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<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 name="l00001"></a><span class="lineno"> 1</span>&#160;<span class="comment">// Copyright 2010-2021 Google LLC</span></div>
<div class="line"><a name="l00002"></a><span class="lineno"> 2</span>&#160;<span class="comment">// Licensed under the Apache License, Version 2.0 (the &quot;License&quot;);</span></div>
<div class="line"><a name="l00003"></a><span class="lineno"> 3</span>&#160;<span class="comment">// you may not use this file except in compliance with the License.</span></div>
<div class="line"><a name="l00004"></a><span class="lineno"> 4</span>&#160;<span class="comment">// You may obtain a copy of the License at</span></div>
<div class="line"><a name="l00005"></a><span class="lineno"> 5</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00006"></a><span class="lineno"> 6</span>&#160;<span class="comment">// http://www.apache.org/licenses/LICENSE-2.0</span></div>
<div class="line"><a name="l00007"></a><span class="lineno"> 7</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00008"></a><span class="lineno"> 8</span>&#160;<span class="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
<div class="line"><a name="l00009"></a><span class="lineno"> 9</span>&#160;<span class="comment">// distributed under the License is distributed on an &quot;AS IS&quot; BASIS,</span></div>
<div class="line"><a name="l00010"></a><span class="lineno"> 10</span>&#160;<span class="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
<div class="line"><a name="l00011"></a><span class="lineno"> 11</span>&#160;<span class="comment">// See the License for the specific language governing permissions and</span></div>
<div class="line"><a name="l00012"></a><span class="lineno"> 12</span>&#160;<span class="comment">// limitations under the License.</span></div>
<div class="line"><a name="l00013"></a><span class="lineno"> 13</span>&#160; </div>
<div class="line"><a name="l00014"></a><span class="lineno"> 14</span>&#160;<span class="comment">// Simple linear programming example</span></div>
<div class="line"><a name="l00015"></a><span class="lineno"> 15</span>&#160; </div>
<div class="line"><a name="l00016"></a><span class="lineno"> 16</span>&#160;<span class="preprocessor">#include &lt;algorithm&gt;</span></div>
<div class="line"><a name="l00017"></a><span class="lineno"> 17</span>&#160;<span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a name="l00018"></a><span class="lineno"> 18</span>&#160;<span class="preprocessor">#include &lt;limits&gt;</span></div>
<div class="line"><a name="l00019"></a><span class="lineno"> 19</span>&#160;<span class="preprocessor">#include &lt;utility&gt;</span></div>
<div class="line"><a name="l00020"></a><span class="lineno"> 20</span>&#160;<span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a name="l00021"></a><span class="lineno"> 21</span>&#160; </div>
<div class="line"><a name="l00022"></a><span class="lineno"> 22</span>&#160;<span class="preprocessor">#include &quot;absl/flags/parse.h&quot;</span></div>
<div class="line"><a name="l00023"></a><span class="lineno"> 23</span>&#160;<span class="preprocessor">#include &quot;absl/flags/usage.h&quot;</span></div>
<div class="line"><a name="l00024"></a><span class="lineno"> 24</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="base_2logging_8h.html">ortools/base/logging.h</a>&quot;</span></div>
<div class="line"><a name="l00025"></a><span class="lineno"> 25</span>&#160;<span class="preprocessor">#include &quot;absl/container/flat_hash_map.h&quot;</span></div>
<div class="line"><a name="l00026"></a><span class="lineno"> 26</span>&#160;<span class="preprocessor">#include &quot;absl/flags/flag.h&quot;</span></div>
<div class="line"><a name="l00027"></a><span class="lineno"> 27</span>&#160;<span class="preprocessor">#include &quot;absl/random/random.h&quot;</span></div>
<div class="line"><a name="l00028"></a><span class="lineno"> 28</span>&#160;<span class="preprocessor">#include &quot;absl/random/uniform_int_distribution.h&quot;</span></div>
<div class="line"><a name="l00029"></a><span class="lineno"> 29</span>&#160;<span class="preprocessor">#include &quot;absl/status/statusor.h&quot;</span></div>
<div class="line"><a name="l00030"></a><span class="lineno"> 30</span>&#160;<span class="preprocessor">#include &quot;absl/strings/str_format.h&quot;</span></div>
<div class="line"><a name="l00031"></a><span class="lineno"> 31</span>&#160;<span class="preprocessor">#include &quot;absl/strings/string_view.h&quot;</span></div>
<div class="line"><a name="l00032"></a><span class="lineno"> 32</span>&#160;<span class="preprocessor">#include &quot;absl/time/clock.h&quot;</span></div>
<div class="line"><a name="l00033"></a><span class="lineno"> 33</span>&#160;<span class="preprocessor">#include &quot;absl/time/time.h&quot;</span></div>
<div class="line"><a name="l00034"></a><span class="lineno"> 34</span>&#160;<span class="preprocessor">#include &quot;<a class="code" href="math__opt_8h.html">ortools/math_opt/cpp/math_opt.h</a>&quot;</span></div>
<div class="line"><a name="l00035"></a><span class="lineno"> 35</span>&#160; </div>
<div class="line"><a name="l00036"></a><span class="lineno"><a class="line" href="facility__lp__benders_8cc.html#ab408ded47ed4632487b6f538ae4df9d0"> 36</a></span>&#160;<a class="code" href="facility__lp__benders_8cc.html#ab408ded47ed4632487b6f538ae4df9d0">ABSL_FLAG</a>(<span class="keywordtype">int</span>, num_facilities, 3000, <span class="stringliteral">&quot;Number of facilities.&quot;</span>);</div>
<div class="line"><a name="l00037"></a><span class="lineno"><a class="line" href="facility__lp__benders_8cc.html#a187b2452ce7ffbf3dc80a9c6ccc8b4d4"> 37</a></span>&#160;<a class="code" href="facility__lp__benders_8cc.html#ab408ded47ed4632487b6f538ae4df9d0">ABSL_FLAG</a>(<span class="keywordtype">int</span>, num_locations, 50, <span class="stringliteral">&quot;Number of locations.&quot;</span>);</div>
<div class="line"><a name="l00038"></a><span class="lineno"><a class="line" href="facility__lp__benders_8cc.html#a589d83de6bdfda324029266b63574e44"> 38</a></span>&#160;<a class="code" href="facility__lp__benders_8cc.html#ab408ded47ed4632487b6f538ae4df9d0">ABSL_FLAG</a>(<span class="keywordtype">double</span>, edge_probability, 0.99, <span class="stringliteral">&quot;Edge probability.&quot;</span>);</div>
<div class="line"><a name="l00039"></a><span class="lineno"><a class="line" href="facility__lp__benders_8cc.html#ab26c80732ec6702942ce6b3d16027861"> 39</a></span>&#160;<a class="code" href="facility__lp__benders_8cc.html#ab408ded47ed4632487b6f538ae4df9d0">ABSL_FLAG</a>(<span class="keywordtype">double</span>, benders_precission, 1e-9, <span class="stringliteral">&quot;Benders target precission.&quot;</span>);</div>
<div class="line"><a name="l00040"></a><span class="lineno"><a class="line" href="facility__lp__benders_8cc.html#a3d6782a997bb7c460159f23717a3a622"> 40</a></span>&#160;<a class="code" href="facility__lp__benders_8cc.html#ab408ded47ed4632487b6f538ae4df9d0">ABSL_FLAG</a>(<span class="keywordtype">double</span>, location_demand, 1, <span class="stringliteral">&quot;Client demands.&quot;</span>);</div>
<div class="line"><a name="l00041"></a><span class="lineno"><a class="line" href="facility__lp__benders_8cc.html#a70ca27183ea1caa3da0c437d9124d7b2"> 41</a></span>&#160;<a class="code" href="facility__lp__benders_8cc.html#ab408ded47ed4632487b6f538ae4df9d0">ABSL_FLAG</a>(<span class="keywordtype">double</span>, facility_cost, 100, <span class="stringliteral">&quot;Facility capacity cost.&quot;</span>);</div>
<div class="line"><a name="l00042"></a><span class="lineno"><a class="line" href="facility__lp__benders_8cc.html#a36423080607ac8d3b16d220c1f4d0c62"> 42</a></span>&#160;<a class="code" href="facility__lp__benders_8cc.html#ab408ded47ed4632487b6f538ae4df9d0">ABSL_FLAG</a>(</div>
<div class="line"><a name="l00043"></a><span class="lineno"> 43</span>&#160; <span class="keywordtype">double</span>, location_fraction, 0.001,</div>
<div class="line"><a name="l00044"></a><span class="lineno"> 44</span>&#160; <span class="stringliteral">&quot;Fraction of a facility&#39;s capacity that can be used by each location.&quot;</span>);</div>
<div class="line"><a name="l00045"></a><span class="lineno"> 45</span>&#160; </div>
<div class="line"><a name="l00046"></a><span class="lineno"> 46</span>&#160;<span class="keyword">namespace </span>{</div>
<div class="line"><a name="l00047"></a><span class="lineno"> 47</span>&#160;using ::operations_research::math_opt::GurobiParametersProto;</div>
<div class="line"><a name="l00048"></a><span class="lineno"> 48</span>&#160;using ::operations_research::math_opt::LinearConstraint;</div>
<div class="line"><a name="l00049"></a><span class="lineno"> 49</span>&#160;using ::operations_research::math_opt::LinearExpression;</div>
<div class="line"><a name="l00050"></a><span class="lineno"> 50</span>&#160;using ::operations_research::math_opt::MathOpt;</div>
<div class="line"><a name="l00051"></a><span class="lineno"> 51</span>&#160;using ::operations_research::math_opt::Objective;</div>
<div class="line"><a name="l00052"></a><span class="lineno"> 52</span>&#160;using ::operations_research::math_opt::Result;</div>
<div class="line"><a name="l00053"></a><span class="lineno"> 53</span>&#160;using ::operations_research::math_opt::SolveParametersProto;</div>
<div class="line"><a name="l00054"></a><span class="lineno"> 54</span>&#160;using ::operations_research::math_opt::SolveResultProto;</div>
<div class="line"><a name="l00055"></a><span class="lineno"> 55</span>&#160;<a class="code" href="namespaceoperations__research_1_1math__opt.html#a2d3e7a73de1ae32066be431b5e68f613">using ::operations_research::math_opt::Sum</a>;</div>
<div class="line"><a name="l00056"></a><span class="lineno"> 56</span>&#160;using ::operations_research::math_opt::Variable;</div>
<div class="line"><a name="l00057"></a><span class="lineno"> 57</span>&#160; </div>
<div class="line"><a name="l00058"></a><span class="lineno"> 58</span>&#160;<span class="comment">// First element is a facility and second is a location.</span></div>
<div class="line"><a name="l00059"></a><span class="lineno"> 59</span>&#160;<span class="keyword">using</span> Edge = std::pair&lt;int, int&gt;;</div>
<div class="line"><a name="l00060"></a><span class="lineno"> 60</span>&#160; </div>
<div class="line"><a name="l00061"></a><span class="lineno"> 61</span>&#160;<span class="comment">// A simple randomly-generated facility-location network.</span></div>
<div class="line"><a name="l00062"></a><span class="lineno"> 62</span>&#160;<span class="keyword">class </span>Network {</div>
<div class="line"><a name="l00063"></a><span class="lineno"> 63</span>&#160; <span class="keyword">public</span>:</div>
<div class="line"><a name="l00064"></a><span class="lineno"> 64</span>&#160; Network(<span class="keywordtype">int</span> num_facilities, <span class="keywordtype">int</span> num_locations, <span class="keywordtype">double</span> edge_probability);</div>
<div class="line"><a name="l00065"></a><span class="lineno"> 65</span>&#160; </div>
<div class="line"><a name="l00066"></a><span class="lineno"> 66</span>&#160; <span class="keywordtype">int</span> num_facilities()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> num_facilities_; }</div>
<div class="line"><a name="l00067"></a><span class="lineno"> 67</span>&#160; <span class="keywordtype">int</span> num_locations()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> num_locations_; }</div>
<div class="line"><a name="l00068"></a><span class="lineno"> 68</span>&#160; </div>
<div class="line"><a name="l00069"></a><span class="lineno"> 69</span>&#160; <span class="keyword">const</span> std::vector&lt;Edge&gt;&amp; edges()<span class="keyword"> const </span>{ <span class="keywordflow">return</span> edges_; }</div>
<div class="line"><a name="l00070"></a><span class="lineno"> 70</span>&#160; </div>
<div class="line"><a name="l00071"></a><span class="lineno"> 71</span>&#160; <span class="keyword">const</span> std::vector&lt;Edge&gt;&amp; edges_incident_to_facility(</div>
<div class="line"><a name="l00072"></a><span class="lineno"> 72</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> facility)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00073"></a><span class="lineno"> 73</span>&#160; <span class="keywordflow">return</span> facility_edge_incidence_[facility];</div>
<div class="line"><a name="l00074"></a><span class="lineno"> 74</span>&#160; }</div>
<div class="line"><a name="l00075"></a><span class="lineno"> 75</span>&#160; </div>
<div class="line"><a name="l00076"></a><span class="lineno"> 76</span>&#160; <span class="keyword">const</span> std::vector&lt;Edge&gt;&amp; edges_incident_to_location(</div>
<div class="line"><a name="l00077"></a><span class="lineno"> 77</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> location)<span class="keyword"> const </span>{</div>
<div class="line"><a name="l00078"></a><span class="lineno"> 78</span>&#160; <span class="keywordflow">return</span> location_edge_incidence_[location];</div>
<div class="line"><a name="l00079"></a><span class="lineno"> 79</span>&#160; }</div>
<div class="line"><a name="l00080"></a><span class="lineno"> 80</span>&#160; </div>
<div class="line"><a name="l00081"></a><span class="lineno"> 81</span>&#160; <span class="keywordtype">double</span> edge_cost(<span class="keyword">const</span> Edge&amp; edge)<span class="keyword"> const </span>{ <span class="keywordflow">return</span> edge_costs_.at(edge); }</div>
<div class="line"><a name="l00082"></a><span class="lineno"> 82</span>&#160; </div>
<div class="line"><a name="l00083"></a><span class="lineno"> 83</span>&#160; <span class="keyword">private</span>:</div>
<div class="line"><a name="l00084"></a><span class="lineno"> 84</span>&#160; <span class="keywordtype">int</span> num_facilities_;</div>
<div class="line"><a name="l00085"></a><span class="lineno"> 85</span>&#160; <span class="keywordtype">int</span> num_locations_;</div>
<div class="line"><a name="l00086"></a><span class="lineno"> 86</span>&#160; <span class="comment">// No order is assumed for the following lists of edges.</span></div>
<div class="line"><a name="l00087"></a><span class="lineno"> 87</span>&#160; std::vector&lt;Edge&gt; edges_;</div>
<div class="line"><a name="l00088"></a><span class="lineno"> 88</span>&#160; absl::flat_hash_map&lt;Edge, double&gt; edge_costs_;</div>
<div class="line"><a name="l00089"></a><span class="lineno"> 89</span>&#160; std::vector&lt;std::vector&lt;Edge&gt;&gt; facility_edge_incidence_;</div>
<div class="line"><a name="l00090"></a><span class="lineno"> 90</span>&#160; std::vector&lt;std::vector&lt;Edge&gt;&gt; location_edge_incidence_;</div>
<div class="line"><a name="l00091"></a><span class="lineno"> 91</span>&#160;};</div>
<div class="line"><a name="l00092"></a><span class="lineno"> 92</span>&#160; </div>
<div class="line"><a name="l00093"></a><span class="lineno"> 93</span>&#160;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>
<div class="line"><a name="l00094"></a><span class="lineno"> 94</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span> edge_probability) {</div>
<div class="line"><a name="l00095"></a><span class="lineno"> 95</span>&#160; absl::BitGen bitgen;</div>
<div class="line"><a name="l00096"></a><span class="lineno"> 96</span>&#160; </div>
<div class="line"><a name="l00097"></a><span class="lineno"> 97</span>&#160; num_facilities_ = num_facilities;</div>
<div class="line"><a name="l00098"></a><span class="lineno"> 98</span>&#160; num_locations_ = num_locations;</div>
<div class="line"><a name="l00099"></a><span class="lineno"> 99</span>&#160; facility_edge_incidence_ =</div>
<div class="line"><a name="l00100"></a><span class="lineno"> 100</span>&#160; std::vector&lt;std::vector&lt;std::pair&lt;int, int&gt;&gt;&gt;(num_facilities);</div>
<div class="line"><a name="l00101"></a><span class="lineno"> 101</span>&#160; location_edge_incidence_ = std::vector&lt;std::vector&lt;std::pair&lt;int, int&gt;&gt;&gt;(</div>
<div class="line"><a name="l00102"></a><span class="lineno"> 102</span>&#160; num_locations, std::vector&lt;std::pair&lt;int, int&gt;&gt;());</div>
<div class="line"><a name="l00103"></a><span class="lineno"> 103</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> facility = 0; facility &lt; num_facilities_; ++facility) {</div>
<div class="line"><a name="l00104"></a><span class="lineno"> 104</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> location = 0; location &lt; num_locations_; ++location) {</div>
<div class="line"><a name="l00105"></a><span class="lineno"> 105</span>&#160; <span class="keywordflow">if</span> (absl::Bernoulli(bitgen, edge_probability)) {</div>
<div class="line"><a name="l00106"></a><span class="lineno"> 106</span>&#160; <span class="keyword">const</span> std::pair&lt;int, int&gt; edge({facility, location});</div>
<div class="line"><a name="l00107"></a><span class="lineno"> 107</span>&#160; facility_edge_incidence_[facility].push_back(edge);</div>
<div class="line"><a name="l00108"></a><span class="lineno"> 108</span>&#160; location_edge_incidence_[location].push_back(edge);</div>
<div class="line"><a name="l00109"></a><span class="lineno"> 109</span>&#160; edges_.push_back(edge);</div>
<div class="line"><a name="l00110"></a><span class="lineno"> 110</span>&#160; edge_costs_.insert({edge, absl::Uniform(bitgen, 0, 1.0)});</div>
<div class="line"><a name="l00111"></a><span class="lineno"> 111</span>&#160; }</div>
<div class="line"><a name="l00112"></a><span class="lineno"> 112</span>&#160; }</div>
<div class="line"><a name="l00113"></a><span class="lineno"> 113</span>&#160; }</div>
<div class="line"><a name="l00114"></a><span class="lineno"> 114</span>&#160; <span class="comment">// Ensure every facility is connected to at least one location and every</span></div>
<div class="line"><a name="l00115"></a><span class="lineno"> 115</span>&#160; <span class="comment">// location is connected to at least one facility.</span></div>
<div class="line"><a name="l00116"></a><span class="lineno"> 116</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> facility = 0; facility &lt; num_facilities; ++facility) {</div>
<div class="line"><a name="l00117"></a><span class="lineno"> 117</span>&#160; <span class="keyword">auto</span>&amp; locations = facility_edge_incidence_[facility];</div>
<div class="line"><a name="l00118"></a><span class="lineno"> 118</span>&#160; <span class="keywordflow">if</span> (locations.empty()) {</div>
<div class="line"><a name="l00119"></a><span class="lineno"> 119</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> location =</div>
<div class="line"><a name="l00120"></a><span class="lineno"> 120</span>&#160; absl::uniform_int_distribution&lt;int&gt;(0, num_locations - 1)(bitgen);</div>
<div class="line"><a name="l00121"></a><span class="lineno"> 121</span>&#160; <span class="keyword">const</span> std::pair&lt;int, int&gt; edge({facility, location});</div>
<div class="line"><a name="l00122"></a><span class="lineno"> 122</span>&#160; locations.push_back(edge);</div>
<div class="line"><a name="l00123"></a><span class="lineno"> 123</span>&#160; location_edge_incidence_[location].push_back(edge);</div>
<div class="line"><a name="l00124"></a><span class="lineno"> 124</span>&#160; edges_.push_back(edge);</div>
<div class="line"><a name="l00125"></a><span class="lineno"> 125</span>&#160; edge_costs_.insert({edge, absl::Uniform(bitgen, 0, 1.0)});</div>
<div class="line"><a name="l00126"></a><span class="lineno"> 126</span>&#160; }</div>
<div class="line"><a name="l00127"></a><span class="lineno"> 127</span>&#160; }</div>
<div class="line"><a name="l00128"></a><span class="lineno"> 128</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> location = 0; location &lt; num_locations; ++location) {</div>
<div class="line"><a name="l00129"></a><span class="lineno"> 129</span>&#160; <span class="keyword">auto</span>&amp; facilities = location_edge_incidence_[location];</div>
<div class="line"><a name="l00130"></a><span class="lineno"> 130</span>&#160; <span class="keywordflow">if</span> (facilities.empty()) {</div>
<div class="line"><a name="l00131"></a><span class="lineno"> 131</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> facility =</div>
<div class="line"><a name="l00132"></a><span class="lineno"> 132</span>&#160; absl::uniform_int_distribution&lt;int&gt;(0, num_facilities - 1)(bitgen);</div>
<div class="line"><a name="l00133"></a><span class="lineno"> 133</span>&#160; <span class="keyword">const</span> std::pair&lt;int, int&gt; edge({facility, location});</div>
<div class="line"><a name="l00134"></a><span class="lineno"> 134</span>&#160; facilities.push_back(edge);</div>
<div class="line"><a name="l00135"></a><span class="lineno"> 135</span>&#160; facility_edge_incidence_[facility].push_back(edge);</div>
<div class="line"><a name="l00136"></a><span class="lineno"> 136</span>&#160; edges_.push_back(edge);</div>
<div class="line"><a name="l00137"></a><span class="lineno"> 137</span>&#160; edge_costs_.insert({edge, absl::Uniform(bitgen, 0, 1.0)});</div>
<div class="line"><a name="l00138"></a><span class="lineno"> 138</span>&#160; }</div>
<div class="line"><a name="l00139"></a><span class="lineno"> 139</span>&#160; }</div>
<div class="line"><a name="l00140"></a><span class="lineno"> 140</span>&#160;}</div>
<div class="line"><a name="l00141"></a><span class="lineno"> 141</span>&#160; </div>
<div class="line"><a name="l00142"></a><span class="lineno"> 142</span>&#160;constexpr <span class="keywordtype">double</span> <a class="code" href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">kInf</a> = std::numeric_limits&lt;double&gt;::infinity();</div>
<div class="line"><a name="l00143"></a><span class="lineno"> 143</span>&#160; </div>
<div class="line"><a name="l00144"></a><span class="lineno"> 144</span>&#160;<span class="comment">// We consider a network design problem where each location has a demand that</span></div>
<div class="line"><a name="l00145"></a><span class="lineno"> 145</span>&#160;<span class="comment">// must be met by its neighboring facilities, and each facility can control</span></div>
<div class="line"><a name="l00146"></a><span class="lineno"> 146</span>&#160;<span class="comment">// its total capacity. In this version we also require that locations cannot</span></div>
<div class="line"><a name="l00147"></a><span class="lineno"> 147</span>&#160;<span class="comment">// use more that a specified fraction of a facilities capacity.</span></div>
<div class="line"><a name="l00148"></a><span class="lineno"> 148</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00149"></a><span class="lineno"> 149</span>&#160;<span class="comment">// Problem data:</span></div>
<div class="line"><a name="l00150"></a><span class="lineno"> 150</span>&#160;<span class="comment">// * F: set of facilities.</span></div>
<div class="line"><a name="l00151"></a><span class="lineno"> 151</span>&#160;<span class="comment">// * L: set of locations.</span></div>
<div class="line"><a name="l00152"></a><span class="lineno"> 152</span>&#160;<span class="comment">// * E: subset of {(f,l) : f in F, l in L} that describes the network between</span></div>
<div class="line"><a name="l00153"></a><span class="lineno"> 153</span>&#160;<span class="comment">// facilities and locations.</span></div>
<div class="line"><a name="l00154"></a><span class="lineno"> 154</span>&#160;<span class="comment">// * d: demand at location (all demands are equal for simplicity).</span></div>
<div class="line"><a name="l00155"></a><span class="lineno"> 155</span>&#160;<span class="comment">// * c: cost per unit of capacity at a facility (all facilities are have the</span></div>
<div class="line"><a name="l00156"></a><span class="lineno"> 156</span>&#160;<span class="comment">// same cost for simplicity).</span></div>
<div class="line"><a name="l00157"></a><span class="lineno"> 157</span>&#160;<span class="comment">// * h: cost per unit transported through an edge.</span></div>
<div class="line"><a name="l00158"></a><span class="lineno"> 158</span>&#160;<span class="comment">// * a: fraction of a facility&#39;s capacity that can be used by each location.</span></div>
<div class="line"><a name="l00159"></a><span class="lineno"> 159</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00160"></a><span class="lineno"> 160</span>&#160;<span class="comment">// Decision variables:</span></div>
<div class="line"><a name="l00161"></a><span class="lineno"> 161</span>&#160;<span class="comment">// * z_f: capacity at facility f in F.</span></div>
<div class="line"><a name="l00162"></a><span class="lineno"> 162</span>&#160;<span class="comment">// * x_(f,l): flow from facility f to location l for all (f,l) in E.</span></div>
<div class="line"><a name="l00163"></a><span class="lineno"> 163</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00164"></a><span class="lineno"> 164</span>&#160;<span class="comment">// Formulation:</span></div>
<div class="line"><a name="l00165"></a><span class="lineno"> 165</span>&#160;<span class="comment">// min c * sum(z_f : f in F) + sum(h_e * x_e : e in E)</span></div>
<div class="line"><a name="l00166"></a><span class="lineno"> 166</span>&#160;<span class="comment">// s.t.</span></div>
<div class="line"><a name="l00167"></a><span class="lineno"> 167</span>&#160;<span class="comment">// x_(f,l) &lt;= a * z_f for all (f,l) in E</span></div>
<div class="line"><a name="l00168"></a><span class="lineno"> 168</span>&#160;<span class="comment">// sum(x_(f,l) : l such that (f,l) in E) &lt;= z_f for all f in F</span></div>
<div class="line"><a name="l00169"></a><span class="lineno"> 169</span>&#160;<span class="comment">// sum(x_(f,l) : f such that (f,l) in E) &gt;= d for all l in L</span></div>
<div class="line"><a name="l00170"></a><span class="lineno"> 170</span>&#160;<span class="comment">// x_e &gt;= 0 for all e in E</span></div>
<div class="line"><a name="l00171"></a><span class="lineno"> 171</span>&#160;<span class="comment">// z_f &gt;= 0 for all f in F</span></div>
<div class="line"><a name="l00172"></a><span class="lineno"> 172</span>&#160;<span class="comment">//</span></div>
<div class="line"><a name="l00173"></a><span class="lineno"> 173</span>&#160;<span class="keywordtype">void</span> FullProblem(<span class="keyword">const</span> Network&amp; network, <span class="keyword">const</span> <span class="keywordtype">double</span> location_demand,</div>
<div class="line"><a name="l00174"></a><span class="lineno"> 174</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span> facility_cost, <span class="keyword">const</span> <span class="keywordtype">double</span> location_fraction) {</div>
<div class="line"><a name="l00175"></a><span class="lineno"> 175</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> num_facilities = network.num_facilities();</div>
<div class="line"><a name="l00176"></a><span class="lineno"> 176</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> num_locations = network.num_locations();</div>
<div class="line"><a name="l00177"></a><span class="lineno"> 177</span>&#160; </div>
<div class="line"><a name="l00178"></a><span class="lineno"> 178</span>&#160; MathOpt <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>(operations_research::math_opt::SOLVER_TYPE_GUROBI,</div>
<div class="line"><a name="l00179"></a><span class="lineno"> 179</span>&#160; <span class="stringliteral">&quot;Full network design problem&quot;</span>);</div>
<div class="line"><a name="l00180"></a><span class="lineno"> 180</span>&#160; <span class="keyword">const</span> Objective objective = <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.objective();</div>
<div class="line"><a name="l00181"></a><span class="lineno"> 181</span>&#160; objective.set_minimize();</div>
<div class="line"><a name="l00182"></a><span class="lineno"> 182</span>&#160; </div>
<div class="line"><a name="l00183"></a><span class="lineno"> 183</span>&#160; <span class="comment">// Capacity variables</span></div>
<div class="line"><a name="l00184"></a><span class="lineno"> 184</span>&#160; std::vector&lt;Variable&gt; z;</div>
<div class="line"><a name="l00185"></a><span class="lineno"> 185</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; num_facilities; j++) {</div>
<div class="line"><a name="l00186"></a><span class="lineno"> 186</span>&#160; <span class="keyword">const</span> Variable z_j = <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.AddContinuousVariable(0.0, <a class="code" href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">kInf</a>);</div>
<div class="line"><a name="l00187"></a><span class="lineno"> 187</span>&#160; z.push_back(z_j);</div>
<div class="line"><a name="l00188"></a><span class="lineno"> 188</span>&#160; objective.set_linear_coefficient(z_j, facility_cost);</div>
<div class="line"><a name="l00189"></a><span class="lineno"> 189</span>&#160; }</div>
<div class="line"><a name="l00190"></a><span class="lineno"> 190</span>&#160; </div>
<div class="line"><a name="l00191"></a><span class="lineno"> 191</span>&#160; <span class="comment">// Flow variables</span></div>
<div class="line"><a name="l00192"></a><span class="lineno"> 192</span>&#160; absl::flat_hash_map&lt;Edge, Variable&gt; x;</div>
<div class="line"><a name="l00193"></a><span class="lineno"> 193</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>&amp; edge : network.edges()) {</div>
<div class="line"><a name="l00194"></a><span class="lineno"> 194</span>&#160; <span class="keyword">const</span> Variable x_edge = <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.AddContinuousVariable(0.0, <a class="code" href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">kInf</a>);</div>
<div class="line"><a name="l00195"></a><span class="lineno"> 195</span>&#160; x.insert({edge, x_edge});</div>
<div class="line"><a name="l00196"></a><span class="lineno"> 196</span>&#160; objective.set_linear_coefficient(x_edge, network.edge_cost(edge));</div>
<div class="line"><a name="l00197"></a><span class="lineno"> 197</span>&#160; }</div>
<div class="line"><a name="l00198"></a><span class="lineno"> 198</span>&#160; </div>
<div class="line"><a name="l00199"></a><span class="lineno"> 199</span>&#160; <span class="comment">// Demand constraints</span></div>
<div class="line"><a name="l00200"></a><span class="lineno"> 200</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> location = 0; location &lt; num_locations; ++location) {</div>
<div class="line"><a name="l00201"></a><span class="lineno"> 201</span>&#160; LinearExpression linear_expression;</div>
<div class="line"><a name="l00202"></a><span class="lineno"> 202</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>&amp; edge : network.edges_incident_to_location(location)) {</div>
<div class="line"><a name="l00203"></a><span class="lineno"> 203</span>&#160; linear_expression += x.at(edge);</div>
<div class="line"><a name="l00204"></a><span class="lineno"> 204</span>&#160; }</div>
<div class="line"><a name="l00205"></a><span class="lineno"> 205</span>&#160; <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.AddLinearConstraint(linear_expression &gt;= location_demand);</div>
<div class="line"><a name="l00206"></a><span class="lineno"> 206</span>&#160; }</div>
<div class="line"><a name="l00207"></a><span class="lineno"> 207</span>&#160; </div>
<div class="line"><a name="l00208"></a><span class="lineno"> 208</span>&#160; <span class="comment">// Supply constraints</span></div>
<div class="line"><a name="l00209"></a><span class="lineno"> 209</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> facility = 0; facility &lt; num_facilities; ++facility) {</div>
<div class="line"><a name="l00210"></a><span class="lineno"> 210</span>&#160; LinearExpression linear_expression;</div>
<div class="line"><a name="l00211"></a><span class="lineno"> 211</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>&amp; edge : network.edges_incident_to_facility(facility)) {</div>
<div class="line"><a name="l00212"></a><span class="lineno"> 212</span>&#160; linear_expression += x.at(edge);</div>
<div class="line"><a name="l00213"></a><span class="lineno"> 213</span>&#160; }</div>
<div class="line"><a name="l00214"></a><span class="lineno"> 214</span>&#160; <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.AddLinearConstraint(linear_expression &lt;= z[facility]);</div>
<div class="line"><a name="l00215"></a><span class="lineno"> 215</span>&#160; }</div>
<div class="line"><a name="l00216"></a><span class="lineno"> 216</span>&#160; </div>
<div class="line"><a name="l00217"></a><span class="lineno"> 217</span>&#160; <span class="comment">// Arc constraints</span></div>
<div class="line"><a name="l00218"></a><span class="lineno"> 218</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> facility = 0; facility &lt; num_facilities; ++facility) {</div>
<div class="line"><a name="l00219"></a><span class="lineno"> 219</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>&amp; edge : network.edges_incident_to_facility(facility)) {</div>
<div class="line"><a name="l00220"></a><span class="lineno"> 220</span>&#160; <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.AddLinearConstraint(x.at(edge) &lt;= location_fraction * z[facility]);</div>
<div class="line"><a name="l00221"></a><span class="lineno"> 221</span>&#160; }</div>
<div class="line"><a name="l00222"></a><span class="lineno"> 222</span>&#160; }</div>
<div class="line"><a name="l00223"></a><span class="lineno"> 223</span>&#160; <span class="keyword">const</span> Result result = <a class="code" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.Solve(SolveParametersProto()).value();</div>
<div class="line"><a name="l00224"></a><span class="lineno"> 224</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>&amp; warning : result.warnings) {</div>
<div class="line"><a name="l00225"></a><span class="lineno"> 225</span>&#160; <a class="code" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code" href="log__severity_8h.html#a50e5762f38854b37ee3e2851bc1bb0e7">WARNING</a>) &lt;&lt; <span class="stringliteral">&quot;Solver warning: &quot;</span> &lt;&lt; warning &lt;&lt; std::endl;</div>
<div class="line"><a name="l00226"></a><span class="lineno"> 226</span>&#160; }</div>
<div class="line"><a name="l00227"></a><span class="lineno"> 227</span>&#160; <a class="code" href="base_2logging_8h.html#acdd435d10e595c91b6861a233b8e8432">QCHECK_EQ</a>(result.termination_reason, <a class="code" href="namespaceoperations__research_1_1data_1_1vbp.html#a4604191fbd84a43686f44c25d7bd0161a2579881e7c83261bc21bafb5a5c92cad">SolveResultProto::OPTIMAL</a>)</div>
<div class="line"><a name="l00228"></a><span class="lineno"> 228</span>&#160; &lt;&lt; <span class="stringliteral">&quot;Failed to find an optimal solution: &quot;</span> &lt;&lt; result.termination_detail;</div>
<div class="line"><a name="l00229"></a><span class="lineno"> 229</span>&#160; std::cout &lt;&lt; <span class="stringliteral">&quot;Full problem optimal objective: &quot;</span></div>
<div class="line"><a name="l00230"></a><span class="lineno"> 230</span>&#160; &lt;&lt; absl::StrFormat(<span class="stringliteral">&quot;%.9f&quot;</span>, result.objective_value()) &lt;&lt; std::endl;</div>
<div class="line"><a name="l00231"></a><span class="lineno"> 231</span>&#160;}</div>
<div class="line"><a name="l00232"></a><span class="lineno"> 232</span>&#160; </div>
<div class="line"><a name="l00233"></a><span class="lineno"> 233</span>&#160;<span class="keywordtype">void</span> Benders(<span class="keyword">const</span> Network network, <span class="keyword">const</span> <span class="keywordtype">double</span> location_demand,</div>
<div class="line"><a name="l00234"></a><span class="lineno"> 234</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span> facility_cost, <span class="keyword">const</span> <span class="keywordtype">double</span> location_fraction,</div>
<div class="line"><a name="l00235"></a><span class="lineno"> 235</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span> target_precission,</div>
<div class="line"><a name="l00236"></a><span class="lineno"> 236</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> maximum_iterations = 30000) {</div>
<div class="line"><a name="l00237"></a><span class="lineno"> 237</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> num_facilities = network.num_facilities();</div>
<div class="line"><a name="l00238"></a><span class="lineno"> 238</span>&#160; <span class="keyword">const</span> <span class="keywordtype">int</span> num_locations = network.num_locations();</div>
<div class="line"><a name="l00239"></a><span class="lineno"> 239</span>&#160; </div>
<div class="line"><a name="l00240"></a><span class="lineno"> 240</span>&#160; <span class="comment">// Setup first stage model.</span></div>
<div class="line"><a name="l00241"></a><span class="lineno"> 241</span>&#160; <span class="comment">//</span></div>
<div class="line"><a name="l00242"></a><span class="lineno"> 242</span>&#160; <span class="comment">// min c * sum(z_f : f in F) + w</span></div>
<div class="line"><a name="l00243"></a><span class="lineno"> 243</span>&#160; <span class="comment">// s.t.</span></div>
<div class="line"><a name="l00244"></a><span class="lineno"> 244</span>&#160; <span class="comment">// z_f &gt;= 0 for all f in F</span></div>
<div class="line"><a name="l00245"></a><span class="lineno"> 245</span>&#160; <span class="comment">// sum(fcut_f^i z_f) + fcut_const^i &lt;= 0 for i = 1,...</span></div>
<div class="line"><a name="l00246"></a><span class="lineno"> 246</span>&#160; <span class="comment">// sum(ocut_f^j z_f) + ocut_const^j &lt;= w for j = 1,...</span></div>
<div class="line"><a name="l00247"></a><span class="lineno"> 247</span>&#160; MathOpt first_stage_model(operations_research::math_opt::SOLVER_TYPE_GUROBI,</div>
<div class="line"><a name="l00248"></a><span class="lineno"> 248</span>&#160; <span class="stringliteral">&quot;First stage problem&quot;</span>);</div>
<div class="line"><a name="l00249"></a><span class="lineno"> 249</span>&#160; std::vector&lt;Variable&gt; z;</div>
<div class="line"><a name="l00250"></a><span class="lineno"> 250</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> j = 0; j &lt; num_facilities; j++) {</div>
<div class="line"><a name="l00251"></a><span class="lineno"> 251</span>&#160; z.push_back(first_stage_model.AddContinuousVariable(0.0, <a class="code" href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">kInf</a>));</div>
<div class="line"><a name="l00252"></a><span class="lineno"> 252</span>&#160; }</div>
<div class="line"><a name="l00253"></a><span class="lineno"> 253</span>&#160; </div>
<div class="line"><a name="l00254"></a><span class="lineno"> 254</span>&#160; <span class="keyword">const</span> Variable w = first_stage_model.AddContinuousVariable(0.0, <a class="code" href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">kInf</a>);</div>
<div class="line"><a name="l00255"></a><span class="lineno"> 255</span>&#160; </div>
<div class="line"><a name="l00256"></a><span class="lineno"> 256</span>&#160; first_stage_model.objective().Minimize(facility_cost * <a class="code" href="namespaceoperations__research_1_1math__opt.html#a2d3e7a73de1ae32066be431b5e68f613">Sum</a>(z) + w);</div>
<div class="line"><a name="l00257"></a><span class="lineno"> 257</span>&#160; </div>
<div class="line"><a name="l00258"></a><span class="lineno"> 258</span>&#160; SolveParametersProto first_stage_params;</div>
<div class="line"><a name="l00259"></a><span class="lineno"> 259</span>&#160; first_stage_params.mutable_common_parameters()-&gt;set_enable_output(<span class="keyword">false</span>);</div>
<div class="line"><a name="l00260"></a><span class="lineno"> 260</span>&#160; </div>
<div class="line"><a name="l00261"></a><span class="lineno"> 261</span>&#160; <span class="comment">// Setup second stage model.</span></div>
<div class="line"><a name="l00262"></a><span class="lineno"> 262</span>&#160; <span class="comment">// min sum(h_e * x_e : e in E)</span></div>
<div class="line"><a name="l00263"></a><span class="lineno"> 263</span>&#160; <span class="comment">// s.t.</span></div>
<div class="line"><a name="l00264"></a><span class="lineno"> 264</span>&#160; <span class="comment">// x_(f,l) &lt;= a * zz_f for all (f,l) in E</span></div>
<div class="line"><a name="l00265"></a><span class="lineno"> 265</span>&#160; <span class="comment">// sum(x_(f,l) : l such that (f,l) in E) &lt;= zz_f for all f in F</span></div>
<div class="line"><a name="l00266"></a><span class="lineno"> 266</span>&#160; <span class="comment">// sum(x_(f,l) : f such that (f,l) in E) &gt;= d for all l in L</span></div>
<div class="line"><a name="l00267"></a><span class="lineno"> 267</span>&#160; <span class="comment">// x_e &gt;= 0 for all e in E</span></div>
<div class="line"><a name="l00268"></a><span class="lineno"> 268</span>&#160; <span class="comment">//</span></div>
<div class="line"><a name="l00269"></a><span class="lineno"> 269</span>&#160; <span class="comment">// where zz_f are fixed values for z_f from the first stage model.</span></div>
<div class="line"><a name="l00270"></a><span class="lineno"> 270</span>&#160; MathOpt second_stage_model(operations_research::math_opt::SOLVER_TYPE_GUROBI,</div>
<div class="line"><a name="l00271"></a><span class="lineno"> 271</span>&#160; <span class="stringliteral">&quot;Second stage model&quot;</span>);</div>
<div class="line"><a name="l00272"></a><span class="lineno"> 272</span>&#160; <span class="keyword">const</span> Objective second_stage_objective = second_stage_model.objective();</div>
<div class="line"><a name="l00273"></a><span class="lineno"> 273</span>&#160; second_stage_objective.set_minimize();</div>
<div class="line"><a name="l00274"></a><span class="lineno"> 274</span>&#160; absl::flat_hash_map&lt;Edge, Variable&gt; x;</div>
<div class="line"><a name="l00275"></a><span class="lineno"> 275</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>&amp; edge : network.edges()) {</div>
<div class="line"><a name="l00276"></a><span class="lineno"> 276</span>&#160; <span class="keyword">const</span> Variable x_edge = second_stage_model.AddContinuousVariable(0.0, <a class="code" href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">kInf</a>);</div>
<div class="line"><a name="l00277"></a><span class="lineno"> 277</span>&#160; x.insert({edge, x_edge});</div>
<div class="line"><a name="l00278"></a><span class="lineno"> 278</span>&#160; second_stage_objective.set_linear_coefficient(x_edge,</div>
<div class="line"><a name="l00279"></a><span class="lineno"> 279</span>&#160; network.edge_cost(edge));</div>
<div class="line"><a name="l00280"></a><span class="lineno"> 280</span>&#160; }</div>
<div class="line"><a name="l00281"></a><span class="lineno"> 281</span>&#160; std::vector&lt;LinearConstraint&gt; demand_constraints;</div>
<div class="line"><a name="l00282"></a><span class="lineno"> 282</span>&#160; </div>
<div class="line"><a name="l00283"></a><span class="lineno"> 283</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> location = 0; location &lt; num_locations; ++location) {</div>
<div class="line"><a name="l00284"></a><span class="lineno"> 284</span>&#160; LinearExpression linear_expression;</div>
<div class="line"><a name="l00285"></a><span class="lineno"> 285</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>&amp; edge : network.edges_incident_to_location(location)) {</div>
<div class="line"><a name="l00286"></a><span class="lineno"> 286</span>&#160; linear_expression += x.at(edge);</div>
<div class="line"><a name="l00287"></a><span class="lineno"> 287</span>&#160; }</div>
<div class="line"><a name="l00288"></a><span class="lineno"> 288</span>&#160; demand_constraints.push_back(second_stage_model.AddLinearConstraint(</div>
<div class="line"><a name="l00289"></a><span class="lineno"> 289</span>&#160; linear_expression &gt;= location_demand));</div>
<div class="line"><a name="l00290"></a><span class="lineno"> 290</span>&#160; }</div>
<div class="line"><a name="l00291"></a><span class="lineno"> 291</span>&#160; std::vector&lt;LinearConstraint&gt; supply_constraints;</div>
<div class="line"><a name="l00292"></a><span class="lineno"> 292</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> facility = 0; facility &lt; num_facilities; ++facility) {</div>
<div class="line"><a name="l00293"></a><span class="lineno"> 293</span>&#160; LinearExpression linear_expression;</div>
<div class="line"><a name="l00294"></a><span class="lineno"> 294</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>&amp; edge : network.edges_incident_to_facility(facility)) {</div>
<div class="line"><a name="l00295"></a><span class="lineno"> 295</span>&#160; linear_expression += x.at(edge);</div>
<div class="line"><a name="l00296"></a><span class="lineno"> 296</span>&#160; }</div>
<div class="line"><a name="l00297"></a><span class="lineno"> 297</span>&#160; supply_constraints.push_back(</div>
<div class="line"><a name="l00298"></a><span class="lineno"> 298</span>&#160; second_stage_model.AddLinearConstraint(linear_expression &lt;= <a class="code" href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">kInf</a>));</div>
<div class="line"><a name="l00299"></a><span class="lineno"> 299</span>&#160; }</div>
<div class="line"><a name="l00300"></a><span class="lineno"> 300</span>&#160; </div>
<div class="line"><a name="l00301"></a><span class="lineno"> 301</span>&#160; SolveParametersProto second_stage_params;</div>
<div class="line"><a name="l00302"></a><span class="lineno"> 302</span>&#160; second_stage_params.mutable_common_parameters()-&gt;set_enable_output(<span class="keyword">false</span>);</div>
<div class="line"><a name="l00303"></a><span class="lineno"> 303</span>&#160; GurobiParametersProto::Parameter* param1 =</div>
<div class="line"><a name="l00304"></a><span class="lineno"> 304</span>&#160; second_stage_params.mutable_gurobi_parameters()-&gt;add_parameters();</div>
<div class="line"><a name="l00305"></a><span class="lineno"> 305</span>&#160; param1-&gt;set_name(<span class="stringliteral">&quot;InfUnbdInfo&quot;</span>);</div>
<div class="line"><a name="l00306"></a><span class="lineno"> 306</span>&#160; param1-&gt;set_value(<span class="stringliteral">&quot;1&quot;</span>);</div>
<div class="line"><a name="l00307"></a><span class="lineno"> 307</span>&#160; </div>
<div class="line"><a name="l00308"></a><span class="lineno"> 308</span>&#160; <span class="comment">// Start Benders</span></div>
<div class="line"><a name="l00309"></a><span class="lineno"> 309</span>&#160; <span class="keywordtype">int</span> iteration = 0;</div>
<div class="line"><a name="l00310"></a><span class="lineno"> 310</span>&#160; <span class="keywordtype">double</span> best_upper_bound = <a class="code" href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">kInf</a>;</div>
<div class="line"><a name="l00311"></a><span class="lineno"> 311</span>&#160; <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
<div class="line"><a name="l00312"></a><span class="lineno"> 312</span>&#160; <a class="code" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code" href="log__severity_8h.html#ab4a2cbab234914b320b7fae11b6e8cb9">INFO</a>) &lt;&lt; <span class="stringliteral">&quot;Iteration: &quot;</span> &lt;&lt; iteration;</div>
<div class="line"><a name="l00313"></a><span class="lineno"> 313</span>&#160; <span class="comment">// Solve and process first stage.</span></div>
<div class="line"><a name="l00314"></a><span class="lineno"> 314</span>&#160; <span class="keyword">const</span> Result first_stage_result =</div>
<div class="line"><a name="l00315"></a><span class="lineno"> 315</span>&#160; first_stage_model.Solve(first_stage_params).value();</div>
<div class="line"><a name="l00316"></a><span class="lineno"> 316</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>&amp; warning : first_stage_result.warnings) {</div>
<div class="line"><a name="l00317"></a><span class="lineno"> 317</span>&#160; <a class="code" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code" href="log__severity_8h.html#a50e5762f38854b37ee3e2851bc1bb0e7">WARNING</a>) &lt;&lt; <span class="stringliteral">&quot;Solver warning: &quot;</span> &lt;&lt; warning &lt;&lt; std::endl;</div>
<div class="line"><a name="l00318"></a><span class="lineno"> 318</span>&#160; }</div>
<div class="line"><a name="l00319"></a><span class="lineno"> 319</span>&#160; <a class="code" href="base_2logging_8h.html#acdd435d10e595c91b6861a233b8e8432">QCHECK_EQ</a>(first_stage_result.termination_reason, <a class="code" href="namespaceoperations__research_1_1data_1_1vbp.html#a4604191fbd84a43686f44c25d7bd0161a2579881e7c83261bc21bafb5a5c92cad">SolveResultProto::OPTIMAL</a>);</div>
<div class="line"><a name="l00320"></a><span class="lineno"> 320</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span> <a class="code" href="gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a> = first_stage_result.objective_value();</div>
<div class="line"><a name="l00321"></a><span class="lineno"> 321</span>&#160; <a class="code" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code" href="log__severity_8h.html#ab4a2cbab234914b320b7fae11b6e8cb9">INFO</a>) &lt;&lt; <span class="stringliteral">&quot;LB = &quot;</span> &lt;&lt; <a class="code" href="gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a>;</div>
<div class="line"><a name="l00322"></a><span class="lineno"> 322</span>&#160; </div>
<div class="line"><a name="l00323"></a><span class="lineno"> 323</span>&#160; <span class="comment">// Setup second stage.</span></div>
<div class="line"><a name="l00324"></a><span class="lineno"> 324</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> facility = 0; facility &lt; num_facilities; ++facility) {</div>
<div class="line"><a name="l00325"></a><span class="lineno"> 325</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span> capacity_value =</div>
<div class="line"><a name="l00326"></a><span class="lineno"> 326</span>&#160; first_stage_result.variable_values().at(z[facility]);</div>
<div class="line"><a name="l00327"></a><span class="lineno"> 327</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>&amp; edge : network.edges_incident_to_facility(facility)) {</div>
<div class="line"><a name="l00328"></a><span class="lineno"> 328</span>&#160; x.at(edge).set_upper_bound(location_fraction * capacity_value);</div>
<div class="line"><a name="l00329"></a><span class="lineno"> 329</span>&#160; }</div>
<div class="line"><a name="l00330"></a><span class="lineno"> 330</span>&#160; supply_constraints[facility].set_upper_bound(capacity_value);</div>
<div class="line"><a name="l00331"></a><span class="lineno"> 331</span>&#160; }</div>
<div class="line"><a name="l00332"></a><span class="lineno"> 332</span>&#160; </div>
<div class="line"><a name="l00333"></a><span class="lineno"> 333</span>&#160; <span class="comment">// Solve and process second stage.</span></div>
<div class="line"><a name="l00334"></a><span class="lineno"> 334</span>&#160; <span class="keyword">const</span> Result second_stage_result =</div>
<div class="line"><a name="l00335"></a><span class="lineno"> 335</span>&#160; second_stage_model.Solve(second_stage_params).value();</div>
<div class="line"><a name="l00336"></a><span class="lineno"> 336</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>&amp; warning : second_stage_result.warnings) {</div>
<div class="line"><a name="l00337"></a><span class="lineno"> 337</span>&#160; <a class="code" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code" href="log__severity_8h.html#a50e5762f38854b37ee3e2851bc1bb0e7">WARNING</a>) &lt;&lt; <span class="stringliteral">&quot;Solver warning: &quot;</span> &lt;&lt; warning &lt;&lt; std::endl;</div>
<div class="line"><a name="l00338"></a><span class="lineno"> 338</span>&#160; }</div>
<div class="line"><a name="l00339"></a><span class="lineno"> 339</span>&#160; <span class="keywordflow">if</span> (second_stage_result.termination_reason ==</div>
<div class="line"><a name="l00340"></a><span class="lineno"> 340</span>&#160; <a class="code" href="namespaceoperations__research_1_1data_1_1vbp.html#a4604191fbd84a43686f44c25d7bd0161a2884fa43446c0cbc9c7a9b74d41d7483">SolveResultProto::INFEASIBLE</a>) {</div>
<div class="line"><a name="l00341"></a><span class="lineno"> 341</span>&#160; <span class="comment">// If the second stage problem is infeasible we will get a dual ray</span></div>
<div class="line"><a name="l00342"></a><span class="lineno"> 342</span>&#160; <span class="comment">// (r, y) such that</span></div>
<div class="line"><a name="l00343"></a><span class="lineno"> 343</span>&#160; <span class="comment">//</span></div>
<div class="line"><a name="l00344"></a><span class="lineno"> 344</span>&#160; <span class="comment">// sum(r_(f,l)*a*zz_f : (f,l) in E, r_(f,l) &lt; 0)</span></div>
<div class="line"><a name="l00345"></a><span class="lineno"> 345</span>&#160; <span class="comment">// + sum(y_f*zz_f : f in F, y_f &lt; 0)</span></div>
<div class="line"><a name="l00346"></a><span class="lineno"> 346</span>&#160; <span class="comment">// + sum(y_l*d : l in L, y_l &gt; 0) &gt; 0.</span></div>
<div class="line"><a name="l00347"></a><span class="lineno"> 347</span>&#160; <span class="comment">//</span></div>
<div class="line"><a name="l00348"></a><span class="lineno"> 348</span>&#160; <span class="comment">// Then we get the feasibility cut (go/mathopt-advanced-dual-use#benders)</span></div>
<div class="line"><a name="l00349"></a><span class="lineno"> 349</span>&#160; <span class="comment">//</span></div>
<div class="line"><a name="l00350"></a><span class="lineno"> 350</span>&#160; <span class="comment">// sum(fcut_f*z_f) + fcut_const &lt;= 0,</span></div>
<div class="line"><a name="l00351"></a><span class="lineno"> 351</span>&#160; <span class="comment">//</span></div>
<div class="line"><a name="l00352"></a><span class="lineno"> 352</span>&#160; <span class="comment">// where</span></div>
<div class="line"><a name="l00353"></a><span class="lineno"> 353</span>&#160; <span class="comment">//</span></div>
<div class="line"><a name="l00354"></a><span class="lineno"> 354</span>&#160; <span class="comment">// fcut_f = sum(r_(f,l)*a : (f,l) in E, r_(f,l) &lt; 0)</span></div>
<div class="line"><a name="l00355"></a><span class="lineno"> 355</span>&#160; <span class="comment">// + min{y_f, 0}</span></div>
<div class="line"><a name="l00356"></a><span class="lineno"> 356</span>&#160; <span class="comment">// fcut_const = sum*(y_l*d : l in L, y_l &gt; 0)</span></div>
<div class="line"><a name="l00357"></a><span class="lineno"> 357</span>&#160; <a class="code" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code" href="log__severity_8h.html#ab4a2cbab234914b320b7fae11b6e8cb9">INFO</a>) &lt;&lt; <span class="stringliteral">&quot;Adding feasibility cut...&quot;</span>;</div>
<div class="line"><a name="l00358"></a><span class="lineno"> 358</span>&#160; LinearExpression feasibility_cut_expression;</div>
<div class="line"><a name="l00359"></a><span class="lineno"> 359</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> facility = 0; facility &lt; num_facilities; ++facility) {</div>
<div class="line"><a name="l00360"></a><span class="lineno"> 360</span>&#160; <span class="keywordtype">double</span> <a class="code" href="routing__filters_8cc.html#a8e4ee19dee0e00541dbe9bbc83d806ba">coefficient</a> = 0.0;</div>
<div class="line"><a name="l00361"></a><span class="lineno"> 361</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>&amp; edge : network.edges_incident_to_facility(facility)) {</div>
<div class="line"><a name="l00362"></a><span class="lineno"> 362</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span> reduced_cost =</div>
<div class="line"><a name="l00363"></a><span class="lineno"> 363</span>&#160; second_stage_result.ray_reduced_costs().at(x.at(edge));</div>
<div class="line"><a name="l00364"></a><span class="lineno"> 364</span>&#160; <span class="keywordflow">if</span> (reduced_cost &lt; 0) {</div>
<div class="line"><a name="l00365"></a><span class="lineno"> 365</span>&#160; <a class="code" href="routing__filters_8cc.html#a8e4ee19dee0e00541dbe9bbc83d806ba">coefficient</a> += location_fraction * reduced_cost;</div>
<div class="line"><a name="l00366"></a><span class="lineno"> 366</span>&#160; }</div>
<div class="line"><a name="l00367"></a><span class="lineno"> 367</span>&#160; }</div>
<div class="line"><a name="l00368"></a><span class="lineno"> 368</span>&#160; <span class="keywordtype">double</span> dual_value = second_stage_result.ray_dual_values().at(</div>
<div class="line"><a name="l00369"></a><span class="lineno"> 369</span>&#160; supply_constraints[facility]);</div>
<div class="line"><a name="l00370"></a><span class="lineno"> 370</span>&#160; <a class="code" href="routing__filters_8cc.html#a8e4ee19dee0e00541dbe9bbc83d806ba">coefficient</a> += <a class="code" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(dual_value, 0.0);</div>
<div class="line"><a name="l00371"></a><span class="lineno"> 371</span>&#160; feasibility_cut_expression += <a class="code" href="routing__filters_8cc.html#a8e4ee19dee0e00541dbe9bbc83d806ba">coefficient</a> * z[facility];</div>
<div class="line"><a name="l00372"></a><span class="lineno"> 372</span>&#160; }</div>
<div class="line"><a name="l00373"></a><span class="lineno"> 373</span>&#160; <span class="keywordtype">double</span> constant = 0.0;</div>
<div class="line"><a name="l00374"></a><span class="lineno"> 374</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>&amp; constraint : demand_constraints) {</div>
<div class="line"><a name="l00375"></a><span class="lineno"> 375</span>&#160; <span class="keywordtype">double</span> dual_value =</div>
<div class="line"><a name="l00376"></a><span class="lineno"> 376</span>&#160; second_stage_result.ray_dual_values().at(constraint);</div>
<div class="line"><a name="l00377"></a><span class="lineno"> 377</span>&#160; <span class="keywordflow">if</span> (dual_value &gt; 0) {</div>
<div class="line"><a name="l00378"></a><span class="lineno"> 378</span>&#160; constant += dual_value;</div>
<div class="line"><a name="l00379"></a><span class="lineno"> 379</span>&#160; }</div>
<div class="line"><a name="l00380"></a><span class="lineno"> 380</span>&#160; }</div>
<div class="line"><a name="l00381"></a><span class="lineno"> 381</span>&#160; first_stage_model.AddLinearConstraint(</div>
<div class="line"><a name="l00382"></a><span class="lineno"> 382</span>&#160; feasibility_cut_expression + constant &lt;= 0.0);</div>
<div class="line"><a name="l00383"></a><span class="lineno"> 383</span>&#160; } <span class="keywordflow">else</span> {</div>
<div class="line"><a name="l00384"></a><span class="lineno"> 384</span>&#160; <span class="comment">// If the second stage problem is optimal we will get a dual solution</span></div>
<div class="line"><a name="l00385"></a><span class="lineno"> 385</span>&#160; <span class="comment">// (r, y) such that the optimal objective value is equal to</span></div>
<div class="line"><a name="l00386"></a><span class="lineno"> 386</span>&#160; <span class="comment">//</span></div>
<div class="line"><a name="l00387"></a><span class="lineno"> 387</span>&#160; <span class="comment">// sum(r_(f,l)*a*zz_f : (f,l) in E, r_(f,l) &lt; 0)</span></div>
<div class="line"><a name="l00388"></a><span class="lineno"> 388</span>&#160; <span class="comment">// + sum(y_f*zz_f : f in F, y_f &lt; 0)</span></div>
<div class="line"><a name="l00389"></a><span class="lineno"> 389</span>&#160; <span class="comment">// + sum*(y_l*d : l in L, y_l &gt; 0) &gt; 0.</span></div>
<div class="line"><a name="l00390"></a><span class="lineno"> 390</span>&#160; <span class="comment">//</span></div>
<div class="line"><a name="l00391"></a><span class="lineno"> 391</span>&#160; <span class="comment">// Then we get the optimality cut (go/mathopt-advanced-dual-use#benders)</span></div>
<div class="line"><a name="l00392"></a><span class="lineno"> 392</span>&#160; <span class="comment">//</span></div>
<div class="line"><a name="l00393"></a><span class="lineno"> 393</span>&#160; <span class="comment">// sum(ocut_f*z_f) + ocut_const &lt;= w,</span></div>
<div class="line"><a name="l00394"></a><span class="lineno"> 394</span>&#160; <span class="comment">//</span></div>
<div class="line"><a name="l00395"></a><span class="lineno"> 395</span>&#160; <span class="comment">// where</span></div>
<div class="line"><a name="l00396"></a><span class="lineno"> 396</span>&#160; <span class="comment">//</span></div>
<div class="line"><a name="l00397"></a><span class="lineno"> 397</span>&#160; <span class="comment">// ocut_f = sum(r_(f,l)*a : (f,l) in E, r_(f,l) &lt; 0)</span></div>
<div class="line"><a name="l00398"></a><span class="lineno"> 398</span>&#160; <span class="comment">// + min{y_f, 0}</span></div>
<div class="line"><a name="l00399"></a><span class="lineno"> 399</span>&#160; <span class="comment">// ocut_const = sum*(y_l*d : l in L, y_l &gt; 0)</span></div>
<div class="line"><a name="l00400"></a><span class="lineno"> 400</span>&#160; <a class="code" href="base_2logging_8h.html#acdd435d10e595c91b6861a233b8e8432">QCHECK_EQ</a>(second_stage_result.termination_reason,</div>
<div class="line"><a name="l00401"></a><span class="lineno"> 401</span>&#160; <a class="code" href="namespaceoperations__research_1_1data_1_1vbp.html#a4604191fbd84a43686f44c25d7bd0161a2579881e7c83261bc21bafb5a5c92cad">SolveResultProto::OPTIMAL</a>);</div>
<div class="line"><a name="l00402"></a><span class="lineno"> 402</span>&#160; <a class="code" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code" href="log__severity_8h.html#ab4a2cbab234914b320b7fae11b6e8cb9">INFO</a>) &lt;&lt; <span class="stringliteral">&quot;Adding optimality cut...&quot;</span>;</div>
<div class="line"><a name="l00403"></a><span class="lineno"> 403</span>&#160; LinearExpression optimality_cut_expression;</div>
<div class="line"><a name="l00404"></a><span class="lineno"> 404</span>&#160; <span class="keywordtype">double</span> <a class="code" href="gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35">upper_bound</a> = 0.0;</div>
<div class="line"><a name="l00405"></a><span class="lineno"> 405</span>&#160; <span class="keywordflow">for</span> (<span class="keywordtype">int</span> facility = 0; facility &lt; num_facilities; ++facility) {</div>
<div class="line"><a name="l00406"></a><span class="lineno"> 406</span>&#160; <span class="keywordtype">double</span> <a class="code" href="routing__filters_8cc.html#a8e4ee19dee0e00541dbe9bbc83d806ba">coefficient</a> = 0.0;</div>
<div class="line"><a name="l00407"></a><span class="lineno"> 407</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>&amp; edge : network.edges_incident_to_facility(facility)) {</div>
<div class="line"><a name="l00408"></a><span class="lineno"> 408</span>&#160; <a class="code" href="gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35">upper_bound</a> += network.edge_cost(edge) *</div>
<div class="line"><a name="l00409"></a><span class="lineno"> 409</span>&#160; second_stage_result.variable_values().at(x.at(edge));</div>
<div class="line"><a name="l00410"></a><span class="lineno"> 410</span>&#160; <span class="keyword">const</span> <span class="keywordtype">double</span> reduced_cost =</div>
<div class="line"><a name="l00411"></a><span class="lineno"> 411</span>&#160; second_stage_result.reduced_costs().at(x.at(edge));</div>
<div class="line"><a name="l00412"></a><span class="lineno"> 412</span>&#160; <span class="keywordflow">if</span> (reduced_cost &lt; 0) {</div>
<div class="line"><a name="l00413"></a><span class="lineno"> 413</span>&#160; <a class="code" href="routing__filters_8cc.html#a8e4ee19dee0e00541dbe9bbc83d806ba">coefficient</a> += location_fraction * reduced_cost;</div>
<div class="line"><a name="l00414"></a><span class="lineno"> 414</span>&#160; }</div>
<div class="line"><a name="l00415"></a><span class="lineno"> 415</span>&#160; }</div>
<div class="line"><a name="l00416"></a><span class="lineno"> 416</span>&#160; <span class="keywordtype">double</span> dual_value =</div>
<div class="line"><a name="l00417"></a><span class="lineno"> 417</span>&#160; second_stage_result.dual_values().at(supply_constraints[facility]);</div>
<div class="line"><a name="l00418"></a><span class="lineno"> 418</span>&#160; <a class="code" href="routing__filters_8cc.html#a8e4ee19dee0e00541dbe9bbc83d806ba">coefficient</a> += <a class="code" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(dual_value, 0.0);</div>
<div class="line"><a name="l00419"></a><span class="lineno"> 419</span>&#160; optimality_cut_expression += <a class="code" href="routing__filters_8cc.html#a8e4ee19dee0e00541dbe9bbc83d806ba">coefficient</a> * z[facility];</div>
<div class="line"><a name="l00420"></a><span class="lineno"> 420</span>&#160; }</div>
<div class="line"><a name="l00421"></a><span class="lineno"> 421</span>&#160; <span class="keywordtype">double</span> constant = 0.0;</div>
<div class="line"><a name="l00422"></a><span class="lineno"> 422</span>&#160; <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>&amp; constraint : demand_constraints) {</div>
<div class="line"><a name="l00423"></a><span class="lineno"> 423</span>&#160; <span class="keywordtype">double</span> dual_value = second_stage_result.dual_values().at(constraint);</div>
<div class="line"><a name="l00424"></a><span class="lineno"> 424</span>&#160; <span class="keywordflow">if</span> (dual_value &gt; 0) {</div>
<div class="line"><a name="l00425"></a><span class="lineno"> 425</span>&#160; constant += dual_value;</div>
<div class="line"><a name="l00426"></a><span class="lineno"> 426</span>&#160; }</div>
<div class="line"><a name="l00427"></a><span class="lineno"> 427</span>&#160; }</div>
<div class="line"><a name="l00428"></a><span class="lineno"> 428</span>&#160; <span class="comment">// Add first stage contribution to upper bound = facility_cost * Sum(z)</span></div>
<div class="line"><a name="l00429"></a><span class="lineno"> 429</span>&#160; <a class="code" href="gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35">upper_bound</a> += first_stage_result.objective_value() -</div>
<div class="line"><a name="l00430"></a><span class="lineno"> 430</span>&#160; first_stage_result.variable_values().at(w);</div>
<div class="line"><a name="l00431"></a><span class="lineno"> 431</span>&#160; best_upper_bound = <a class="code" href="alldiff__cst_8cc.html#ad10edae0a852d72fb76afb1c77735045">std::min</a>(best_upper_bound, <a class="code" href="gscip__solver_8cc.html#a1ba5ca0f61f2fa13bd23bf0f89004f35">upper_bound</a>);</div>
<div class="line"><a name="l00432"></a><span class="lineno"> 432</span>&#160; </div>
<div class="line"><a name="l00433"></a><span class="lineno"> 433</span>&#160; first_stage_model.AddLinearConstraint(</div>
<div class="line"><a name="l00434"></a><span class="lineno"> 434</span>&#160; optimality_cut_expression + constant &lt;= w);</div>
<div class="line"><a name="l00435"></a><span class="lineno"> 435</span>&#160; }</div>
<div class="line"><a name="l00436"></a><span class="lineno"> 436</span>&#160; <a class="code" href="base_2logging_8h.html#accad43a85d781d53381cd53a9894b6ae">LOG</a>(<a class="code" href="log__severity_8h.html#ab4a2cbab234914b320b7fae11b6e8cb9">INFO</a>) &lt;&lt; <span class="stringliteral">&quot;UB = &quot;</span> &lt;&lt; best_upper_bound;</div>
<div class="line"><a name="l00437"></a><span class="lineno"> 437</span>&#160; ++iteration;</div>
<div class="line"><a name="l00438"></a><span class="lineno"> 438</span>&#160; <span class="keywordflow">if</span> (best_upper_bound - <a class="code" href="gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a> &lt; target_precission) {</div>
<div class="line"><a name="l00439"></a><span class="lineno"> 439</span>&#160; std::cout &lt;&lt; <span class="stringliteral">&quot;Total iterations = &quot;</span> &lt;&lt; iteration &lt;&lt; std::endl;</div>
<div class="line"><a name="l00440"></a><span class="lineno"> 440</span>&#160; std::cout &lt;&lt; <span class="stringliteral">&quot;Final LB = &quot;</span> &lt;&lt; absl::StrFormat(<span class="stringliteral">&quot;%.9f&quot;</span>, <a class="code" href="gscip__solver_8cc.html#a1e2f9a2352c1d9a6cada9544898fceec">lower_bound</a>)</div>
<div class="line"><a name="l00441"></a><span class="lineno"> 441</span>&#160; &lt;&lt; std::endl;</div>
<div class="line"><a name="l00442"></a><span class="lineno"> 442</span>&#160; std::cout &lt;&lt; <span class="stringliteral">&quot;Final UB = &quot;</span> &lt;&lt; absl::StrFormat(<span class="stringliteral">&quot;%.9f&quot;</span>, best_upper_bound)</div>
<div class="line"><a name="l00443"></a><span class="lineno"> 443</span>&#160; &lt;&lt; std::endl;</div>
<div class="line"><a name="l00444"></a><span class="lineno"> 444</span>&#160; <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00445"></a><span class="lineno"> 445</span>&#160; }</div>
<div class="line"><a name="l00446"></a><span class="lineno"> 446</span>&#160; <span class="keywordflow">if</span> (iteration &gt; maximum_iterations) {</div>
<div class="line"><a name="l00447"></a><span class="lineno"> 447</span>&#160; <span class="keywordflow">break</span>;</div>
<div class="line"><a name="l00448"></a><span class="lineno"> 448</span>&#160; }</div>
<div class="line"><a name="l00449"></a><span class="lineno"> 449</span>&#160; }</div>
<div class="line"><a name="l00450"></a><span class="lineno"> 450</span>&#160;}</div>
<div class="line"><a name="l00451"></a><span class="lineno"> 451</span>&#160; </div>
<div class="line"><a name="l00452"></a><span class="lineno"> 452</span>&#160;} <span class="comment">// namespace</span></div>
<div class="line"><a name="l00453"></a><span class="lineno"> 453</span>&#160; </div>
<div class="line"><a name="l00454"></a><span class="lineno"><a class="line" href="facility__lp__benders_8cc.html#a3c04138a5bfe5d72780bb7e82a18e627"> 454</a></span>&#160;<span class="keywordtype">int</span> <a class="code" href="facility__lp__benders_8cc.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a>(<span class="keywordtype">int</span> argc, <span class="keywordtype">char</span>** argv) {</div>
<div class="line"><a name="l00455"></a><span class="lineno"> 455</span>&#160; <a class="code" href="namespacegoogle.html#a1749056ff206ebc4f581e6bc0bae841d">google::InitGoogleLogging</a>(argv[0]);</div>
<div class="line"><a name="l00456"></a><span class="lineno"> 456</span>&#160;absl::ParseCommandLine(argc, argv);</div>
<div class="line"><a name="l00457"></a><span class="lineno"> 457</span>&#160; <span class="keyword">const</span> Network network(absl::GetFlag(FLAGS_num_facilities),</div>
<div class="line"><a name="l00458"></a><span class="lineno"> 458</span>&#160; absl::GetFlag(FLAGS_num_locations),</div>
<div class="line"><a name="l00459"></a><span class="lineno"> 459</span>&#160; absl::GetFlag(FLAGS_edge_probability));</div>
<div class="line"><a name="l00460"></a><span class="lineno"> 460</span>&#160; absl::Time start = absl::Now();</div>
<div class="line"><a name="l00461"></a><span class="lineno"> 461</span>&#160; FullProblem(network, absl::GetFlag(FLAGS_location_demand),</div>
<div class="line"><a name="l00462"></a><span class="lineno"> 462</span>&#160; absl::GetFlag(FLAGS_facility_cost),</div>
<div class="line"><a name="l00463"></a><span class="lineno"> 463</span>&#160; absl::GetFlag(FLAGS_location_fraction));</div>
<div class="line"><a name="l00464"></a><span class="lineno"> 464</span>&#160; std::cout &lt;&lt; <span class="stringliteral">&quot;Full solve time : &quot;</span> &lt;&lt; absl::Now() - start &lt;&lt; std::endl;</div>
<div class="line"><a name="l00465"></a><span class="lineno"> 465</span>&#160; start = absl::Now();</div>
<div class="line"><a name="l00466"></a><span class="lineno"> 466</span>&#160; Benders(network, absl::GetFlag(FLAGS_location_demand),</div>
<div class="line"><a name="l00467"></a><span class="lineno"> 467</span>&#160; absl::GetFlag(FLAGS_facility_cost),</div>
<div class="line"><a name="l00468"></a><span class="lineno"> 468</span>&#160; absl::GetFlag(FLAGS_location_fraction),</div>
<div class="line"><a name="l00469"></a><span class="lineno"> 469</span>&#160; absl::GetFlag(FLAGS_benders_precission));</div>
<div class="line"><a name="l00470"></a><span class="lineno"> 470</span>&#160; std::cout &lt;&lt; <span class="stringliteral">&quot;Benders solve time : &quot;</span> &lt;&lt; absl::Now() - start &lt;&lt; std::endl;</div>
<div class="line"><a name="l00471"></a><span class="lineno"> 471</span>&#160; <span class="keywordflow">return</span> 0;</div>
<div class="line"><a name="l00472"></a><span class="lineno"> 472</span>&#160;}</div>
<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>
<div class="ttc" id="abase_2logging_8h_html"><div class="ttname"><a href="base_2logging_8h.html">logging.h</a></div></div>
<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#l00423">base/logging.h:423</a></div></div>
<div class="ttc" id="abase_2logging_8h_html_acdd435d10e595c91b6861a233b8e8432"><div class="ttname"><a href="base_2logging_8h.html#acdd435d10e595c91b6861a233b8e8432">QCHECK_EQ</a></div><div class="ttdeci">#define QCHECK_EQ</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00040">base/logging.h:40</a></div></div>
<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#l00454">facility_lp_benders.cc:454</a></div></div>
<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, &quot;Number of facilities.&quot;)</div></div>
<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#l00126">gscip_solver.cc:126</a></div></div>
<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#l00125">gscip_solver.cc:125</a></div></div>
<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#l00273">gurobi_interface.cc:273</a></div></div>
<div class="ttc" id="alog__severity_8h_html_a50e5762f38854b37ee3e2851bc1bb0e7"><div class="ttname"><a href="log__severity_8h.html#a50e5762f38854b37ee3e2851bc1bb0e7">WARNING</a></div><div class="ttdeci">const int WARNING</div><div class="ttdef"><b>Definition:</b> <a href="log__severity_8h_source.html#l00031">log_severity.h:31</a></div></div>
<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>
<div class="ttc" id="amath__opt_8h_html"><div class="ttname"><a href="math__opt_8h.html">math_opt.h</a></div></div>
<div class="ttc" id="anamespacegoogle_html_a1749056ff206ebc4f581e6bc0bae841d"><div class="ttname"><a href="namespacegoogle.html#a1749056ff206ebc4f581e6bc0bae841d">google::InitGoogleLogging</a></div><div class="ttdeci">void InitGoogleLogging(const char *argv0)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8cc_source.html#l01873">base/logging.cc:1873</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1data_1_1vbp_html_a4604191fbd84a43686f44c25d7bd0161a2579881e7c83261bc21bafb5a5c92cad"><div class="ttname"><a href="namespaceoperations__research_1_1data_1_1vbp.html#a4604191fbd84a43686f44c25d7bd0161a2579881e7c83261bc21bafb5a5c92cad">operations_research::data::vbp::OPTIMAL</a></div><div class="ttdeci">@ OPTIMAL</div><div class="ttdef"><b>Definition:</b> <a href="vector__bin__packing_8pb_8h_source.html#l00088">vector_bin_packing.pb.h:88</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1data_1_1vbp_html_a4604191fbd84a43686f44c25d7bd0161a2884fa43446c0cbc9c7a9b74d41d7483"><div class="ttname"><a href="namespaceoperations__research_1_1data_1_1vbp.html#a4604191fbd84a43686f44c25d7bd0161a2884fa43446c0cbc9c7a9b74d41d7483">operations_research::data::vbp::INFEASIBLE</a></div><div class="ttdeci">@ INFEASIBLE</div><div class="ttdef"><b>Definition:</b> <a href="vector__bin__packing_8pb_8h_source.html#l00090">vector_bin_packing.pb.h:90</a></div></div>
<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 &amp;items)</div><div class="ttdef"><b>Definition:</b> <a href="variable__and__expressions_8h_source.html#l00929">variable_and_expressions.h:929</a></div></div>
<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="ids__validator_8cc_source.html#l00035">ids_validator.cc:35</a></div></div>
<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#l00985">routing_filters.cc:985</a></div></div>
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