span class="lineno"> 328</span> </div>
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<div class="line"><a id="l00329" name="l00329"></a><span class="lineno"> 329</span> absl::StatusOr<Cut> OptimalityCut(</div>
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<div class="line"><a id="l00330" name="l00330"></a><span class="lineno"> 330</span> <span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_solve_result.html">math_opt::SolveResult</a>& second_stage_result);</div>
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<div class="line"><a id="l00331" name="l00331"></a><span class="lineno"> 331</span> absl::StatusOr<Cut> FeasibilityCut(</div>
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<div class="line"><a id="l00332" name="l00332"></a><span class="lineno"> 332</span> <span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_solve_result.html">math_opt::SolveResult</a>& second_stage_result);</div>
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<div class="line"><a id="l00333" name="l00333"></a><span class="lineno"> 333</span> </div>
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<div class="line"><a id="l00334" name="l00334"></a><span class="lineno"> 334</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_model.html">math_opt::Model</a> second_stage_model_;</div>
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<div class="line"><a id="l00335" name="l00335"></a><span class="lineno"> 335</span> <span class="keyword">const</span> Network network_;</div>
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<div class="line"><a id="l00336" name="l00336"></a><span class="lineno"> 336</span> <span class="keyword">const</span> <span class="keywordtype">double</span> location_fraction_;</div>
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<div class="line"><a id="l00337" name="l00337"></a><span class="lineno"> 337</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_solve_parameters.html">math_opt::SolveParameters</a> second_stage_params_;</div>
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<div class="line"><a id="l00338" name="l00338"></a><span class="lineno"> 338</span> </div>
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<div class="line"><a id="l00339" name="l00339"></a><span class="lineno"> 339</span> absl::flat_hash_map<Edge, math_opt::Variable> x_;</div>
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<div class="line"><a id="l00340" name="l00340"></a><span class="lineno"> 340</span> std::vector<math_opt::LinearConstraint> supply_constraints_;</div>
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<div class="line"><a id="l00341" name="l00341"></a><span class="lineno"> 341</span> std::vector<math_opt::LinearConstraint> demand_constraints_;</div>
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<div class="line"><a id="l00342" name="l00342"></a><span class="lineno"> 342</span> std::unique_ptr<math_opt::IncrementalSolver> solver_;</div>
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<div class="line"><a id="l00343" name="l00343"></a><span class="lineno"> 343</span>};</div>
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<div class="line"><a id="l00344" name="l00344"></a><span class="lineno"> 344</span> </div>
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<div class="line"><a id="l00345" name="l00345"></a><span class="lineno"> 345</span>absl::StatusOr<math_opt::SolveParameters> EnsureDualRaySolveParameters(</div>
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<div class="line"><a id="l00346" name="l00346"></a><span class="lineno"> 346</span> <span class="keyword">const</span> <a class="code hl_enumeration" href="namespaceoperations__research_1_1math__opt.html#a8b06041d7c1fb05f379714f4312306ec">math_opt::SolverType</a> solver_type) {</div>
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<div class="line"><a id="l00347" name="l00347"></a><span class="lineno"> 347</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_solve_parameters.html">math_opt::SolveParameters</a> <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>;</div>
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<div class="line"><a id="l00348" name="l00348"></a><span class="lineno"> 348</span> <span class="keywordflow">switch</span> (solver_type) {</div>
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<div class="line"><a id="l00349" name="l00349"></a><span class="lineno"> 349</span> <span class="keywordflow">case</span> math_opt::SolverType::kGurobi:</div>
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<div class="line"><a id="l00350" name="l00350"></a><span class="lineno"> 350</span> <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>.gurobi.param_values[<span class="stringliteral">"InfUnbdInfo"</span>] = <span class="stringliteral">"1"</span>;</div>
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<div class="line"><a id="l00351" name="l00351"></a><span class="lineno"> 351</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00352" name="l00352"></a><span class="lineno"> 352</span> <span class="keywordflow">case</span> math_opt::SolverType::kGlop:</div>
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<div class="line"><a id="l00353" name="l00353"></a><span class="lineno"> 353</span> <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>.presolve = math_opt::Emphasis::kOff;</div>
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<div class="line"><a id="l00354" name="l00354"></a><span class="lineno"> 354</span> <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>.scaling = math_opt::Emphasis::kOff;</div>
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<div class="line"><a id="l00355" name="l00355"></a><span class="lineno"> 355</span> <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>.lp_algorithm = math_opt::LPAlgorithm::kDualSimplex;</div>
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<div class="line"><a id="l00356" name="l00356"></a><span class="lineno"> 356</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00357" name="l00357"></a><span class="lineno"> 357</span> <span class="keywordflow">case</span> math_opt::SolverType::kGlpk:</div>
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<div class="line"><a id="l00358" name="l00358"></a><span class="lineno"> 358</span> <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>.presolve = math_opt::Emphasis::kOff;</div>
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<div class="line"><a id="l00359" name="l00359"></a><span class="lineno"> 359</span> <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>.lp_algorithm = math_opt::LPAlgorithm::kDualSimplex;</div>
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<div class="line"><a id="l00360" name="l00360"></a><span class="lineno"> 360</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00361" name="l00361"></a><span class="lineno"> 361</span> <span class="keywordflow">default</span>:</div>
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<div class="line"><a id="l00362" name="l00362"></a><span class="lineno"> 362</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceutil.html#a302ee4bfcb86ea9ed64a193ed0b14648">util::InternalErrorBuilder</a>()</div>
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<div class="line"><a id="l00363" name="l00363"></a><span class="lineno"> 363</span> << <span class="stringliteral">"unsupported solver: "</span> << solver_type;</div>
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<div class="line"><a id="l00364" name="l00364"></a><span class="lineno"> 364</span> }</div>
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<div class="line"><a id="l00365" name="l00365"></a><span class="lineno"> 365</span> <span class="keywordflow">return</span> <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>;</div>
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<div class="line"><a id="l00366" name="l00366"></a><span class="lineno"> 366</span>}</div>
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<div class="line"><a id="l00367" name="l00367"></a><span class="lineno"> 367</span> </div>
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<div class="line"><a id="l00368" name="l00368"></a><span class="lineno"> 368</span>absl::StatusOr<std::unique_ptr<SecondStageSolver>> SecondStageSolver::New(</div>
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<div class="line"><a id="l00369" name="l00369"></a><span class="lineno"> 369</span> FacilityLocationInstance instance, <span class="keyword">const</span> <a class="code hl_enumeration" href="namespaceoperations__research_1_1math__opt.html#a8b06041d7c1fb05f379714f4312306ec">math_opt::SolverType</a> solver_type) {</div>
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<div class="line"><a id="l00370" name="l00370"></a><span class="lineno"> 370</span> <span class="comment">// Set solver arguments to ensure a dual ray is returned.</span></div>
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<div class="line"><a id="l00371" name="l00371"></a><span class="lineno"> 371</span> <a class="code hl_define" href="base_2status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011">ASSIGN_OR_RETURN</a>(<a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_solve_parameters.html">math_opt::SolveParameters</a> <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>,</div>
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<div class="line"><a id="l00372" name="l00372"></a><span class="lineno"> 372</span> EnsureDualRaySolveParameters(solver_type));</div>
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<div class="line"><a id="l00373" name="l00373"></a><span class="lineno"> 373</span> </div>
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<div class="line"><a id="l00374" name="l00374"></a><span class="lineno"> 374</span> std::unique_ptr<SecondStageSolver> second_stage_solver =</div>
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<div class="line"><a id="l00375" name="l00375"></a><span class="lineno"> 375</span> absl::WrapUnique<SecondStageSolver>(</div>
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<div class="line"><a id="l00376" name="l00376"></a><span class="lineno"> 376</span> <span class="keyword">new</span> SecondStageSolver(std::move(instance), <a class="code hl_variable" href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a>));</div>
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<div class="line"><a id="l00377" name="l00377"></a><span class="lineno"> 377</span> <a class="code hl_define" href="base_2status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011">ASSIGN_OR_RETURN</a>(std::unique_ptr<math_opt::IncrementalSolver> solver,</div>
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<div class="line"><a id="l00378" name="l00378"></a><span class="lineno"> 378</span> <a class="code hl_function" href="classoperations__research_1_1math__opt_1_1_incremental_solver.html#ae216d134c8146dadaa9c16ef2ed1f7c4">math_opt::IncrementalSolver::New</a>(</div>
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<div class="line"><a id="l00379" name="l00379"></a><span class="lineno"> 379</span> &second_stage_solver->second_stage_model_, solver_type));</div>
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<div class="line"><a id="l00380" name="l00380"></a><span class="lineno"> 380</span> second_stage_solver->solver_ = std::move(solver);</div>
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<div class="line"><a id="l00381" name="l00381"></a><span class="lineno"> 381</span> <span class="keywordflow">return</span> std::move(second_stage_solver);</div>
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<div class="line"><a id="l00382" name="l00382"></a><span class="lineno"> 382</span>}</div>
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<div class="line"><a id="l00383" name="l00383"></a><span class="lineno"> 383</span> </div>
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<div class="line"><a id="l00384" name="l00384"></a><span class="lineno"> 384</span>SecondStageSolver::SecondStageSolver(</div>
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<div class="line"><a id="l00385" name="l00385"></a><span class="lineno"> 385</span> FacilityLocationInstance instance,</div>
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<div class="line"><a id="l00386" name="l00386"></a><span class="lineno"> 386</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_solve_parameters.html">math_opt::SolveParameters</a> second_stage_params)</div>
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<div class="line"><a id="l00387" name="l00387"></a><span class="lineno"> 387</span> : second_stage_model_(<span class="stringliteral">"Second stage model"</span>),</div>
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<div class="line"><a id="l00388" name="l00388"></a><span class="lineno"> 388</span> network_(<a class="code hl_namespace" href="namespacestd.html">std</a>::move(instance.network)),</div>
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<div class="line"><a id="l00389" name="l00389"></a><span class="lineno"> 389</span> location_fraction_(instance.location_fraction),</div>
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<div class="line"><a id="l00390" name="l00390"></a><span class="lineno"> 390</span> second_stage_params_(second_stage_params) {</div>
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<div class="line"><a id="l00391" name="l00391"></a><span class="lineno"> 391</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_facilities = network_.num_facilities();</div>
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<div class="line"><a id="l00392" name="l00392"></a><span class="lineno"> 392</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_locations = network_.num_locations();</div>
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<div class="line"><a id="l00393" name="l00393"></a><span class="lineno"> 393</span> </div>
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<div class="line"><a id="l00394" name="l00394"></a><span class="lineno"> 394</span> <span class="comment">// Flow variables</span></div>
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<div class="line"><a id="l00395" name="l00395"></a><span class="lineno"> 395</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>& edge : network_.edges()) {</div>
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<div class="line"><a id="l00396" name="l00396"></a><span class="lineno"> 396</span> <span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_variable.html">math_opt::Variable</a> x_edge =</div>
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<div class="line"><a id="l00397" name="l00397"></a><span class="lineno"> 397</span> second_stage_model_.AddContinuousVariable(0.0, <a class="code hl_variable" href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">kInf</a>);</div>
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<div class="line"><a id="l00398" name="l00398"></a><span class="lineno"> 398</span> x_.insert({edge, x_edge});</div>
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<div class="line"><a id="l00399" name="l00399"></a><span class="lineno"> 399</span> }</div>
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<div class="line"><a id="l00400" name="l00400"></a><span class="lineno"> 400</span> </div>
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<div class="line"><a id="l00401" name="l00401"></a><span class="lineno"> 401</span> <span class="comment">// Objective Function</span></div>
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<div class="line"><a id="l00402" name="l00402"></a><span class="lineno"> 402</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_linear_expression.html">math_opt::LinearExpression</a> objective_for_edges;</div>
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<div class="line"><a id="l00403" name="l00403"></a><span class="lineno"> 403</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>& [edge, x_edge] : x_) {</div>
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<div class="line"><a id="l00404" name="l00404"></a><span class="lineno"> 404</span> objective_for_edges += network_.edge_cost(edge) * x_edge;</div>
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<div class="line"><a id="l00405" name="l00405"></a><span class="lineno"> 405</span> }</div>
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<div class="line"><a id="l00406" name="l00406"></a><span class="lineno"> 406</span> second_stage_model_.Minimize(objective_for_edges);</div>
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<div class="line"><a id="l00407" name="l00407"></a><span class="lineno"> 407</span> </div>
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<div class="line"><a id="l00408" name="l00408"></a><span class="lineno"> 408</span> <span class="comment">// Demand constraints</span></div>
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<div class="line"><a id="l00409" name="l00409"></a><span class="lineno"> 409</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> location = 0; location < num_locations; ++location) {</div>
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<div class="line"><a id="l00410" name="l00410"></a><span class="lineno"> 410</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_linear_expression.html">math_opt::LinearExpression</a> incomming_supply;</div>
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<div class="line"><a id="l00411" name="l00411"></a><span class="lineno"> 411</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>& edge : network_.edges_incident_to_location(location)) {</div>
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<div class="line"><a id="l00412" name="l00412"></a><span class="lineno"> 412</span> incomming_supply += x_.at(edge);</div>
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<div class="line"><a id="l00413" name="l00413"></a><span class="lineno"> 413</span> }</div>
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<div class="line"><a id="l00414" name="l00414"></a><span class="lineno"> 414</span> demand_constraints_.push_back(second_stage_model_.AddLinearConstraint(</div>
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<div class="line"><a id="l00415" name="l00415"></a><span class="lineno"> 415</span> incomming_supply >= instance.location_demand));</div>
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<div class="line"><a id="l00416" name="l00416"></a><span class="lineno"> 416</span> }</div>
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<div class="line"><a id="l00417" name="l00417"></a><span class="lineno"> 417</span> </div>
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<div class="line"><a id="l00418" name="l00418"></a><span class="lineno"> 418</span> <span class="comment">// Supply constraints</span></div>
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<div class="line"><a id="l00419" name="l00419"></a><span class="lineno"> 419</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> facility = 0; facility < num_facilities; ++facility) {</div>
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<div class="line"><a id="l00420" name="l00420"></a><span class="lineno"> 420</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_linear_expression.html">math_opt::LinearExpression</a> outgoing_supply;</div>
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<div class="line"><a id="l00421" name="l00421"></a><span class="lineno"> 421</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>& edge : network_.edges_incident_to_facility(facility)) {</div>
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<div class="line"><a id="l00422" name="l00422"></a><span class="lineno"> 422</span> outgoing_supply += x_.at(edge);</div>
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<div class="line"><a id="l00423" name="l00423"></a><span class="lineno"> 423</span> }</div>
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<div class="line"><a id="l00424" name="l00424"></a><span class="lineno"> 424</span> <span class="comment">// Set supply constraint with trivial upper bound to be updated with first</span></div>
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<div class="line"><a id="l00425" name="l00425"></a><span class="lineno"> 425</span> <span class="comment">// stage information.</span></div>
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<div class="line"><a id="l00426" name="l00426"></a><span class="lineno"> 426</span> supply_constraints_.push_back(</div>
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<div class="line"><a id="l00427" name="l00427"></a><span class="lineno"> 427</span> second_stage_model_.AddLinearConstraint(outgoing_supply <= <a class="code hl_variable" href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">kInf</a>));</div>
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<div class="line"><a id="l00428" name="l00428"></a><span class="lineno"> 428</span> }</div>
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<div class="line"><a id="l00429" name="l00429"></a><span class="lineno"> 429</span>}</div>
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<div class="line"><a id="l00430" name="l00430"></a><span class="lineno"> 430</span> </div>
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<div class="line"><a id="l00431" name="l00431"></a><span class="lineno"> 431</span>absl::StatusOr<std::pair<double, Cut>> <a class="code hl_function" href="namespaceoperations__research_1_1math__opt.html#a5767ee23f380e72488d3c7ebf2d742b1">SecondStageSolver::Solve</a>(</div>
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<div class="line"><a id="l00432" name="l00432"></a><span class="lineno"> 432</span> <span class="keyword">const</span> std::vector<double>& z_values, <span class="keyword">const</span> <span class="keywordtype">double</span> w_value,</div>
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<div class="line"><a id="l00433" name="l00433"></a><span class="lineno"> 433</span> <span class="keyword">const</span> <span class="keywordtype">double</span> fist_stage_objective) {</div>
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<div class="line"><a id="l00434" name="l00434"></a><span class="lineno"> 434</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_facilities = network_.num_facilities();</div>
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<div class="line"><a id="l00435" name="l00435"></a><span class="lineno"> 435</span> </div>
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<div class="line"><a id="l00436" name="l00436"></a><span class="lineno"> 436</span> <span class="comment">// Update second stage with first stage solution.</span></div>
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<div class="line"><a id="l00437" name="l00437"></a><span class="lineno"> 437</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> facility = 0; facility < num_facilities; ++facility) {</div>
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<div class="line"><a id="l00438" name="l00438"></a><span class="lineno"> 438</span> <span class="keywordflow">if</span> (z_values[facility] < -<a class="code hl_variable" href="lagrangian__relaxation_8cc.html#a6ffb9a02546adae760787b2366ae6e41">kZeroTol</a>) {</div>
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<div class="line"><a id="l00439" name="l00439"></a><span class="lineno"> 439</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceutil.html#a302ee4bfcb86ea9ed64a193ed0b14648">util::InternalErrorBuilder</a>()</div>
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<div class="line"><a id="l00440" name="l00440"></a><span class="lineno"> 440</span> << <span class="stringliteral">"negative z_value in first stage: "</span> << z_values[facility]</div>
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<div class="line"><a id="l00441" name="l00441"></a><span class="lineno"> 441</span> << <span class="stringliteral">" for facility "</span> << facility;</div>
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<div class="line"><a id="l00442" name="l00442"></a><span class="lineno"> 442</span> }</div>
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<div class="line"><a id="l00443" name="l00443"></a><span class="lineno"> 443</span> <span class="comment">// Make sure variable bounds are valid (lb <= ub).</span></div>
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<div class="line"><a id="l00444" name="l00444"></a><span class="lineno"> 444</span> <span class="keyword">const</span> <span class="keywordtype">double</span> capacity_value = <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(z_values[facility], 0.0);</div>
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<div class="line"><a id="l00445" name="l00445"></a><span class="lineno"> 445</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>& edge : network_.edges_incident_to_facility(facility)) {</div>
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<div class="line"><a id="l00446" name="l00446"></a><span class="lineno"> 446</span> second_stage_model_.set_upper_bound(x_.at(edge),</div>
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<div class="line"><a id="l00447" name="l00447"></a><span class="lineno"> 447</span> location_fraction_ * capacity_value);</div>
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<div class="line"><a id="l00448" name="l00448"></a><span class="lineno"> 448</span> }</div>
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<div class="line"><a id="l00449" name="l00449"></a><span class="lineno"> 449</span> second_stage_model_.set_upper_bound(supply_constraints_[facility],</div>
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<div class="line"><a id="l00450" name="l00450"></a><span class="lineno"> 450</span> capacity_value);</div>
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<div class="line"><a id="l00451" name="l00451"></a><span class="lineno"> 451</span> }</div>
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<div class="line"><a id="l00452" name="l00452"></a><span class="lineno"> 452</span> <span class="comment">// Solve and process second stage.</span></div>
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<div class="line"><a id="l00453" name="l00453"></a><span class="lineno"> 453</span> <a class="code hl_define" href="base_2status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011">ASSIGN_OR_RETURN</a>(<span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_solve_result.html">math_opt::SolveResult</a> second_stage_result,</div>
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<div class="line"><a id="l00454" name="l00454"></a><span class="lineno"> 454</span> solver_->Solve(<a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_solve_arguments.html">math_opt::SolveArguments</a>{</div>
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<div class="line"><a id="l00455" name="l00455"></a><span class="lineno"> 455</span> .parameters = second_stage_params_}));</div>
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<div class="line"><a id="l00456" name="l00456"></a><span class="lineno"> 456</span> <span class="keywordflow">switch</span> (second_stage_result.termination.reason) {</div>
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<div class="line"><a id="l00457" name="l00457"></a><span class="lineno"> 457</span> <span class="keywordflow">case</span> math_opt::TerminationReason::kInfeasible:</div>
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<div class="line"><a id="l00458" name="l00458"></a><span class="lineno"> 458</span> <span class="comment">// If the second stage problem is infeasible we can construct a</span></div>
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<div class="line"><a id="l00459" name="l00459"></a><span class="lineno"> 459</span> <span class="comment">// feasibility cut from a returned dual ray.</span></div>
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<div class="line"><a id="l00460" name="l00460"></a><span class="lineno"> 460</span> {</div>
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<div class="line"><a id="l00461" name="l00461"></a><span class="lineno"> 461</span> <a class="code hl_define" href="util_2status__macros_8h.html#a50de54834da66a6bcb7c9e37902e522b">OR_ASSIGN_OR_RETURN3</a>(<span class="keyword">const</span> Cut feasibility_cut,</div>
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<div class="line"><a id="l00462" name="l00462"></a><span class="lineno"> 462</span> FeasibilityCut(second_stage_result),</div>
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<div class="line"><a id="l00463" name="l00463"></a><span class="lineno"> 463</span> _ << <span class="stringliteral">"on infeasible for second stage solver"</span>);</div>
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<div class="line"><a id="l00464" name="l00464"></a><span class="lineno"> 464</span> <span class="keywordflow">return</span> std::make_pair(<a class="code hl_variable" href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">kInf</a>, feasibility_cut);</div>
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<div class="line"><a id="l00465" name="l00465"></a><span class="lineno"> 465</span> }</div>
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<div class="line"><a id="l00466" name="l00466"></a><span class="lineno"> 466</span> <span class="keywordflow">case</span> math_opt::TerminationReason::kOptimal:</div>
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<div class="line"><a id="l00467" name="l00467"></a><span class="lineno"> 467</span> <span class="comment">// If the second stage problem is optimal we can construct an optimality</span></div>
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<div class="line"><a id="l00468" name="l00468"></a><span class="lineno"> 468</span> <span class="comment">// cut from a returned dual optimal solution. We can also update the upper</span></div>
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<div class="line"><a id="l00469" name="l00469"></a><span class="lineno"> 469</span> <span class="comment">// bound.</span></div>
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<div class="line"><a id="l00470" name="l00470"></a><span class="lineno"> 470</span> {</div>
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<div class="line"><a id="l00471" name="l00471"></a><span class="lineno"> 471</span> <span class="comment">// Upper bound is obtained by switching predicted second stage objective</span></div>
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<div class="line"><a id="l00472" name="l00472"></a><span class="lineno"> 472</span> <span class="comment">// value w with the true second stage objective value.</span></div>
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<div class="line"><a id="l00473" name="l00473"></a><span class="lineno"> 473</span> <span class="keyword">const</span> <span class="keywordtype">double</span> <a class="code hl_variable" href="gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35">upper_bound</a> = fist_stage_objective - w_value +</div>
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<div class="line"><a id="l00474" name="l00474"></a><span class="lineno"> 474</span> second_stage_result.objective_value();</div>
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<div class="line"><a id="l00475" name="l00475"></a><span class="lineno"> 475</span> <a class="code hl_define" href="util_2status__macros_8h.html#a50de54834da66a6bcb7c9e37902e522b">OR_ASSIGN_OR_RETURN3</a>(<span class="keyword">const</span> Cut optimality_cut,</div>
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<div class="line"><a id="l00476" name="l00476"></a><span class="lineno"> 476</span> OptimalityCut(second_stage_result),</div>
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<div class="line"><a id="l00477" name="l00477"></a><span class="lineno"> 477</span> _ << <span class="stringliteral">"on optimal for second stage solver"</span>);</div>
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<div class="line"><a id="l00478" name="l00478"></a><span class="lineno"> 478</span> <span class="keywordflow">return</span> std::make_pair(<a class="code hl_variable" href="gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35">upper_bound</a>, optimality_cut);</div>
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<div class="line"><a id="l00479" name="l00479"></a><span class="lineno"> 479</span> }</div>
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<div class="line"><a id="l00480" name="l00480"></a><span class="lineno"> 480</span> <span class="keywordflow">default</span>:</div>
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<div class="line"><a id="l00481" name="l00481"></a><span class="lineno"> 481</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceutil.html#a302ee4bfcb86ea9ed64a193ed0b14648">util::InternalErrorBuilder</a>()</div>
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<div class="line"><a id="l00482" name="l00482"></a><span class="lineno"> 482</span> << <span class="stringliteral">"second stage was not solved to optimality or infeasibility: "</span></div>
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<div class="line"><a id="l00483" name="l00483"></a><span class="lineno"> 483</span> << second_stage_result.termination;</div>
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<div class="line"><a id="l00484" name="l00484"></a><span class="lineno"> 484</span> }</div>
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<div class="line"><a id="l00485" name="l00485"></a><span class="lineno"> 485</span>}</div>
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<div class="line"><a id="l00486" name="l00486"></a><span class="lineno"> 486</span> </div>
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<div class="line"><a id="l00487" name="l00487"></a><span class="lineno"> 487</span><span class="comment">// If the second stage problem is infeasible we get a dual ray (r, y) such that</span></div>
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<div class="line"><a id="l00488" name="l00488"></a><span class="lineno"> 488</span><span class="comment">//</span></div>
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<div class="line"><a id="l00489" name="l00489"></a><span class="lineno"> 489</span><span class="comment">// sum(r_(f,l)*a*zz_f : (f,l) in E, r_(f,l) < 0)</span></div>
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<div class="line"><a id="l00490" name="l00490"></a><span class="lineno"> 490</span><span class="comment">// + sum(y_f*zz_f : f in F, y_f < 0)</span></div>
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<div class="line"><a id="l00491" name="l00491"></a><span class="lineno"> 491</span><span class="comment">// + sum(y_l*d : l in L, y_l > 0) > 0.</span></div>
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<div class="line"><a id="l00492" name="l00492"></a><span class="lineno"> 492</span><span class="comment">//</span></div>
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<div class="line"><a id="l00493" name="l00493"></a><span class="lineno"> 493</span><span class="comment">// Then we get the feasibility cut (go/math_opt-advanced-dual-use#benders)</span></div>
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<div class="line"><a id="l00494" name="l00494"></a><span class="lineno"> 494</span><span class="comment">//</span></div>
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<div class="line"><a id="l00495" name="l00495"></a><span class="lineno"> 495</span><span class="comment">// sum(fcut_f*z_f) + fcut_const <= 0,</span></div>
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<div class="line"><a id="l00496" name="l00496"></a><span class="lineno"> 496</span><span class="comment">//</span></div>
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<div class="line"><a id="l00497" name="l00497"></a><span class="lineno"> 497</span><span class="comment">// where</span></div>
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<div class="line"><a id="l00498" name="l00498"></a><span class="lineno"> 498</span><span class="comment">//</span></div>
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<div class="line"><a id="l00499" name="l00499"></a><span class="lineno"> 499</span><span class="comment">// fcut_f = sum(r_(f,l)*a : (f,l) in E, r_(f,l) < 0)</span></div>
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<div class="line"><a id="l00500" name="l00500"></a><span class="lineno"> 500</span><span class="comment">// + min{y_f, 0}</span></div>
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<div class="line"><a id="l00501" name="l00501"></a><span class="lineno"> 501</span><span class="comment">// fcut_const = sum*(y_l*d : l in L, y_l > 0)</span></div>
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<div class="line"><a id="l00502" name="l00502"></a><span class="lineno"> 502</span>absl::StatusOr<Cut> SecondStageSolver::FeasibilityCut(</div>
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<div class="line"><a id="l00503" name="l00503"></a><span class="lineno"> 503</span> <span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_solve_result.html">math_opt::SolveResult</a>& second_stage_result) {</div>
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<div class="line"><a id="l00504" name="l00504"></a><span class="lineno"> 504</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_facilities = network_.num_facilities();</div>
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<div class="line"><a id="l00505" name="l00505"></a><span class="lineno"> 505</span> Cut result;</div>
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<div class="line"><a id="l00506" name="l00506"></a><span class="lineno"> 506</span> </div>
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<div class="line"><a id="l00507" name="l00507"></a><span class="lineno"> 507</span> <span class="keywordflow">if</span> (!second_stage_result.<a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_solve_result.html#a240b106da863fbff10545e97c2c72007">has_dual_ray</a>()) {</div>
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<div class="line"><a id="l00508" name="l00508"></a><span class="lineno"> 508</span> <span class="comment">// MathOpt does not require solvers to return a dual solution on optimal,</span></div>
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<div class="line"><a id="l00509" name="l00509"></a><span class="lineno"> 509</span> <span class="comment">// but most LP solvers always will, see go/mathopt-solver-contracts for</span></div>
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<div class="line"><a id="l00510" name="l00510"></a><span class="lineno"> 510</span> <span class="comment">// details.</span></div>
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<div class="line"><a id="l00511" name="l00511"></a><span class="lineno"> 511</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceutil.html#a302ee4bfcb86ea9ed64a193ed0b14648">util::InternalErrorBuilder</a>()</div>
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|
<div class="line"><a id="l00512" name="l00512"></a><span class="lineno"> 512</span> << <span class="stringliteral">"no dual ray available for feasibility cut"</span>;</div>
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<div class="line"><a id="l00513" name="l00513"></a><span class="lineno"> 513</span> }</div>
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<div class="line"><a id="l00514" name="l00514"></a><span class="lineno"> 514</span> </div>
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<div class="line"><a id="l00515" name="l00515"></a><span class="lineno"> 515</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> facility = 0; facility < num_facilities; ++facility) {</div>
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<div class="line"><a id="l00516" name="l00516"></a><span class="lineno"> 516</span> <span class="keywordtype">double</span> <a class="code hl_variable" href="routing__filters_8cc.html#a8e4ee19dee0e00541dbe9bbc83d806ba">coefficient</a> = 0.0;</div>
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<div class="line"><a id="l00517" name="l00517"></a><span class="lineno"> 517</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>& edge : network_.edges_incident_to_facility(facility)) {</div>
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<div class="line"><a id="l00518" name="l00518"></a><span class="lineno"> 518</span> <span class="keyword">const</span> <span class="keywordtype">double</span> reduced_cost =</div>
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<div class="line"><a id="l00519" name="l00519"></a><span class="lineno"> 519</span> second_stage_result.<a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_solve_result.html#aafa2eea97d94bf02b53add568f96a5b7">ray_reduced_costs</a>().at(x_.at(edge));</div>
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<div class="line"><a id="l00520" name="l00520"></a><span class="lineno"> 520</span> <a class="code hl_variable" href="routing__filters_8cc.html#a8e4ee19dee0e00541dbe9bbc83d806ba">coefficient</a> += location_fraction_ * <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(reduced_cost, 0.0);</div>
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<div class="line"><a id="l00521" name="l00521"></a><span class="lineno"> 521</span> }</div>
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<div class="line"><a id="l00522" name="l00522"></a><span class="lineno"> 522</span> <span class="keyword">const</span> <span class="keywordtype">double</span> dual_value =</div>
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<div class="line"><a id="l00523" name="l00523"></a><span class="lineno"> 523</span> second_stage_result.<a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_solve_result.html#a5511ef5b247197964fac748cc4a8de1f">ray_dual_values</a>().at(supply_constraints_[facility]);</div>
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<div class="line"><a id="l00524" name="l00524"></a><span class="lineno"> 524</span> <a class="code hl_variable" href="routing__filters_8cc.html#a8e4ee19dee0e00541dbe9bbc83d806ba">coefficient</a> += <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(dual_value, 0.0);</div>
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<div class="line"><a id="l00525" name="l00525"></a><span class="lineno"> 525</span> result.z_coefficients.push_back(<a class="code hl_variable" href="routing__filters_8cc.html#a8e4ee19dee0e00541dbe9bbc83d806ba">coefficient</a>);</div>
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<div class="line"><a id="l00526" name="l00526"></a><span class="lineno"> 526</span> }</div>
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<div class="line"><a id="l00527" name="l00527"></a><span class="lineno"> 527</span> result.constant = 0.0;</div>
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<div class="line"><a id="l00528" name="l00528"></a><span class="lineno"> 528</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>& constraint : demand_constraints_) {</div>
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<div class="line"><a id="l00529" name="l00529"></a><span class="lineno"> 529</span> <span class="keyword">const</span> <span class="keywordtype">double</span> dual_value =</div>
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<div class="line"><a id="l00530" name="l00530"></a><span class="lineno"> 530</span> second_stage_result.<a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_solve_result.html#a5511ef5b247197964fac748cc4a8de1f">ray_dual_values</a>().at(constraint);</div>
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<div class="line"><a id="l00531" name="l00531"></a><span class="lineno"> 531</span> result.constant += <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(dual_value, 0.0);</div>
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<div class="line"><a id="l00532" name="l00532"></a><span class="lineno"> 532</span> }</div>
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<div class="line"><a id="l00533" name="l00533"></a><span class="lineno"> 533</span> result.w_coefficient = 0.0;</div>
|
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<div class="line"><a id="l00534" name="l00534"></a><span class="lineno"> 534</span> <span class="keywordflow">return</span> result;</div>
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<div class="line"><a id="l00535" name="l00535"></a><span class="lineno"> 535</span>}</div>
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<div class="line"><a id="l00536" name="l00536"></a><span class="lineno"> 536</span> </div>
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<div class="line"><a id="l00537" name="l00537"></a><span class="lineno"> 537</span><span class="comment">// If the second stage problem is optimal we get a dual solution (r, y) such</span></div>
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<div class="line"><a id="l00538" name="l00538"></a><span class="lineno"> 538</span><span class="comment">// that the optimal objective value is equal to</span></div>
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<div class="line"><a id="l00539" name="l00539"></a><span class="lineno"> 539</span><span class="comment">//</span></div>
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<div class="line"><a id="l00540" name="l00540"></a><span class="lineno"> 540</span><span class="comment">// sum(r_(f,l)*a*zz_f : (f,l) in E, r_(f,l) < 0)</span></div>
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<div class="line"><a id="l00541" name="l00541"></a><span class="lineno"> 541</span><span class="comment">// + sum(y_f*zz_f : f in F, y_f < 0)</span></div>
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<div class="line"><a id="l00542" name="l00542"></a><span class="lineno"> 542</span><span class="comment">// + sum*(y_l*d : l in L, y_l > 0) > 0.</span></div>
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<div class="line"><a id="l00543" name="l00543"></a><span class="lineno"> 543</span><span class="comment">//</span></div>
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<div class="line"><a id="l00544" name="l00544"></a><span class="lineno"> 544</span><span class="comment">// Then we get the optimality cut (go/math_opt-advanced-dual-use#benders)</span></div>
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<div class="line"><a id="l00545" name="l00545"></a><span class="lineno"> 545</span><span class="comment">//</span></div>
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<div class="line"><a id="l00546" name="l00546"></a><span class="lineno"> 546</span><span class="comment">// sum(ocut_f*z_f) + ocut_const <= w,</span></div>
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<div class="line"><a id="l00547" name="l00547"></a><span class="lineno"> 547</span><span class="comment">//</span></div>
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<div class="line"><a id="l00548" name="l00548"></a><span class="lineno"> 548</span><span class="comment">// where</span></div>
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<div class="line"><a id="l00549" name="l00549"></a><span class="lineno"> 549</span><span class="comment">//</span></div>
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<div class="line"><a id="l00550" name="l00550"></a><span class="lineno"> 550</span><span class="comment">// ocut_f = sum(r_(f,l)*a : (f,l) in E, r_(f,l) < 0)</span></div>
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<div class="line"><a id="l00551" name="l00551"></a><span class="lineno"> 551</span><span class="comment">// + min{y_f, 0}</span></div>
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<div class="line"><a id="l00552" name="l00552"></a><span class="lineno"> 552</span><span class="comment">// ocut_const = sum*(y_l*d : l in L, y_l > 0)</span></div>
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<div class="line"><a id="l00553" name="l00553"></a><span class="lineno"> 553</span>absl::StatusOr<Cut> SecondStageSolver::OptimalityCut(</div>
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<div class="line"><a id="l00554" name="l00554"></a><span class="lineno"> 554</span> <span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_solve_result.html">math_opt::SolveResult</a>& second_stage_result) {</div>
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<div class="line"><a id="l00555" name="l00555"></a><span class="lineno"> 555</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_facilities = network_.num_facilities();</div>
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<div class="line"><a id="l00556" name="l00556"></a><span class="lineno"> 556</span> Cut result;</div>
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<div class="line"><a id="l00557" name="l00557"></a><span class="lineno"> 557</span> </div>
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<div class="line"><a id="l00558" name="l00558"></a><span class="lineno"> 558</span> <span class="keywordflow">if</span> (!second_stage_result.<a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_solve_result.html#a35cafd54aea7eb0aecf1cb6fa4b33273">has_dual_feasible_solution</a>()) {</div>
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<div class="line"><a id="l00559" name="l00559"></a><span class="lineno"> 559</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceutil.html#a302ee4bfcb86ea9ed64a193ed0b14648">util::InternalErrorBuilder</a>()</div>
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<div class="line"><a id="l00560" name="l00560"></a><span class="lineno"> 560</span> << <span class="stringliteral">"no dual solution available for optimality cut"</span>;</div>
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<div class="line"><a id="l00561" name="l00561"></a><span class="lineno"> 561</span> }</div>
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<div class="line"><a id="l00562" name="l00562"></a><span class="lineno"> 562</span> </div>
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<div class="line"><a id="l00563" name="l00563"></a><span class="lineno"> 563</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> facility = 0; facility < num_facilities; ++facility) {</div>
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<div class="line"><a id="l00564" name="l00564"></a><span class="lineno"> 564</span> <span class="keywordtype">double</span> <a class="code hl_variable" href="routing__filters_8cc.html#a8e4ee19dee0e00541dbe9bbc83d806ba">coefficient</a> = 0.0;</div>
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<div class="line"><a id="l00565" name="l00565"></a><span class="lineno"> 565</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>& edge : network_.edges_incident_to_facility(facility)) {</div>
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<div class="line"><a id="l00566" name="l00566"></a><span class="lineno"> 566</span> <span class="keyword">const</span> <span class="keywordtype">double</span> reduced_cost =</div>
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<div class="line"><a id="l00567" name="l00567"></a><span class="lineno"> 567</span> second_stage_result.<a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_solve_result.html#acc1f8f5ed04e9ea770b526fa34d6076c">reduced_costs</a>().at(x_.at(edge));</div>
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<div class="line"><a id="l00568" name="l00568"></a><span class="lineno"> 568</span> <a class="code hl_variable" href="routing__filters_8cc.html#a8e4ee19dee0e00541dbe9bbc83d806ba">coefficient</a> += location_fraction_ * <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(reduced_cost, 0.0);</div>
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<div class="line"><a id="l00569" name="l00569"></a><span class="lineno"> 569</span> }</div>
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<div class="line"><a id="l00570" name="l00570"></a><span class="lineno"> 570</span> <span class="keywordtype">double</span> dual_value =</div>
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<div class="line"><a id="l00571" name="l00571"></a><span class="lineno"> 571</span> second_stage_result.<a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_solve_result.html#a116b227550e648d43bfbaccf9557ce42">dual_values</a>().at(supply_constraints_[facility]);</div>
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<div class="line"><a id="l00572" name="l00572"></a><span class="lineno"> 572</span> <a class="code hl_variable" href="routing__filters_8cc.html#a8e4ee19dee0e00541dbe9bbc83d806ba">coefficient</a> += <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(dual_value, 0.0);</div>
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<div class="line"><a id="l00573" name="l00573"></a><span class="lineno"> 573</span> result.z_coefficients.push_back(<a class="code hl_variable" href="routing__filters_8cc.html#a8e4ee19dee0e00541dbe9bbc83d806ba">coefficient</a>);</div>
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<div class="line"><a id="l00574" name="l00574"></a><span class="lineno"> 574</span> }</div>
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<div class="line"><a id="l00575" name="l00575"></a><span class="lineno"> 575</span> result.constant = 0.0;</div>
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<div class="line"><a id="l00576" name="l00576"></a><span class="lineno"> 576</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>& constraint : demand_constraints_) {</div>
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<div class="line"><a id="l00577" name="l00577"></a><span class="lineno"> 577</span> <span class="keywordtype">double</span> dual_value = second_stage_result.<a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_solve_result.html#a116b227550e648d43bfbaccf9557ce42">dual_values</a>().at(constraint);</div>
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<div class="line"><a id="l00578" name="l00578"></a><span class="lineno"> 578</span> result.constant += <a class="code hl_variable" href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">std::max</a>(dual_value, 0.0);</div>
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<div class="line"><a id="l00579" name="l00579"></a><span class="lineno"> 579</span> }</div>
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<div class="line"><a id="l00580" name="l00580"></a><span class="lineno"> 580</span> result.w_coefficient = 1.0;</div>
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<div class="line"><a id="l00581" name="l00581"></a><span class="lineno"> 581</span> <span class="keywordflow">return</span> result;</div>
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<div class="line"><a id="l00582" name="l00582"></a><span class="lineno"> 582</span>}</div>
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<div class="line"><a id="l00583" name="l00583"></a><span class="lineno"> 583</span> </div>
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<div class="line"><a id="l00584" name="l00584"></a><span class="lineno"> 584</span>absl::Status Benders(<span class="keyword">const</span> FacilityLocationInstance& instance,</div>
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<div class="line"><a id="l00585" name="l00585"></a><span class="lineno"> 585</span> <span class="keyword">const</span> <span class="keywordtype">double</span> target_precission,</div>
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<div class="line"><a id="l00586" name="l00586"></a><span class="lineno"> 586</span> <span class="keyword">const</span> <a class="code hl_enumeration" href="namespaceoperations__research_1_1math__opt.html#a8b06041d7c1fb05f379714f4312306ec">math_opt::SolverType</a> solver_type,</div>
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<div class="line"><a id="l00587" name="l00587"></a><span class="lineno"> 587</span> <span class="keyword">const</span> <span class="keywordtype">int</span> maximum_iterations = 30000) {</div>
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<div class="line"><a id="l00588" name="l00588"></a><span class="lineno"> 588</span> <span class="keyword">const</span> <span class="keywordtype">int</span> num_facilities = instance.network.num_facilities();</div>
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<div class="line"><a id="l00589" name="l00589"></a><span class="lineno"> 589</span> </div>
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<div class="line"><a id="l00590" name="l00590"></a><span class="lineno"> 590</span> <span class="comment">// Setup first stage model and solver.</span></div>
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<div class="line"><a id="l00591" name="l00591"></a><span class="lineno"> 591</span> FirstStageProblem first_stage(instance.network, instance.facility_cost);</div>
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<div class="line"><a id="l00592" name="l00592"></a><span class="lineno"> 592</span> <a class="code hl_define" href="base_2status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011">ASSIGN_OR_RETURN</a>(</div>
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<div class="line"><a id="l00593" name="l00593"></a><span class="lineno"> 593</span> <span class="keyword">const</span> std::unique_ptr<math_opt::IncrementalSolver> first_stage_solver,</div>
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<div class="line"><a id="l00594" name="l00594"></a><span class="lineno"> 594</span> <a class="code hl_function" href="classoperations__research_1_1math__opt_1_1_incremental_solver.html#ae216d134c8146dadaa9c16ef2ed1f7c4">math_opt::IncrementalSolver::New</a>(&first_stage.model, solver_type));</div>
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<div class="line"><a id="l00595" name="l00595"></a><span class="lineno"> 595</span> <span class="comment">// Setup second stage solver.</span></div>
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<div class="line"><a id="l00596" name="l00596"></a><span class="lineno"> 596</span> <a class="code hl_define" href="base_2status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011">ASSIGN_OR_RETURN</a>(std::unique_ptr<SecondStageSolver> second_stage_solver,</div>
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<div class="line"><a id="l00597" name="l00597"></a><span class="lineno"> 597</span> SecondStageSolver::New(instance, solver_type));</div>
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<div class="line"><a id="l00598" name="l00598"></a><span class="lineno"> 598</span> <span class="comment">// Start Benders</span></div>
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<div class="line"><a id="l00599" name="l00599"></a><span class="lineno"> 599</span> <span class="keywordtype">int</span> iteration = 0;</div>
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<div class="line"><a id="l00600" name="l00600"></a><span class="lineno"> 600</span> <span class="keywordtype">double</span> best_upper_bound = <a class="code hl_variable" href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">kInf</a>;</div>
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<div class="line"><a id="l00601" name="l00601"></a><span class="lineno"> 601</span> std::vector<double> z_values;</div>
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<div class="line"><a id="l00602" name="l00602"></a><span class="lineno"> 602</span> z_values.resize(num_facilities);</div>
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<div class="line"><a id="l00603" name="l00603"></a><span class="lineno"> 603</span> <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
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<div class="line"><a id="l00604" name="l00604"></a><span class="lineno"> 604</span> <a class="code hl_define" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code hl_variable" href="log__severity_8h.html#ab4a2cbab234914b320b7fae11b6e8cb9">INFO</a>) << <span class="stringliteral">"Iteration: "</span> << iteration;</div>
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<div class="line"><a id="l00605" name="l00605"></a><span class="lineno"> 605</span> </div>
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<div class="line"><a id="l00606" name="l00606"></a><span class="lineno"> 606</span> <span class="comment">// Solve and process first stage.</span></div>
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<div class="line"><a id="l00607" name="l00607"></a><span class="lineno"> 607</span> <a class="code hl_define" href="base_2status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011">ASSIGN_OR_RETURN</a>(<span class="keyword">const</span> <a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_solve_result.html">math_opt::SolveResult</a> first_stage_result,</div>
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<div class="line"><a id="l00608" name="l00608"></a><span class="lineno"> 608</span> first_stage_solver->Solve());</div>
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<div class="line"><a id="l00609" name="l00609"></a><span class="lineno"> 609</span> <span class="keywordflow">if</span> (first_stage_result.termination.reason !=</div>
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<div class="line"><a id="l00610" name="l00610"></a><span class="lineno"> 610</span> math_opt::TerminationReason::kOptimal) {</div>
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<div class="line"><a id="l00611" name="l00611"></a><span class="lineno"> 611</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceutil.html#a302ee4bfcb86ea9ed64a193ed0b14648">util::InternalErrorBuilder</a>()</div>
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<div class="line"><a id="l00612" name="l00612"></a><span class="lineno"> 612</span> << <span class="stringliteral">"could not solve first stage problem to optimality:"</span></div>
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<div class="line"><a id="l00613" name="l00613"></a><span class="lineno"> 613</span> << first_stage_result.termination;</div>
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<div class="line"><a id="l00614" name="l00614"></a><span class="lineno"> 614</span> }</div>
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<div class="line"><a id="l00615" name="l00615"></a><span class="lineno"> 615</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < num_facilities; j++) {</div>
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<div class="line"><a id="l00616" name="l00616"></a><span class="lineno"> 616</span> z_values[j] = first_stage_result.variable_values().at(first_stage.z[j]);</div>
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<div class="line"><a id="l00617" name="l00617"></a><span class="lineno"> 617</span> }</div>
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<div class="line"><a id="l00618" name="l00618"></a><span class="lineno"> 618</span> <span class="keyword">const</span> <span class="keywordtype">double</span> <a class="code hl_variable" href="gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a> = first_stage_result.objective_value();</div>
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<div class="line"><a id="l00619" name="l00619"></a><span class="lineno"> 619</span> <a class="code hl_define" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code hl_variable" href="log__severity_8h.html#ab4a2cbab234914b320b7fae11b6e8cb9">INFO</a>) << <span class="stringliteral">"LB = "</span> << <a class="code hl_variable" href="gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a>;</div>
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<div class="line"><a id="l00620" name="l00620"></a><span class="lineno"> 620</span> <span class="comment">// Solve and process second stage.</span></div>
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<div class="line"><a id="l00621" name="l00621"></a><span class="lineno"> 621</span> <a class="code hl_define" href="base_2status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011">ASSIGN_OR_RETURN</a>(</div>
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<div class="line"><a id="l00622" name="l00622"></a><span class="lineno"> 622</span> (<span class="keyword">auto</span> [<a class="code hl_variable" href="gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35">upper_bound</a>, cut]),</div>
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<div class="line"><a id="l00623" name="l00623"></a><span class="lineno"> 623</span> second_stage_solver->Solve(</div>
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<div class="line"><a id="l00624" name="l00624"></a><span class="lineno"> 624</span> z_values, first_stage_result.variable_values().at(first_stage.w),</div>
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<div class="line"><a id="l00625" name="l00625"></a><span class="lineno"> 625</span> first_stage_result.objective_value()));</div>
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<div class="line"><a id="l00626" name="l00626"></a><span class="lineno"> 626</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_linear_expression.html">math_opt::LinearExpression</a> cut_expression;</div>
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<div class="line"><a id="l00627" name="l00627"></a><span class="lineno"> 627</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j < num_facilities; j++) {</div>
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<div class="line"><a id="l00628" name="l00628"></a><span class="lineno"> 628</span> cut_expression += cut.z_coefficients[j] * first_stage.z[j];</div>
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<div class="line"><a id="l00629" name="l00629"></a><span class="lineno"> 629</span> }</div>
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<div class="line"><a id="l00630" name="l00630"></a><span class="lineno"> 630</span> cut_expression += cut.constant;</div>
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<div class="line"><a id="l00631" name="l00631"></a><span class="lineno"> 631</span> first_stage.model.AddLinearConstraint(cut_expression <=</div>
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<div class="line"><a id="l00632" name="l00632"></a><span class="lineno"> 632</span> cut.w_coefficient * first_stage.w);</div>
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<div class="line"><a id="l00633" name="l00633"></a><span class="lineno"> 633</span> best_upper_bound = <a class="code hl_variable" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(<a class="code hl_variable" href="gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35">upper_bound</a>, best_upper_bound);</div>
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<div class="line"><a id="l00634" name="l00634"></a><span class="lineno"> 634</span> <a class="code hl_define" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code hl_variable" href="log__severity_8h.html#ab4a2cbab234914b320b7fae11b6e8cb9">INFO</a>) << <span class="stringliteral">"UB = "</span> << best_upper_bound;</div>
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<div class="line"><a id="l00635" name="l00635"></a><span class="lineno"> 635</span> ++iteration;</div>
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<div class="line"><a id="l00636" name="l00636"></a><span class="lineno"> 636</span> <span class="keywordflow">if</span> (best_upper_bound - <a class="code hl_variable" href="gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a> < target_precission) {</div>
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<div class="line"><a id="l00637" name="l00637"></a><span class="lineno"> 637</span> std::cout << <span class="stringliteral">"Total iterations = "</span> << iteration << std::endl;</div>
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<div class="line"><a id="l00638" name="l00638"></a><span class="lineno"> 638</span> std::cout << <span class="stringliteral">"Final LB = "</span> << absl::StrFormat(<span class="stringliteral">"%.9f"</span>, <a class="code hl_variable" href="gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a>)</div>
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<div class="line"><a id="l00639" name="l00639"></a><span class="lineno"> 639</span> << std::endl;</div>
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<div class="line"><a id="l00640" name="l00640"></a><span class="lineno"> 640</span> std::cout << <span class="stringliteral">"Final UB = "</span> << absl::StrFormat(<span class="stringliteral">"%.9f"</span>, best_upper_bound)</div>
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<div class="line"><a id="l00641" name="l00641"></a><span class="lineno"> 641</span> << std::endl;</div>
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<div class="line"><a id="l00642" name="l00642"></a><span class="lineno"> 642</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00643" name="l00643"></a><span class="lineno"> 643</span> }</div>
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<div class="line"><a id="l00644" name="l00644"></a><span class="lineno"> 644</span> <span class="keywordflow">if</span> (iteration > maximum_iterations) {</div>
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<div class="line"><a id="l00645" name="l00645"></a><span class="lineno"> 645</span> <span class="keywordflow">break</span>;</div>
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<div class="line"><a id="l00646" name="l00646"></a><span class="lineno"> 646</span> }</div>
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<div class="line"><a id="l00647" name="l00647"></a><span class="lineno"> 647</span> }</div>
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<div class="line"><a id="l00648" name="l00648"></a><span class="lineno"> 648</span> <span class="keywordflow">return</span> absl::OkStatus();</div>
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<div class="line"><a id="l00649" name="l00649"></a><span class="lineno"> 649</span>}</div>
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<div class="line"><a id="l00650" name="l00650"></a><span class="lineno"> 650</span>absl::Status Main() {</div>
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<div class="line"><a id="l00651" name="l00651"></a><span class="lineno"> 651</span> <span class="keyword">const</span> FacilityLocationInstance instance{</div>
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<div class="line"><a id="l00652" name="l00652"></a><span class="lineno"> 652</span> .network = Network(absl::GetFlag(FLAGS_num_facilities),</div>
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<div class="line"><a id="l00653" name="l00653"></a><span class="lineno"> 653</span> absl::GetFlag(FLAGS_num_locations),</div>
|
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<div class="line"><a id="l00654" name="l00654"></a><span class="lineno"> 654</span> absl::GetFlag(FLAGS_edge_probability)),</div>
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<div class="line"><a id="l00655" name="l00655"></a><span class="lineno"> 655</span> .location_demand = absl::GetFlag(FLAGS_location_demand),</div>
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<div class="line"><a id="l00656" name="l00656"></a><span class="lineno"> 656</span> .facility_cost = absl::GetFlag(FLAGS_facility_cost),</div>
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<div class="line"><a id="l00657" name="l00657"></a><span class="lineno"> 657</span> .location_fraction = absl::GetFlag(FLAGS_location_fraction)};</div>
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<div class="line"><a id="l00658" name="l00658"></a><span class="lineno"> 658</span> absl::Time <a class="code hl_variable" href="sparse__submatrix_8cc.html#a9b7656b922ea4ec96097d7380c0e61fe">start</a> = absl::Now();</div>
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<div class="line"><a id="l00659" name="l00659"></a><span class="lineno"> 659</span> <a class="code hl_define" href="base_2status__macros_8h.html#acdc223d8c59d5c591dc6b4e88257627b">RETURN_IF_ERROR</a>(FullProblem(instance, absl::GetFlag(FLAGS_solver_type)))</div>
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<div class="line"><a id="l00660" name="l00660"></a><span class="lineno"> 660</span> << <span class="stringliteral">"full solve failed"</span>;</div>
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<div class="line"><a id="l00661" name="l00661"></a><span class="lineno"> 661</span> std::cout << <span class="stringliteral">"Full solve time : "</span> << absl::Now() - <a class="code hl_variable" href="sparse__submatrix_8cc.html#a9b7656b922ea4ec96097d7380c0e61fe">start</a> << std::endl;</div>
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<div class="line"><a id="l00662" name="l00662"></a><span class="lineno"> 662</span> <a class="code hl_variable" href="sparse__submatrix_8cc.html#a9b7656b922ea4ec96097d7380c0e61fe">start</a> = absl::Now();</div>
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<div class="line"><a id="l00663" name="l00663"></a><span class="lineno"> 663</span> <a class="code hl_define" href="base_2status__macros_8h.html#acdc223d8c59d5c591dc6b4e88257627b">RETURN_IF_ERROR</a>(Benders(instance, absl::GetFlag(FLAGS_benders_precission),</div>
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<div class="line"><a id="l00664" name="l00664"></a><span class="lineno"> 664</span> absl::GetFlag(FLAGS_solver_type)))</div>
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<div class="line"><a id="l00665" name="l00665"></a><span class="lineno"> 665</span> << <span class="stringliteral">"Benders solve failed"</span>;</div>
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<div class="line"><a id="l00666" name="l00666"></a><span class="lineno"> 666</span> std::cout << <span class="stringliteral">"Benders solve time : "</span> << absl::Now() - <a class="code hl_variable" href="sparse__submatrix_8cc.html#a9b7656b922ea4ec96097d7380c0e61fe">start</a> << std::endl;</div>
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<div class="line"><a id="l00667" name="l00667"></a><span class="lineno"> 667</span> <span class="keywordflow">return</span> absl::OkStatus();</div>
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<div class="line"><a id="l00668" name="l00668"></a><span class="lineno"> 668</span>}</div>
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<div class="line"><a id="l00669" name="l00669"></a><span class="lineno"> 669</span>} <span class="comment">// namespace</span></div>
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<div class="line"><a id="l00670" name="l00670"></a><span class="lineno"> 670</span> </div>
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<div class="line"><a id="l00671" name="l00671"></a><span class="lineno"><a class="line" href="facility__lp__benders_8cc.html#a3c04138a5bfe5d72780bb7e82a18e627"> 671</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="facility__lp__benders_8cc.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a>(<span class="keywordtype">int</span> argc, <span class="keywordtype">char</span>** argv) {</div>
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<div class="line"><a id="l00672" name="l00672"></a><span class="lineno"> 672</span> <a class="code hl_function" href="init__google_8h.html#a16af2bccb0196e1a9bb628559c95b7cb">InitGoogle</a>(argv[0], &argc, &argv, <span class="keyword">true</span>);</div>
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<div class="line"><a id="l00673" name="l00673"></a><span class="lineno"> 673</span> <span class="keyword">const</span> absl::Status <a class="code hl_variable" href="g__gurobi_8cc.html#a2237393c7ae7ad7344c9885066d5ab6d">status</a> = Main();</div>
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<div class="line"><a id="l00674" name="l00674"></a><span class="lineno"> 674</span> <span class="keywordflow">if</span> (!<a class="code hl_variable" href="g__gurobi_8cc.html#a2237393c7ae7ad7344c9885066d5ab6d">status</a>.ok()) {</div>
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<div class="line"><a id="l00675" name="l00675"></a><span class="lineno"> 675</span> <a class="code hl_define" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(QFATAL) << <a class="code hl_variable" href="g__gurobi_8cc.html#a2237393c7ae7ad7344c9885066d5ab6d">status</a>;</div>
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<div class="line"><a id="l00676" name="l00676"></a><span class="lineno"> 676</span> }</div>
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<div class="line"><a id="l00677" name="l00677"></a><span class="lineno"> 677</span> <span class="keywordflow">return</span> 0;</div>
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<div class="line"><a id="l00678" name="l00678"></a><span class="lineno"> 678</span>}</div>
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<div class="ttc" id="aalldiff__cst_8cc_html_a26e6db9bcc64b584051ecc28171ed11f"><div class="ttname"><a href="alldiff__cst_8cc.html#a26e6db9bcc64b584051ecc28171ed11f">max</a></div><div class="ttdeci">int64_t max</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00140">alldiff_cst.cc:140</a></div></div>
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<div class="ttc" id="aalldiff__cst_8cc_html_ad10edae0a852d72fb76afb1c77735045"><div class="ttname"><a href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">min</a></div><div class="ttdeci">int64_t min</div><div class="ttdef"><b>Definition:</b> <a href="alldiff__cst_8cc_source.html#l00139">alldiff_cst.cc:139</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html"><div class="ttname"><a href="base_2logging_8h.html">logging.h</a></div></div>
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<div class="ttc" id="abase_2logging_8h_html_accad43a85d781d53381cd53a9894b6ae"><div class="ttname"><a href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a></div><div class="ttdeci">#define LOG(severity)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00420">base/logging.h:420</a></div></div>
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<div class="ttc" id="abase_2status__macros_8h_html"><div class="ttname"><a href="base_2status__macros_8h.html">status_macros.h</a></div></div>
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<div class="ttc" id="abase_2status__macros_8h_html_a600de4b8f65fe0a4b1898041634f9011"><div class="ttname"><a href="base_2status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011">ASSIGN_OR_RETURN</a></div><div class="ttdeci">#define ASSIGN_OR_RETURN(lhs, rexpr)</div><div class="ttdef"><b>Definition:</b> <a href="base_2status__macros_8h_source.html#l00046">base/status_macros.h:46</a></div></div>
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<div class="ttc" id="abase_2status__macros_8h_html_acdc223d8c59d5c591dc6b4e88257627b"><div class="ttname"><a href="base_2status__macros_8h.html#acdc223d8c59d5c591dc6b4e88257627b">RETURN_IF_ERROR</a></div><div class="ttdeci">#define RETURN_IF_ERROR(expr)</div><div class="ttdef"><b>Definition:</b> <a href="base_2status__macros_8h_source.html#l00027">base/status_macros.h:27</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1math__opt_1_1_incremental_solver_html_ae216d134c8146dadaa9c16ef2ed1f7c4"><div class="ttname"><a href="classoperations__research_1_1math__opt_1_1_incremental_solver.html#ae216d134c8146dadaa9c16ef2ed1f7c4">operations_research::math_opt::IncrementalSolver::New</a></div><div class="ttdeci">static absl::StatusOr< std::unique_ptr< IncrementalSolver > > New(Model *model, SolverType solver_type, SolverInitArguments arguments={})</div><div class="ttdef"><b>Definition:</b> <a href="solve_8cc_source.html#l00104">solve.cc:104</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1math__opt_1_1_linear_expression_html"><div class="ttname"><a href="classoperations__research_1_1math__opt_1_1_linear_expression.html">operations_research::math_opt::LinearExpression</a></div><div class="ttdef"><b>Definition:</b> <a href="variable__and__expressions_8h_source.html#l00193">variable_and_expressions.h:193</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1math__opt_1_1_model_html"><div class="ttname"><a href="classoperations__research_1_1math__opt_1_1_model.html">operations_research::math_opt::Model</a></div><div class="ttdef"><b>Definition:</b> <a href="math__opt_2cpp_2model_8h_source.html#l00091">math_opt/cpp/model.h:91</a></div></div>
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<div class="ttc" id="aclassoperations__research_1_1math__opt_1_1_variable_html"><div class="ttname"><a href="classoperations__research_1_1math__opt_1_1_variable.html">operations_research::math_opt::Variable</a></div><div class="ttdef"><b>Definition:</b> <a href="variable__and__expressions_8h_source.html#l00115">variable_and_expressions.h:115</a></div></div>
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<div class="ttc" id="acp__model__fz__solver_8cc_html_a10a1eab179b472c030bdc2a2efef7219"><div class="ttname"><a href="cp__model__fz__solver_8cc.html#a10a1eab179b472c030bdc2a2efef7219">parameters</a></div><div class="ttdeci">SatParameters parameters</div><div class="ttdef"><b>Definition:</b> <a href="cp__model__fz__solver_8cc_source.html#l00119">cp_model_fz_solver.cc:119</a></div></div>
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<div class="ttc" id="afacility__lp__benders_8cc_html_a3c04138a5bfe5d72780bb7e82a18e627"><div class="ttname"><a href="facility__lp__benders_8cc.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a></div><div class="ttdeci">int main(int argc, char **argv)</div><div class="ttdef"><b>Definition:</b> <a href="facility__lp__benders_8cc_source.html#l00671">facility_lp_benders.cc:671</a></div></div>
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<div class="ttc" id="afacility__lp__benders_8cc_html_ab408ded47ed4632487b6f538ae4df9d0"><div class="ttname"><a href="facility__lp__benders_8cc.html#ab408ded47ed4632487b6f538ae4df9d0">ABSL_FLAG</a></div><div class="ttdeci">ABSL_FLAG(int, num_facilities, 3000, "Number of facilities.")</div></div>
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<div class="ttc" id="ag__gurobi_8cc_html_a2237393c7ae7ad7344c9885066d5ab6d"><div class="ttname"><a href="g__gurobi_8cc.html#a2237393c7ae7ad7344c9885066d5ab6d">status</a></div><div class="ttdeci">absl::Status status</div><div class="ttdef"><b>Definition:</b> <a href="g__gurobi_8cc_source.html#l00035">g_gurobi.cc:35</a></div></div>
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<div class="ttc" id="agscip__solver_8cc_html_a1ba5ca0f61f2fa13bd23bf0f89004f35"><div class="ttname"><a href="gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35">upper_bound</a></div><div class="ttdeci">double upper_bound</div><div class="ttdef"><b>Definition:</b> <a href="gscip__solver_8cc_source.html#l00137">gscip_solver.cc:137</a></div></div>
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<div class="ttc" id="agscip__solver_8cc_html_a1e2f9a2352c1d9a6cada9544898fceec"><div class="ttname"><a href="gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a></div><div class="ttdeci">double lower_bound</div><div class="ttdef"><b>Definition:</b> <a href="gscip__solver_8cc_source.html#l00136">gscip_solver.cc:136</a></div></div>
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<div class="ttc" id="agurobi__interface_8cc_html_a0728f23c9a47655d38e0bf1a2f200bcf"><div class="ttname"><a href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a></div><div class="ttdeci">GRBmodel * model</div><div class="ttdef"><b>Definition:</b> <a href="gurobi__interface_8cc_source.html#l00274">gurobi_interface.cc:274</a></div></div>
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<div class="ttc" id="ainit__google_8h_html"><div class="ttname"><a href="init__google_8h.html">init_google.h</a></div></div>
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<div class="ttc" id="ainit__google_8h_html_a16af2bccb0196e1a9bb628559c95b7cb"><div class="ttname"><a href="init__google_8h.html#a16af2bccb0196e1a9bb628559c95b7cb">InitGoogle</a></div><div class="ttdeci">void InitGoogle(const char *usage, int *argc, char ***argv, bool deprecated)</div><div class="ttdef"><b>Definition:</b> <a href="init__google_8h_source.html#l00032">init_google.h:32</a></div></div>
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<div class="ttc" id="alagrangian__relaxation_8cc_html_a6ffb9a02546adae760787b2366ae6e41"><div class="ttname"><a href="lagrangian__relaxation_8cc.html#a6ffb9a02546adae760787b2366ae6e41">kZeroTol</a></div><div class="ttdeci">constexpr double kZeroTol</div><div class="ttdef"><b>Definition:</b> <a href="lagrangian__relaxation_8cc_source.html#l00115">lagrangian_relaxation.cc:115</a></div></div>
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<div class="ttc" id="alog__severity_8h_html_ab4a2cbab234914b320b7fae11b6e8cb9"><div class="ttname"><a href="log__severity_8h.html#ab4a2cbab234914b320b7fae11b6e8cb9">INFO</a></div><div class="ttdeci">const int INFO</div><div class="ttdef"><b>Definition:</b> <a href="log__severity_8h_source.html#l00031">log_severity.h:31</a></div></div>
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<div class="ttc" id="amath__opt_8h_html"><div class="ttname"><a href="math__opt_8h.html">math_opt.h</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html">operations_research::math_opt</a></div><div class="ttdef"><b>Definition:</b> <a href="arrow__operator__proxy_8h_source.html#l00020">arrow_operator_proxy.h:20</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_a2d3e7a73de1ae32066be431b5e68f613"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#a2d3e7a73de1ae32066be431b5e68f613">operations_research::math_opt::Sum</a></div><div class="ttdeci">LinearExpression Sum(const Iterable &items)</div><div class="ttdef"><b>Definition:</b> <a href="variable__and__expressions_8h_source.html#l01220">variable_and_expressions.h:1220</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_a5767ee23f380e72488d3c7ebf2d742b1"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#a5767ee23f380e72488d3c7ebf2d742b1">operations_research::math_opt::Solve</a></div><div class="ttdeci">absl::StatusOr< SolveResult > Solve(const Model &model, const SolverType solver_type, const SolveArguments &solve_args, const SolverInitArguments &init_args)</div><div class="ttdef"><b>Definition:</b> <a href="solve_8cc_source.html#l00094">solve.cc:94</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_a8b06041d7c1fb05f379714f4312306ec"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#a8b06041d7c1fb05f379714f4312306ec">operations_research::math_opt::SolverType</a></div><div class="ttdeci">SolverType</div><div class="ttdef"><b>Definition:</b> <a href="parameters_8h_source.html#l00037">parameters.h:37</a></div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_a8b06041d7c1fb05f379714f4312306eca512b5059e1ca814e697fb191d93aaf7f"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#a8b06041d7c1fb05f379714f4312306eca512b5059e1ca814e697fb191d93aaf7f">operations_research::math_opt::SolverType::kGlop</a></div><div class="ttdeci">@ kGlop</div></div>
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<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_ad9f50c9313b35cc1e8887057dc4d9645"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">operations_research::math_opt::kInf</a></div><div class="ttdeci">constexpr double kInf</div><div class="ttdef"><b>Definition:</b> <a href="variable__and__expressions_8cc_source.html#l00029">variable_and_expressions.cc:29</a></div></div>
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<div class="ttc" id="anamespacestd_html"><div class="ttname"><a href="namespacestd.html">std</a></div><div class="ttdoc">STL namespace.</div></div>
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<div class="ttc" id="anamespaceutil_html_a302ee4bfcb86ea9ed64a193ed0b14648"><div class="ttname"><a href="namespaceutil.html#a302ee4bfcb86ea9ed64a193ed0b14648">util::InternalErrorBuilder</a></div><div class="ttdeci">StatusBuilder InternalErrorBuilder()</div><div class="ttdef"><b>Definition:</b> <a href="status__builder_8h_source.html#l00084">status_builder.h:84</a></div></div>
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<div class="ttc" id="arouting__filters_8cc_html_a8e4ee19dee0e00541dbe9bbc83d806ba"><div class="ttname"><a href="routing__filters_8cc.html#a8e4ee19dee0e00541dbe9bbc83d806ba">coefficient</a></div><div class="ttdeci">int64_t coefficient</div><div class="ttdef"><b>Definition:</b> <a href="routing__filters_8cc_source.html#l00969">routing_filters.cc:969</a></div></div>
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<div class="ttc" id="asparse__submatrix_8cc_html_a9b7656b922ea4ec96097d7380c0e61fe"><div class="ttname"><a href="sparse__submatrix_8cc.html#a9b7656b922ea4ec96097d7380c0e61fe">start</a></div><div class="ttdeci">int64_t start</div><div class="ttdef"><b>Definition:</b> <a href="sparse__submatrix_8cc_source.html#l00035">sparse_submatrix.cc:35</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solve_arguments_html"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solve_arguments.html">operations_research::math_opt::SolveArguments</a></div><div class="ttdef"><b>Definition:</b> <a href="solve__arguments_8h_source.html#l00027">solve_arguments.h:27</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solve_parameters_html"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solve_parameters.html">operations_research::math_opt::SolveParameters</a></div><div class="ttdef"><b>Definition:</b> <a href="parameters_8h_source.html#l00175">parameters.h:175</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solve_result_html"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solve_result.html">operations_research::math_opt::SolveResult</a></div><div class="ttdef"><b>Definition:</b> <a href="solve__result_8h_source.html#l00295">solve_result.h:295</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solve_result_html_a116b227550e648d43bfbaccf9557ce42"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solve_result.html#a116b227550e648d43bfbaccf9557ce42">operations_research::math_opt::SolveResult::dual_values</a></div><div class="ttdeci">const LinearConstraintMap< double > & dual_values() const</div><div class="ttdef"><b>Definition:</b> <a href="solve__result_8cc_source.html#l00385">solve_result.cc:385</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solve_result_html_a240b106da863fbff10545e97c2c72007"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solve_result.html#a240b106da863fbff10545e97c2c72007">operations_research::math_opt::SolveResult::has_dual_ray</a></div><div class="ttdeci">bool has_dual_ray() const</div><div class="ttdef"><b>Definition:</b> <a href="solve__result_8h_source.html#l00390">solve_result.h:390</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solve_result_html_a35cafd54aea7eb0aecf1cb6fa4b33273"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solve_result.html#a35cafd54aea7eb0aecf1cb6fa4b33273">operations_research::math_opt::SolveResult::has_dual_feasible_solution</a></div><div class="ttdeci">bool has_dual_feasible_solution() const</div><div class="ttdef"><b>Definition:</b> <a href="solve__result_8cc_source.html#l00379">solve_result.cc:379</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solve_result_html_a5511ef5b247197964fac748cc4a8de1f"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solve_result.html#a5511ef5b247197964fac748cc4a8de1f">operations_research::math_opt::SolveResult::ray_dual_values</a></div><div class="ttdeci">const LinearConstraintMap< double > & ray_dual_values() const</div><div class="ttdef"><b>Definition:</b> <a href="solve__result_8cc_source.html#l00394">solve_result.cc:394</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solve_result_html_a77d1ea96211300e9417b965981953c81"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solve_result.html#a77d1ea96211300e9417b965981953c81">operations_research::math_opt::SolveResult::termination</a></div><div class="ttdeci">Termination termination</div><div class="ttdef"><b>Definition:</b> <a href="solve__result_8h_source.html#l00300">solve_result.h:300</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solve_result_html_a84f066c304d8bcbb9567be094feb9b08"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solve_result.html#a84f066c304d8bcbb9567be094feb9b08">operations_research::math_opt::SolveResult::objective_value</a></div><div class="ttdeci">double objective_value() const</div><div class="ttdef"><b>Definition:</b> <a href="solve__result_8cc_source.html#l00358">solve_result.cc:358</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solve_result_html_aafa2eea97d94bf02b53add568f96a5b7"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solve_result.html#aafa2eea97d94bf02b53add568f96a5b7">operations_research::math_opt::SolveResult::ray_reduced_costs</a></div><div class="ttdeci">const VariableMap< double > & ray_reduced_costs() const</div><div class="ttdef"><b>Definition:</b> <a href="solve__result_8cc_source.html#l00399">solve_result.cc:399</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solve_result_html_acc1f8f5ed04e9ea770b526fa34d6076c"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solve_result.html#acc1f8f5ed04e9ea770b526fa34d6076c">operations_research::math_opt::SolveResult::reduced_costs</a></div><div class="ttdeci">const VariableMap< double > & reduced_costs() const</div><div class="ttdef"><b>Definition:</b> <a href="solve__result_8cc_source.html#l00390">solve_result.cc:390</a></div></div>
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<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_termination_html_a36d5365d462f57468ba3a9d8ae6bbec9"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_termination.html#a36d5365d462f57468ba3a9d8ae6bbec9">operations_research::math_opt::Termination::reason</a></div><div class="ttdeci">TerminationReason reason</div><div class="ttdef"><b>Definition:</b> <a href="solve__result_8h_source.html#l00261">solve_result.h:261</a></div></div>
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<div class="ttc" id="autil_2status__macros_8h_html"><div class="ttname"><a href="util_2status__macros_8h.html">status_macros.h</a></div></div>
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<div class="ttc" id="autil_2status__macros_8h_html_a50de54834da66a6bcb7c9e37902e522b"><div class="ttname"><a href="util_2status__macros_8h.html#a50de54834da66a6bcb7c9e37902e522b">OR_ASSIGN_OR_RETURN3</a></div><div class="ttdeci">#define OR_ASSIGN_OR_RETURN3(lhs, rexpr, error_expression)</div><div class="ttdef"><b>Definition:</b> <a href="util_2status__macros_8h_source.html#l00032">util/status_macros.h:32</a></div></div>
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<div class="ttc" id="avariable__and__expressions_8cc_html_a98c17ae8d99a73259ea78de8c4b66254"><div class="ttname"><a href="variable__and__expressions_8cc.html#a98c17ae8d99a73259ea78de8c4b66254">constant</a></div><div class="ttdeci">const double constant</div><div class="ttdef"><b>Definition:</b> <a href="variable__and__expressions_8cc_source.html#l00140">variable_and_expressions.cc:140</a></div></div>
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