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<a href="cutting__stock_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>
<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 &quot;License&quot;);</span></div>
<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>
<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>
<div class="line"><a id="l00005" name="l00005"></a><span class="lineno"> 5</span><span class="comment">//</span></div>
<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>
<div class="line"><a id="l00007" name="l00007"></a><span class="lineno"> 7</span><span class="comment">//</span></div>
<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>
<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 &quot;AS IS&quot; BASIS,</span></div>
<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>
<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>
<div class="line"><a id="l00012" name="l00012"></a><span class="lineno"> 12</span><span class="comment">// limitations under the License.</span></div>
<div class="line"><a id="l00013" name="l00013"></a><span class="lineno"> 13</span> </div>
<div class="line"><a id="l00014" name="l00014"></a><span class="lineno"> 14</span><span class="comment">// The Cutting Stock problem is as follows. You begin with unlimited boards, all</span></div>
<div class="line"><a id="l00015" name="l00015"></a><span class="lineno"> 15</span><span class="comment">// of the same length. You are also given a list of smaller pieces to cut out,</span></div>
<div class="line"><a id="l00016" name="l00016"></a><span class="lineno"> 16</span><span class="comment">// each with a length and a demanded quantity. You want to cut out all these</span></div>
<div class="line"><a id="l00017" name="l00017"></a><span class="lineno"> 17</span><span class="comment">// pieces using as few of your starting boards as possible.</span></div>
<div class="line"><a id="l00018" name="l00018"></a><span class="lineno"> 18</span><span class="comment">//</span></div>
<div class="line"><a id="l00019" name="l00019"></a><span class="lineno"> 19</span><span class="comment">// E.g. you begin with boards that are 20 feet long, and you must cut out 3</span></div>
<div class="line"><a id="l00020" name="l00020"></a><span class="lineno"> 20</span><span class="comment">// pieces that are 6 feet long and 5 pieces that are 8 feet long. An optimal</span></div>
<div class="line"><a id="l00021" name="l00021"></a><span class="lineno"> 21</span><span class="comment">// solution is:</span></div>
<div class="line"><a id="l00022" name="l00022"></a><span class="lineno"> 22</span><span class="comment">// [(6,), (8, 8) (8, 8), (6, 6, 8)]</span></div>
<div class="line"><a id="l00023" name="l00023"></a><span class="lineno"> 23</span><span class="comment">// (We cut a 6 foot piece from the first board, two 8 foot pieces from</span></div>
<div class="line"><a id="l00024" name="l00024"></a><span class="lineno"> 24</span><span class="comment">// the second board, and so on.)</span></div>
<div class="line"><a id="l00025" name="l00025"></a><span class="lineno"> 25</span><span class="comment">//</span></div>
<div class="line"><a id="l00026" name="l00026"></a><span class="lineno"> 26</span><span class="comment">// This example approximately solves the problem with a column generation</span></div>
<div class="line"><a id="l00027" name="l00027"></a><span class="lineno"> 27</span><span class="comment">// heuristic. The leader problem is a set cover problem, and the worker is a</span></div>
<div class="line"><a id="l00028" name="l00028"></a><span class="lineno"> 28</span><span class="comment">// knapsack problem. We alternate between solving the LP relaxation of the</span></div>
<div class="line"><a id="l00029" name="l00029"></a><span class="lineno"> 29</span><span class="comment">// leader incrementally, and solving the worker to generate new a configuration</span></div>
<div class="line"><a id="l00030" name="l00030"></a><span class="lineno"> 30</span><span class="comment">// (a column) for the leader. When the worker can no longer find a column</span></div>
<div class="line"><a id="l00031" name="l00031"></a><span class="lineno"> 31</span><span class="comment">// improving the LP cost, we convert the leader problem to a MIP and solve</span></div>
<div class="line"><a id="l00032" name="l00032"></a><span class="lineno"> 32</span><span class="comment">// again. We now give precise statements of the leader and worker.</span></div>
<div class="line"><a id="l00033" name="l00033"></a><span class="lineno"> 33</span><span class="comment">//</span></div>
<div class="line"><a id="l00034" name="l00034"></a><span class="lineno"> 34</span><span class="comment">// Problem data:</span></div>
<div class="line"><a id="l00035" name="l00035"></a><span class="lineno"> 35</span><span class="comment">// * l_i: the length of each piece we need to cut out.</span></div>
<div class="line"><a id="l00036" name="l00036"></a><span class="lineno"> 36</span><span class="comment">// * d_i: how many copies each piece we need.</span></div>
<div class="line"><a id="l00037" name="l00037"></a><span class="lineno"> 37</span><span class="comment">// * L: the length of our initial boards.</span></div>
<div class="line"><a id="l00038" name="l00038"></a><span class="lineno"> 38</span><span class="comment">// * q_ci: for configuration c, the quantity of piece i produced.</span></div>
<div class="line"><a id="l00039" name="l00039"></a><span class="lineno"> 39</span><span class="comment">//</span></div>
<div class="line"><a id="l00040" name="l00040"></a><span class="lineno"> 40</span><span class="comment">// Leader problem variables:</span></div>
<div class="line"><a id="l00041" name="l00041"></a><span class="lineno"> 41</span><span class="comment">// * x_c: how many copies of configuration c to produce.</span></div>
<div class="line"><a id="l00042" name="l00042"></a><span class="lineno"> 42</span><span class="comment">//</span></div>
<div class="line"><a id="l00043" name="l00043"></a><span class="lineno"> 43</span><span class="comment">// Leader problem formulation:</span></div>
<div class="line"><a id="l00044" name="l00044"></a><span class="lineno"> 44</span><span class="comment">// min sum_c x_c</span></div>
<div class="line"><a id="l00045" name="l00045"></a><span class="lineno"> 45</span><span class="comment">// s.t. sum_c q_ci * x_c = d_i for all i</span></div>
<div class="line"><a id="l00046" name="l00046"></a><span class="lineno"> 46</span><span class="comment">// x_c &gt;= 0, integer for all c.</span></div>
<div class="line"><a id="l00047" name="l00047"></a><span class="lineno"> 47</span><span class="comment">//</span></div>
<div class="line"><a id="l00048" name="l00048"></a><span class="lineno"> 48</span><span class="comment">// The worker problem is to generate new configurations for the leader problem</span></div>
<div class="line"><a id="l00049" name="l00049"></a><span class="lineno"> 49</span><span class="comment">// based on the dual variables of the demand constraints in the LP relaxation.</span></div>
<div class="line"><a id="l00050" name="l00050"></a><span class="lineno"> 50</span><span class="comment">// Worker problem data:</span></div>
<div class="line"><a id="l00051" name="l00051"></a><span class="lineno"> 51</span><span class="comment">// * p_i: The &quot;price&quot; of piece i (dual value from leader&#39;s demand constraint)</span></div>
<div class="line"><a id="l00052" name="l00052"></a><span class="lineno"> 52</span><span class="comment">//</span></div>
<div class="line"><a id="l00053" name="l00053"></a><span class="lineno"> 53</span><span class="comment">// Worker decision variables:</span></div>
<div class="line"><a id="l00054" name="l00054"></a><span class="lineno"> 54</span><span class="comment">// * y_i: How many copies of piece i should be in the configuration.</span></div>
<div class="line"><a id="l00055" name="l00055"></a><span class="lineno"> 55</span><span class="comment">//</span></div>
<div class="line"><a id="l00056" name="l00056"></a><span class="lineno"> 56</span><span class="comment">// Worker formulation</span></div>
<div class="line"><a id="l00057" name="l00057"></a><span class="lineno"> 57</span><span class="comment">// max sum_i p_i * y_i</span></div>
<div class="line"><a id="l00058" name="l00058"></a><span class="lineno"> 58</span><span class="comment">// s.t. sum_i l_i * y_i &lt;= L</span></div>
<div class="line"><a id="l00059" name="l00059"></a><span class="lineno"> 59</span><span class="comment">// y_i &gt;= 0, integer for all i</span></div>
<div class="line"><a id="l00060" name="l00060"></a><span class="lineno"> 60</span><span class="comment">//</span></div>
<div class="line"><a id="l00061" name="l00061"></a><span class="lineno"> 61</span><span class="comment">// An optimal solution y* defines a new configuration c with q_ci = y_i* for all</span></div>
<div class="line"><a id="l00062" name="l00062"></a><span class="lineno"> 62</span><span class="comment">// i. If the solution has objective value &lt;= 1, no further improvement on the LP</span></div>
<div class="line"><a id="l00063" name="l00063"></a><span class="lineno"> 63</span><span class="comment">// is possible. For additional background and proofs see:</span></div>
<div class="line"><a id="l00064" name="l00064"></a><span class="lineno"> 64</span><span class="comment">// https://people.orie.cornell.edu/shmoys/or630/notes-06/lec16.pdf</span></div>
<div class="line"><a id="l00065" name="l00065"></a><span class="lineno"> 65</span><span class="comment">// or any other reference on the &quot;Cutting Stock Problem&quot;.</span></div>
<div class="line"><a id="l00066" name="l00066"></a><span class="lineno"> 66</span><span class="comment">//</span></div>
<div class="line"><a id="l00067" name="l00067"></a><span class="lineno"> 67</span><span class="comment">// Note: this problem is equivalent to symmetric bin packing:</span></div>
<div class="line"><a id="l00068" name="l00068"></a><span class="lineno"> 68</span><span class="comment">// https://en.wikipedia.org/wiki/Bin_packing_problem#Formal_statement</span></div>
<div class="line"><a id="l00069" name="l00069"></a><span class="lineno"> 69</span><span class="comment">// but typically in bin packing it is not assumed that you should exploit having</span></div>
<div class="line"><a id="l00070" name="l00070"></a><span class="lineno"> 70</span><span class="comment">// multiple items of the same size.</span></div>
<div class="line"><a id="l00071" name="l00071"></a><span class="lineno"> 71</span><span class="preprocessor">#include &lt;iostream&gt;</span></div>
<div class="line"><a id="l00072" name="l00072"></a><span class="lineno"> 72</span><span class="preprocessor">#include &lt;limits&gt;</span></div>
<div class="line"><a id="l00073" name="l00073"></a><span class="lineno"> 73</span><span class="preprocessor">#include &lt;utility&gt;</span></div>
<div class="line"><a id="l00074" name="l00074"></a><span class="lineno"> 74</span><span class="preprocessor">#include &lt;vector&gt;</span></div>
<div class="line"><a id="l00075" name="l00075"></a><span class="lineno"> 75</span> </div>
<div class="line"><a id="l00076" name="l00076"></a><span class="lineno"> 76</span><span class="preprocessor">#include &quot;absl/flags/parse.h&quot;</span></div>
<div class="line"><a id="l00077" name="l00077"></a><span class="lineno"> 77</span><span class="preprocessor">#include &quot;absl/flags/usage.h&quot;</span></div>
<div class="line"><a id="l00078" name="l00078"></a><span class="lineno"> 78</span><span class="preprocessor">#include &quot;absl/status/status.h&quot;</span></div>
<div class="line"><a id="l00079" name="l00079"></a><span class="lineno"> 79</span><span class="preprocessor">#include &quot;absl/status/statusor.h&quot;</span></div>
<div class="line"><a id="l00080" name="l00080"></a><span class="lineno"> 80</span><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 id="l00081" name="l00081"></a><span class="lineno"> 81</span><span class="preprocessor">#include &quot;<a class="code" href="status__builder_8h.html">ortools/base/status_builder.h</a>&quot;</span></div>
<div class="line"><a id="l00082" name="l00082"></a><span class="lineno"> 82</span><span class="preprocessor">#include &quot;<a class="code" href="status__macros_8h.html">ortools/base/status_macros.h</a>&quot;</span></div>
<div class="line"><a id="l00083" name="l00083"></a><span class="lineno"> 83</span><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 id="l00084" name="l00084"></a><span class="lineno"> 84</span> </div>
<div class="line"><a id="l00085" name="l00085"></a><span class="lineno"> 85</span><span class="keyword">namespace </span>{</div>
<div class="line"><a id="l00086" name="l00086"></a><span class="lineno"> 86</span> </div>
<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>
<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&lt;double&gt;::infinity();</div>
<div class="line"><a id="l00089" name="l00089"></a><span class="lineno"> 89</span> </div>
<div class="line"><a id="l00090" name="l00090"></a><span class="lineno"> 90</span><span class="comment">// piece_sizes and piece_demands must have equal length.</span></div>
<div class="line"><a id="l00091" name="l00091"></a><span class="lineno"> 91</span><span class="comment">// every piece must have 0 &lt; size &lt;= board_length.</span></div>
<div class="line"><a id="l00092" name="l00092"></a><span class="lineno"> 92</span><span class="comment">// every piece must have demand &gt; 0.</span></div>
<div class="line"><a id="l00093" name="l00093"></a><span class="lineno"> 93</span><span class="keyword">struct </span>CuttingStockInstance {</div>
<div class="line"><a id="l00094" name="l00094"></a><span class="lineno"> 94</span> std::vector&lt;int&gt; piece_sizes;</div>
<div class="line"><a id="l00095" name="l00095"></a><span class="lineno"> 95</span> std::vector&lt;int&gt; piece_demands;</div>
<div class="line"><a id="l00096" name="l00096"></a><span class="lineno"> 96</span> <span class="keywordtype">int</span> board_length;</div>
<div class="line"><a id="l00097" name="l00097"></a><span class="lineno"> 97</span>};</div>
<div class="line"><a id="l00098" name="l00098"></a><span class="lineno"> 98</span> </div>
<div class="line"><a id="l00099" name="l00099"></a><span class="lineno"> 99</span><span class="comment">// pieces and quantity must have equal size.</span></div>
<div class="line"><a id="l00100" name="l00100"></a><span class="lineno"> 100</span><span class="comment">// Defined for a related CuttingStockInstance, the total length all pieces</span></div>
<div class="line"><a id="l00101" name="l00101"></a><span class="lineno"> 101</span><span class="comment">// weighted by their quantity must not exceed board_length.</span></div>
<div class="line"><a id="l00102" name="l00102"></a><span class="lineno"> 102</span><span class="keyword">struct </span>Configuration {</div>
<div class="line"><a id="l00103" name="l00103"></a><span class="lineno"> 103</span> std::vector&lt;int&gt; pieces;</div>
<div class="line"><a id="l00104" name="l00104"></a><span class="lineno"> 104</span> std::vector&lt;int&gt; quantity;</div>
<div class="line"><a id="l00105" name="l00105"></a><span class="lineno"> 105</span>};</div>
<div class="line"><a id="l00106" name="l00106"></a><span class="lineno"> 106</span> </div>
<div class="line"><a id="l00107" name="l00107"></a><span class="lineno"> 107</span><span class="comment">// configurations and quantity must have equal size.</span></div>
<div class="line"><a id="l00108" name="l00108"></a><span class="lineno"> 108</span><span class="comment">// objective_value is the sum of the vales in quantity (how many total boards</span></div>
<div class="line"><a id="l00109" name="l00109"></a><span class="lineno"> 109</span><span class="comment">// are used).</span></div>
<div class="line"><a id="l00110" name="l00110"></a><span class="lineno"> 110</span><span class="comment">// To be feasible, the demand for each piece type must be met by the produced</span></div>
<div class="line"><a id="l00111" name="l00111"></a><span class="lineno"> 111</span><span class="comment">// configurations.</span></div>
<div class="line"><a id="l00112" name="l00112"></a><span class="lineno"> 112</span><span class="keyword">struct </span>CuttingStockSolution {</div>
<div class="line"><a id="l00113" name="l00113"></a><span class="lineno"> 113</span> std::vector&lt;Configuration&gt; configurations;</div>
<div class="line"><a id="l00114" name="l00114"></a><span class="lineno"> 114</span> std::vector&lt;int&gt; quantity;</div>
<div class="line"><a id="l00115" name="l00115"></a><span class="lineno"> 115</span> <span class="keywordtype">int</span> objective_value = 0;</div>
<div class="line"><a id="l00116" name="l00116"></a><span class="lineno"> 116</span>};</div>
<div class="line"><a id="l00117" name="l00117"></a><span class="lineno"> 117</span> </div>
<div class="line"><a id="l00118" name="l00118"></a><span class="lineno"> 118</span><span class="comment">// Solves the worker problem.</span></div>
<div class="line"><a id="l00119" name="l00119"></a><span class="lineno"> 119</span><span class="comment">//</span></div>
<div class="line"><a id="l00120" name="l00120"></a><span class="lineno"> 120</span><span class="comment">// Solves the problem on finding the configuration (with its objective value) to</span></div>
<div class="line"><a id="l00121" name="l00121"></a><span class="lineno"> 121</span><span class="comment">// add the to model that will give the greatest improvement in the LP</span></div>
<div class="line"><a id="l00122" name="l00122"></a><span class="lineno"> 122</span><span class="comment">// relaxation. This is equivalent to a knapsack problem.</span></div>
<div class="line"><a id="l00123" name="l00123"></a><span class="lineno"> 123</span>absl::StatusOr&lt;std::pair&lt;Configuration, double&gt;&gt; BestConfiguration(</div>
<div class="line"><a id="l00124" name="l00124"></a><span class="lineno"> 124</span> <span class="keyword">const</span> std::vector&lt;double&gt;&amp; piece_prices,</div>
<div class="line"><a id="l00125" name="l00125"></a><span class="lineno"> 125</span> <span class="keyword">const</span> std::vector&lt;int&gt;&amp; piece_sizes, <span class="keyword">const</span> <span class="keywordtype">int</span> board_size) {</div>
<div class="line"><a id="l00126" name="l00126"></a><span class="lineno"> 126</span> <span class="keywordtype">int</span> num_pieces = piece_prices.size();</div>
<div class="line"><a id="l00127" name="l00127"></a><span class="lineno"> 127</span> <a class="code hl_define" href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a>(piece_sizes.size(), num_pieces);</div>
<div class="line"><a id="l00128" name="l00128"></a><span class="lineno"> 128</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">&quot;knapsack&quot;</span>);</div>
<div class="line"><a id="l00129" name="l00129"></a><span class="lineno"> 129</span> std::vector&lt;math_opt::Variable&gt; pieces;</div>
<div class="line"><a id="l00130" name="l00130"></a><span class="lineno"> 130</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; num_pieces; ++i) {</div>
<div class="line"><a id="l00131" name="l00131"></a><span class="lineno"> 131</span> pieces.push_back(</div>
<div class="line"><a id="l00132" name="l00132"></a><span class="lineno"> 132</span> <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.AddIntegerVariable(0, <a class="code hl_variable" href="namespaceoperations__research_1_1math__opt.html#ad9f50c9313b35cc1e8887057dc4d9645">kInf</a>, absl::StrCat(<span class="stringliteral">&quot;item_&quot;</span>, i)));</div>
<div class="line"><a id="l00133" name="l00133"></a><span class="lineno"> 133</span> }</div>
<div class="line"><a id="l00134" name="l00134"></a><span class="lineno"> 134</span> <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.Maximize(<a class="code hl_function" href="namespaceoperations__research_1_1math__opt.html#a7e30ee72c333408fd39ddd21c527794c">math_opt::InnerProduct</a>(pieces, piece_prices));</div>
<div class="line"><a id="l00135" name="l00135"></a><span class="lineno"> 135</span> <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.AddLinearConstraint(<a class="code hl_function" href="namespaceoperations__research_1_1math__opt.html#a7e30ee72c333408fd39ddd21c527794c">math_opt::InnerProduct</a>(pieces, piece_sizes) &lt;=</div>
<div class="line"><a id="l00136" name="l00136"></a><span class="lineno"> 136</span> board_size);</div>
<div class="line"><a id="l00137" name="l00137"></a><span class="lineno"> 137</span> <a class="code hl_define" href="status__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> solve_result,</div>
<div class="line"><a id="l00138" name="l00138"></a><span class="lineno"> 138</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>, math_opt::SolverType::kCpSat));</div>
<div class="line"><a id="l00139" name="l00139"></a><span class="lineno"> 139</span> <span class="keywordflow">if</span> (solve_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> !=</div>
<div class="line"><a id="l00140" name="l00140"></a><span class="lineno"> 140</span> math_opt::TerminationReason::kOptimal) {</div>
<div class="line"><a id="l00141" name="l00141"></a><span class="lineno"> 141</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceutil.html#ad0c886e6b95bc531d4a39884a87c0101">util::InvalidArgumentErrorBuilder</a>()</div>
<div class="line"><a id="l00142" name="l00142"></a><span class="lineno"> 142</span> &lt;&lt; <span class="stringliteral">&quot;Failed to solve knapsack pricing problem: &quot;</span></div>
<div class="line"><a id="l00143" name="l00143"></a><span class="lineno"> 143</span> &lt;&lt; solve_result.<a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_solve_result.html#a77d1ea96211300e9417b965981953c81">termination</a>;</div>
<div class="line"><a id="l00144" name="l00144"></a><span class="lineno"> 144</span> }</div>
<div class="line"><a id="l00145" name="l00145"></a><span class="lineno"> 145</span> Configuration config;</div>
<div class="line"><a id="l00146" name="l00146"></a><span class="lineno"> 146</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; num_pieces; ++i) {</div>
<div class="line"><a id="l00147" name="l00147"></a><span class="lineno"> 147</span> <span class="keyword">const</span> <span class="keywordtype">int</span> use = <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(</div>
<div class="line"><a id="l00148" name="l00148"></a><span class="lineno"> 148</span> std::round(solve_result.<a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_solve_result.html#ac4a6e078f25aa73eec5271d449a12532">variable_values</a>().at(pieces[i])));</div>
<div class="line"><a id="l00149" name="l00149"></a><span class="lineno"> 149</span> <span class="keywordflow">if</span> (use &gt; 0) {</div>
<div class="line"><a id="l00150" name="l00150"></a><span class="lineno"> 150</span> config.pieces.push_back(i);</div>
<div class="line"><a id="l00151" name="l00151"></a><span class="lineno"> 151</span> config.quantity.push_back(use);</div>
<div class="line"><a id="l00152" name="l00152"></a><span class="lineno"> 152</span> }</div>
<div class="line"><a id="l00153" name="l00153"></a><span class="lineno"> 153</span> }</div>
<div class="line"><a id="l00154" name="l00154"></a><span class="lineno"> 154</span> <span class="keywordflow">return</span> std::make_pair(config, solve_result.<a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_solve_result.html#a84f066c304d8bcbb9567be094feb9b08">objective_value</a>());</div>
<div class="line"><a id="l00155" name="l00155"></a><span class="lineno"> 155</span>}</div>
<div class="line"><a id="l00156" name="l00156"></a><span class="lineno"> 156</span> </div>
<div class="line"><a id="l00157" name="l00157"></a><span class="lineno"> 157</span><span class="comment">// Solves the full cutting stock problem by decomposition.</span></div>
<div class="line"><a id="l00158" name="l00158"></a><span class="lineno"> 158</span>absl::StatusOr&lt;CuttingStockSolution&gt; SolveCuttingStock(</div>
<div class="line"><a id="l00159" name="l00159"></a><span class="lineno"> 159</span> <span class="keyword">const</span> CuttingStockInstance&amp; instance) {</div>
<div class="line"><a id="l00160" name="l00160"></a><span class="lineno"> 160</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">&quot;cutting_stock&quot;</span>);</div>
<div class="line"><a id="l00161" name="l00161"></a><span class="lineno"> 161</span> <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.set_minimize();</div>
<div class="line"><a id="l00162" name="l00162"></a><span class="lineno"> 162</span> <span class="keyword">const</span> <span class="keywordtype">int</span> n = instance.piece_sizes.size();</div>
<div class="line"><a id="l00163" name="l00163"></a><span class="lineno"> 163</span> std::vector&lt;math_opt::LinearConstraint&gt; demand_met;</div>
<div class="line"><a id="l00164" name="l00164"></a><span class="lineno"> 164</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) {</div>
<div class="line"><a id="l00165" name="l00165"></a><span class="lineno"> 165</span> <span class="keyword">const</span> <span class="keywordtype">int</span> d = instance.piece_demands[i];</div>
<div class="line"><a id="l00166" name="l00166"></a><span class="lineno"> 166</span> demand_met.push_back(<a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.AddLinearConstraint(d, d));</div>
<div class="line"><a id="l00167" name="l00167"></a><span class="lineno"> 167</span> }</div>
<div class="line"><a id="l00168" name="l00168"></a><span class="lineno"> 168</span> std::vector&lt;std::pair&lt;Configuration, math_opt::Variable&gt;&gt; configs;</div>
<div class="line"><a id="l00169" name="l00169"></a><span class="lineno"> 169</span> <span class="keyword">auto</span> add_config = [&amp;](<span class="keyword">const</span> Configuration&amp; config) {</div>
<div class="line"><a id="l00170" name="l00170"></a><span class="lineno"> 170</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> v = <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>
<div class="line"><a id="l00171" name="l00171"></a><span class="lineno"> 171</span> <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.set_objective_coefficient(v, 1);</div>
<div class="line"><a id="l00172" name="l00172"></a><span class="lineno"> 172</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; config.pieces.size(); ++i) {</div>
<div class="line"><a id="l00173" name="l00173"></a><span class="lineno"> 173</span> <span class="keyword">const</span> <span class="keywordtype">int</span> item = config.pieces[i];</div>
<div class="line"><a id="l00174" name="l00174"></a><span class="lineno"> 174</span> <span class="keyword">const</span> <span class="keywordtype">int</span> use = config.quantity[i];</div>
<div class="line"><a id="l00175" name="l00175"></a><span class="lineno"> 175</span> <span class="keywordflow">if</span> (use &gt;= 1) {</div>
<div class="line"><a id="l00176" name="l00176"></a><span class="lineno"> 176</span> <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.set_coefficient(demand_met[item], v, use);</div>
<div class="line"><a id="l00177" name="l00177"></a><span class="lineno"> 177</span> }</div>
<div class="line"><a id="l00178" name="l00178"></a><span class="lineno"> 178</span> }</div>
<div class="line"><a id="l00179" name="l00179"></a><span class="lineno"> 179</span> configs.push_back({config, v});</div>
<div class="line"><a id="l00180" name="l00180"></a><span class="lineno"> 180</span> };</div>
<div class="line"><a id="l00181" name="l00181"></a><span class="lineno"> 181</span> </div>
<div class="line"><a id="l00182" name="l00182"></a><span class="lineno"> 182</span> <span class="comment">// To ensure the leader problem is always feasible, begin a configuration for</span></div>
<div class="line"><a id="l00183" name="l00183"></a><span class="lineno"> 183</span> <span class="comment">// every item that has a single copy of the item.</span></div>
<div class="line"><a id="l00184" name="l00184"></a><span class="lineno"> 184</span> <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i &lt; n; ++i) {</div>
<div class="line"><a id="l00185" name="l00185"></a><span class="lineno"> 185</span> add_config(Configuration{.pieces = {i}, .quantity = {1}});</div>
<div class="line"><a id="l00186" name="l00186"></a><span class="lineno"> 186</span> }</div>
<div class="line"><a id="l00187" name="l00187"></a><span class="lineno"> 187</span> </div>
<div class="line"><a id="l00188" name="l00188"></a><span class="lineno"> 188</span> <a class="code hl_define" href="status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011">ASSIGN_OR_RETURN</a>(<span class="keyword">auto</span> solver, <a class="code hl_function" href="classoperations__research_1_1math__opt_1_1_incremental_solver.html#aec52d0242a0f74b9951c7eed2f81709d">math_opt::IncrementalSolver::New</a>(</div>
<div class="line"><a id="l00189" name="l00189"></a><span class="lineno"> 189</span> <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>, math_opt::SolverType::kGlop));</div>
<div class="line"><a id="l00190" name="l00190"></a><span class="lineno"> 190</span> <span class="keywordtype">int</span> pricing_round = 0;</div>
<div class="line"><a id="l00191" name="l00191"></a><span class="lineno"> 191</span> <span class="keywordflow">while</span> (<span class="keyword">true</span>) {</div>
<div class="line"><a id="l00192" name="l00192"></a><span class="lineno"> 192</span> <a class="code hl_define" href="status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011">ASSIGN_OR_RETURN</a>(<a class="code hl_struct" href="structoperations__research_1_1math__opt_1_1_solve_result.html">math_opt::SolveResult</a> solve_result, solver-&gt;Solve());</div>
<div class="line"><a id="l00193" name="l00193"></a><span class="lineno"> 193</span> <span class="keywordflow">if</span> (solve_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> !=</div>
<div class="line"><a id="l00194" name="l00194"></a><span class="lineno"> 194</span> math_opt::TerminationReason::kOptimal) {</div>
<div class="line"><a id="l00195" name="l00195"></a><span class="lineno"> 195</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceutil.html#a302ee4bfcb86ea9ed64a193ed0b14648">util::InternalErrorBuilder</a>()</div>
<div class="line"><a id="l00196" name="l00196"></a><span class="lineno"> 196</span> &lt;&lt; <span class="stringliteral">&quot;Failed to solve leader LP problem at iteration &quot;</span></div>
<div class="line"><a id="l00197" name="l00197"></a><span class="lineno"> 197</span> &lt;&lt; pricing_round &lt;&lt; <span class="stringliteral">&quot; termination: &quot;</span> &lt;&lt; solve_result.<a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_solve_result.html#a77d1ea96211300e9417b965981953c81">termination</a>;</div>
<div class="line"><a id="l00198" name="l00198"></a><span class="lineno"> 198</span> }</div>
<div class="line"><a id="l00199" name="l00199"></a><span class="lineno"> 199</span> <span class="comment">// GLOP always returns a dual solution on optimal</span></div>
<div class="line"><a id="l00200" name="l00200"></a><span class="lineno"> 200</span> <a class="code hl_define" href="base_2logging_8h.html#a3e1cfef60e774a81f30eaddf26a3a274">CHECK</a>(solve_result.<a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_solve_result.html#a35cafd54aea7eb0aecf1cb6fa4b33273">has_dual_feasible_solution</a>());</div>
<div class="line"><a id="l00201" name="l00201"></a><span class="lineno"> 201</span> std::vector&lt;double&gt; prices;</div>
<div class="line"><a id="l00202" name="l00202"></a><span class="lineno"> 202</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <a class="code hl_class" href="classoperations__research_1_1math__opt_1_1_linear_constraint.html">math_opt::LinearConstraint</a> d : demand_met) {</div>
<div class="line"><a id="l00203" name="l00203"></a><span class="lineno"> 203</span> prices.push_back(solve_result.<a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_solve_result.html#a116b227550e648d43bfbaccf9557ce42">dual_values</a>().at(d));</div>
<div class="line"><a id="l00204" name="l00204"></a><span class="lineno"> 204</span> }</div>
<div class="line"><a id="l00205" name="l00205"></a><span class="lineno"> 205</span> <a class="code hl_define" href="status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011">ASSIGN_OR_RETURN</a>(</div>
<div class="line"><a id="l00206" name="l00206"></a><span class="lineno"> 206</span> (<span class="keyword">const</span> <span class="keyword">auto</span> [config, <a class="code hl_variable" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a>]),</div>
<div class="line"><a id="l00207" name="l00207"></a><span class="lineno"> 207</span> BestConfiguration(prices, instance.piece_sizes, instance.board_length));</div>
<div class="line"><a id="l00208" name="l00208"></a><span class="lineno"> 208</span> <span class="keywordflow">if</span> (<a class="code hl_variable" href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a> &lt;= 1 + 1e-3) {</div>
<div class="line"><a id="l00209" name="l00209"></a><span class="lineno"> 209</span> <span class="comment">// The LP relaxation is solved, we can stop adding columns.</span></div>
<div class="line"><a id="l00210" name="l00210"></a><span class="lineno"> 210</span> <span class="keywordflow">break</span>;</div>
<div class="line"><a id="l00211" name="l00211"></a><span class="lineno"> 211</span> }</div>
<div class="line"><a id="l00212" name="l00212"></a><span class="lineno"> 212</span> add_config(config);</div>
<div class="line"><a id="l00213" name="l00213"></a><span class="lineno"> 213</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>) &lt;&lt; <span class="stringliteral">&quot;round: &quot;</span> &lt;&lt; pricing_round</div>
<div class="line"><a id="l00214" name="l00214"></a><span class="lineno"> 214</span> &lt;&lt; <span class="stringliteral">&quot; lp objective: &quot;</span> &lt;&lt; solve_result.<a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_solve_result.html#a84f066c304d8bcbb9567be094feb9b08">objective_value</a>();</div>
<div class="line"><a id="l00215" name="l00215"></a><span class="lineno"> 215</span> pricing_round++;</div>
<div class="line"><a id="l00216" name="l00216"></a><span class="lineno"> 216</span> }</div>
<div class="line"><a id="l00217" name="l00217"></a><span class="lineno"> 217</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>) &lt;&lt; <span class="stringliteral">&quot;Done adding columns, switching to MIP&quot;</span>;</div>
<div class="line"><a id="l00218" name="l00218"></a><span class="lineno"> 218</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>&amp; [config, <a class="code hl_variable" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>] : configs) {</div>
<div class="line"><a id="l00219" name="l00219"></a><span class="lineno"> 219</span> <a class="code hl_variable" href="gurobi__interface_8cc.html#a0728f23c9a47655d38e0bf1a2f200bcf">model</a>.set_integer(<a class="code hl_variable" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>);</div>
<div class="line"><a id="l00220" name="l00220"></a><span class="lineno"> 220</span> }</div>
<div class="line"><a id="l00221" name="l00221"></a><span class="lineno"> 221</span> <a class="code hl_define" href="status__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> solve_result,</div>
<div class="line"><a id="l00222" name="l00222"></a><span class="lineno"> 222</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>, math_opt::SolverType::kCpSat));</div>
<div class="line"><a id="l00223" name="l00223"></a><span class="lineno"> 223</span> <span class="keywordflow">if</span> (solve_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> !=</div>
<div class="line"><a id="l00224" name="l00224"></a><span class="lineno"> 224</span> math_opt::TerminationReason::kOptimal) {</div>
<div class="line"><a id="l00225" name="l00225"></a><span class="lineno"> 225</span> <span class="keywordflow">return</span> <a class="code hl_function" href="namespaceutil.html#a302ee4bfcb86ea9ed64a193ed0b14648">util::InternalErrorBuilder</a>()</div>
<div class="line"><a id="l00226" name="l00226"></a><span class="lineno"> 226</span> &lt;&lt; <span class="stringliteral">&quot;Failed to solve final cutting stock MIP, termination: &quot;</span></div>
<div class="line"><a id="l00227" name="l00227"></a><span class="lineno"> 227</span> &lt;&lt; solve_result.<a class="code hl_variable" href="structoperations__research_1_1math__opt_1_1_solve_result.html#a77d1ea96211300e9417b965981953c81">termination</a>;</div>
<div class="line"><a id="l00228" name="l00228"></a><span class="lineno"> 228</span> }</div>
<div class="line"><a id="l00229" name="l00229"></a><span class="lineno"> 229</span> CuttingStockSolution solution;</div>
<div class="line"><a id="l00230" name="l00230"></a><span class="lineno"> 230</span> <span class="keywordflow">for</span> (<span class="keyword">const</span> <span class="keyword">auto</span>&amp; [config, <a class="code hl_variable" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>] : configs) {</div>
<div class="line"><a id="l00231" name="l00231"></a><span class="lineno"> 231</span> <span class="keywordtype">int</span> use =</div>
<div class="line"><a id="l00232" name="l00232"></a><span class="lineno"> 232</span> <span class="keyword">static_cast&lt;</span><span class="keywordtype">int</span><span class="keyword">&gt;</span>(std::round(solve_result.<a class="code hl_function" href="structoperations__research_1_1math__opt_1_1_solve_result.html#ac4a6e078f25aa73eec5271d449a12532">variable_values</a>().at(<a class="code hl_variable" href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a>)));</div>
<div class="line"><a id="l00233" name="l00233"></a><span class="lineno"> 233</span> <span class="keywordflow">if</span> (use &gt; 0) {</div>
<div class="line"><a id="l00234" name="l00234"></a><span class="lineno"> 234</span> solution.configurations.push_back(config);</div>
<div class="line"><a id="l00235" name="l00235"></a><span class="lineno"> 235</span> solution.quantity.push_back(use);</div>
<div class="line"><a id="l00236" name="l00236"></a><span class="lineno"> 236</span> solution.objective_value += use;</div>
<div class="line"><a id="l00237" name="l00237"></a><span class="lineno"> 237</span> }</div>
<div class="line"><a id="l00238" name="l00238"></a><span class="lineno"> 238</span> }</div>
<div class="line"><a id="l00239" name="l00239"></a><span class="lineno"> 239</span> <span class="keywordflow">return</span> solution;</div>
<div class="line"><a id="l00240" name="l00240"></a><span class="lineno"> 240</span>}</div>
<div class="line"><a id="l00241" name="l00241"></a><span class="lineno"> 241</span> </div>
<div class="line"><a id="l00242" name="l00242"></a><span class="lineno"> 242</span>absl::Status RealMain() {</div>
<div class="line"><a id="l00243" name="l00243"></a><span class="lineno"> 243</span> <span class="comment">// Data from https://en.wikipedia.org/wiki/Cutting_stock_problem</span></div>
<div class="line"><a id="l00244" name="l00244"></a><span class="lineno"> 244</span> CuttingStockInstance instance;</div>
<div class="line"><a id="l00245" name="l00245"></a><span class="lineno"> 245</span> instance.board_length = 5600;</div>
<div class="line"><a id="l00246" name="l00246"></a><span class="lineno"> 246</span> instance.piece_sizes = {1380, 1520, 1560, 1710, 1820, 1880, 1930,</div>
<div class="line"><a id="l00247" name="l00247"></a><span class="lineno"> 247</span> 2000, 2050, 2100, 2140, 2150, 2200};</div>
<div class="line"><a id="l00248" name="l00248"></a><span class="lineno"> 248</span> instance.piece_demands = {22, 25, 12, 14, 18, 18, 20, 10, 12, 14, 16, 18, 20};</div>
<div class="line"><a id="l00249" name="l00249"></a><span class="lineno"> 249</span> <a class="code hl_define" href="status__macros_8h.html#a600de4b8f65fe0a4b1898041634f9011">ASSIGN_OR_RETURN</a>(CuttingStockSolution solution, SolveCuttingStock(instance));</div>
<div class="line"><a id="l00250" name="l00250"></a><span class="lineno"> 250</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Best known solution uses 73 rolls.&quot;</span> &lt;&lt; std::endl;</div>
<div class="line"><a id="l00251" name="l00251"></a><span class="lineno"> 251</span> std::cout &lt;&lt; <span class="stringliteral">&quot;Total rolls used in actual solution found: &quot;</span></div>
<div class="line"><a id="l00252" name="l00252"></a><span class="lineno"> 252</span> &lt;&lt; solution.objective_value &lt;&lt; std::endl;</div>
<div class="line"><a id="l00253" name="l00253"></a><span class="lineno"> 253</span> <span class="keywordflow">return</span> absl::OkStatus();</div>
<div class="line"><a id="l00254" name="l00254"></a><span class="lineno"> 254</span>}</div>
<div class="line"><a id="l00255" name="l00255"></a><span class="lineno"> 255</span> </div>
<div class="line"><a id="l00256" name="l00256"></a><span class="lineno"> 256</span>} <span class="comment">// namespace</span></div>
<div class="line"><a id="l00257" name="l00257"></a><span class="lineno"> 257</span> </div>
<div class="line"><a id="l00258" name="l00258"></a><span class="lineno"><a class="line" href="cutting__stock_8cc.html#a3c04138a5bfe5d72780bb7e82a18e627"> 258</a></span><span class="keywordtype">int</span> <a class="code hl_function" href="cutting__stock_8cc.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a>(<span class="keywordtype">int</span> argc, <span class="keywordtype">char</span>** argv) {</div>
<div class="line"><a id="l00259" name="l00259"></a><span class="lineno"> 259</span> <a class="code hl_function" href="namespacegoogle.html#a1749056ff206ebc4f581e6bc0bae841d">google::InitGoogleLogging</a>(argv[0]);</div>
<div class="line"><a id="l00260" name="l00260"></a><span class="lineno"> 260</span> absl::ParseCommandLine(argc, argv);</div>
<div class="line"><a id="l00261" name="l00261"></a><span class="lineno"> 261</span> absl::Status result = RealMain();</div>
<div class="line"><a id="l00262" name="l00262"></a><span class="lineno"> 262</span> <span class="keywordflow">if</span> (!result.ok()) {</div>
<div class="line"><a id="l00263" name="l00263"></a><span class="lineno"> 263</span> std::cout &lt;&lt; result;</div>
<div class="line"><a id="l00264" name="l00264"></a><span class="lineno"> 264</span> <span class="keywordflow">return</span> 1;</div>
<div class="line"><a id="l00265" name="l00265"></a><span class="lineno"> 265</span> }</div>
<div class="line"><a id="l00266" name="l00266"></a><span class="lineno"> 266</span> <span class="keywordflow">return</span> 0;</div>
<div class="line"><a id="l00267" name="l00267"></a><span class="lineno"> 267</span>}</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_a3e1cfef60e774a81f30eaddf26a3a274"><div class="ttname"><a href="base_2logging_8h.html#a3e1cfef60e774a81f30eaddf26a3a274">CHECK</a></div><div class="ttdeci">#define CHECK(condition)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00495">base/logging.h:495</a></div></div>
<div class="ttc" id="abase_2logging_8h_html_a7c0ce053b28d53aa4eaf3eb7fb71663b"><div class="ttname"><a href="base_2logging_8h.html#a7c0ce053b28d53aa4eaf3eb7fb71663b">CHECK_EQ</a></div><div class="ttdeci">#define CHECK_EQ(val1, val2)</div><div class="ttdef"><b>Definition:</b> <a href="base_2logging_8h_source.html#l00702">base/logging.h:702</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#l00420">base/logging.h:420</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1math__opt_1_1_incremental_solver_html_aec52d0242a0f74b9951c7eed2f81709d"><div class="ttname"><a href="classoperations__research_1_1math__opt_1_1_incremental_solver.html#aec52d0242a0f74b9951c7eed2f81709d">operations_research::math_opt::IncrementalSolver::New</a></div><div class="ttdeci">static absl::StatusOr&lt; std::unique_ptr&lt; IncrementalSolver &gt; &gt; New(Model &amp;model, SolverType solver_type, SolverInitArguments arguments={})</div><div class="ttdef"><b>Definition:</b> <a href="solve_8cc_source.html#l00165">solve.cc:165</a></div></div>
<div class="ttc" id="aclassoperations__research_1_1math__opt_1_1_linear_constraint_html"><div class="ttname"><a href="classoperations__research_1_1math__opt_1_1_linear_constraint.html">operations_research::math_opt::LinearConstraint</a></div><div class="ttdef"><b>Definition:</b> <a href="math__opt_2cpp_2linear__constraint_8h_source.html#l00034">math_opt/cpp/linear_constraint.h:34</a></div></div>
<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#l00127">math_opt/cpp/model.h:127</a></div></div>
<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>
<div class="ttc" id="acutting__stock_8cc_html_a3c04138a5bfe5d72780bb7e82a18e627"><div class="ttname"><a href="cutting__stock_8cc.html#a3c04138a5bfe5d72780bb7e82a18e627">main</a></div><div class="ttdeci">int main(int argc, char **argv)</div><div class="ttdef"><b>Definition:</b> <a href="cutting__stock_8cc_source.html#l00258">cutting_stock.cc:258</a></div></div>
<div class="ttc" id="ademon__profiler_8cc_html_ac072af30c4ffbc834bb4c681f6ecb514"><div class="ttname"><a href="demon__profiler_8cc.html#ac072af30c4ffbc834bb4c681f6ecb514">value</a></div><div class="ttdeci">int64_t value</div><div class="ttdef"><b>Definition:</b> <a href="demon__profiler_8cc_source.html#l00044">demon_profiler.cc:44</a></div></div>
<div class="ttc" id="aexpr__array_8cc_html_a472a99923cbe11ae7b5a5d157d9ad465"><div class="ttname"><a href="expr__array_8cc.html#a472a99923cbe11ae7b5a5d157d9ad465">var</a></div><div class="ttdeci">IntVar * var</div><div class="ttdef"><b>Definition:</b> <a href="expr__array_8cc_source.html#l01874">expr_array.cc:1874</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#l00274">gurobi_interface.cc:274</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_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>
<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&lt; SolveResult &gt; Solve(const Model &amp;model, const SolverType solver_type, const SolveArguments &amp;solve_args, const SolverInitArguments &amp;init_args)</div><div class="ttdef"><b>Definition:</b> <a href="solve_8cc_source.html#l00155">solve.cc:155</a></div></div>
<div class="ttc" id="anamespaceoperations__research_1_1math__opt_html_a7e30ee72c333408fd39ddd21c527794c"><div class="ttname"><a href="namespaceoperations__research_1_1math__opt.html#a7e30ee72c333408fd39ddd21c527794c">operations_research::math_opt::InnerProduct</a></div><div class="ttdeci">LinearExpression InnerProduct(const LeftIterable &amp;left, const RightIterable &amp;right)</div><div class="ttdef"><b>Definition:</b> <a href="variable__and__expressions_8h_source.html#l01245">variable_and_expressions.h:1245</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="variable__and__expressions_8cc_source.html#l00028">variable_and_expressions.cc:28</a></div></div>
<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#l00073">status_builder.h:73</a></div></div>
<div class="ttc" id="anamespaceutil_html_ad0c886e6b95bc531d4a39884a87c0101"><div class="ttname"><a href="namespaceutil.html#ad0c886e6b95bc531d4a39884a87c0101">util::InvalidArgumentErrorBuilder</a></div><div class="ttdeci">StatusBuilder InvalidArgumentErrorBuilder()</div><div class="ttdef"><b>Definition:</b> <a href="status__builder_8h_source.html#l00077">status_builder.h:77</a></div></div>
<div class="ttc" id="astatus__builder_8h_html"><div class="ttname"><a href="status__builder_8h.html">status_builder.h</a></div></div>
<div class="ttc" id="astatus__macros_8h_html"><div class="ttname"><a href="status__macros_8h.html">status_macros.h</a></div></div>
<div class="ttc" id="astatus__macros_8h_html_a600de4b8f65fe0a4b1898041634f9011"><div class="ttname"><a href="status__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="status__macros_8h_source.html#l00048">status_macros.h:48</a></div></div>
<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#l00293">solve_result.h:293</a></div></div>
<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&lt; double &gt; &amp; dual_values() const</div><div class="ttdef"><b>Definition:</b> <a href="solve__result_8cc_source.html#l00375">solve_result.cc:375</a></div></div>
<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#l00369">solve_result.cc:369</a></div></div>
<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#l00301">solve_result.h:301</a></div></div>
<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#l00348">solve_result.cc:348</a></div></div>
<div class="ttc" id="astructoperations__research_1_1math__opt_1_1_solve_result_html_ac4a6e078f25aa73eec5271d449a12532"><div class="ttname"><a href="structoperations__research_1_1math__opt_1_1_solve_result.html#ac4a6e078f25aa73eec5271d449a12532">operations_research::math_opt::SolveResult::variable_values</a></div><div class="ttdeci">const VariableMap&lt; double &gt; &amp; variable_values() const</div><div class="ttdef"><b>Definition:</b> <a href="solve__result_8cc_source.html#l00359">solve_result.cc:359</a></div></div>
<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#l00259">solve_result.h:259</a></div></div>
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