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<div class="title">SimpleMinCostFlowProgram.cs</div> </div>
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<a href="SimpleMinCostFlowProgram_8cs.html">Go to the documentation of this file.</a><div class="fragment"><div class="line"><a name="l00001"></a><span class="lineno"> 1</span> <span class="comment">// Copyright 2010-2018 Google LLC</span></div><div class="line"><a name="l00002"></a><span class="lineno"> 2</span> <span class="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div><div class="line"><a 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 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 name="l00005"></a><span class="lineno"> 5</span> <span class="comment">//</span></div><div class="line"><a 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 name="l00007"></a><span class="lineno"> 7</span> <span class="comment">//</span></div><div class="line"><a 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 name="l00009"></a><span class="lineno"> 9</span> <span class="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div><div class="line"><a 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 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 name="l00012"></a><span class="lineno"> 12</span> <span class="comment">// limitations under the License.</span></div><div class="line"><a name="l00013"></a><span class="lineno"> 13</span> </div><div class="line"><a name="l00014"></a><span class="lineno"> 14</span> <span class="comment">// """From Bradley, Hax, and Magnanti, 'Applied Mathematical Programming', figure 8.1."""</span></div><div class="line"><a name="l00015"></a><span class="lineno"> 15</span> <span class="comment">// [START program]</span></div><div class="line"><a name="l00016"></a><span class="lineno"> 16</span> <span class="keyword">using</span> System;</div><div class="line"><a name="l00017"></a><span class="lineno"> 17</span> <span class="keyword">using</span> <a class="code" href="namespaceGoogle.html">Google</a>.<a class="code" href="namespaceGoogle_1_1OrTools.html">OrTools</a>.Graph;</div><div class="line"><a name="l00018"></a><span class="lineno"> 18</span> </div><div class="line"><a name="l00019"></a><span class="lineno"><a class="line" href="classSimpleMinCostFlowProgram.html"> 19</a></span> <span class="keyword">public</span> <span class="keyword">class </span><a class="code" href="classSimpleMinCostFlowProgram.html">SimpleMinCostFlowProgram</a></div><div class="line"><a name="l00020"></a><span class="lineno"> 20</span> {</div><div class="line"><a name="l00021"></a><span class="lineno"> 21</span>  <span class="keyword">static</span> <span class="keywordtype">void</span> Main()</div><div class="line"><a name="l00022"></a><span class="lineno"> 22</span>  {</div><div class="line"><a name="l00023"></a><span class="lineno"> 23</span>  <span class="comment">// [START data]</span></div><div class="line"><a name="l00024"></a><span class="lineno"> 24</span>  <span class="comment">// Define four parallel arrays: sources, destinations, capacities, and unit costs</span></div><div class="line"><a name="l00025"></a><span class="lineno"> 25</span>  <span class="comment">// between each pair. For instance, the arc from node 0 to node 1 has a</span></div><div class="line"><a name="l00026"></a><span class="lineno"> 26</span>  <span class="comment">// capacity of 15.</span></div><div class="line"><a name="l00027"></a><span class="lineno"> 27</span>  <span class="comment">// Problem taken From Taha's 'Introduction to Operations Research',</span></div><div class="line"><a name="l00028"></a><span class="lineno"> 28</span>  <span class="comment">// example 6.4-2.</span></div><div class="line"><a name="l00029"></a><span class="lineno"> 29</span>  <span class="keywordtype">int</span>[] startNodes = {0, 0, 1, 1, 1, 2, 2, 3, 4};</div><div class="line"><a name="l00030"></a><span class="lineno"> 30</span>  <span class="keywordtype">int</span>[] endNodes = {1, 2, 2, 3, 4, 3, 4, 4, 2};</div><div class="line"><a name="l00031"></a><span class="lineno"> 31</span>  <span class="keywordtype">int</span>[] capacities = {15, 8, 20, 4, 10, 15, 4, 20, 5};</div><div class="line"><a name="l00032"></a><span class="lineno"> 32</span>  <span class="keywordtype">int</span>[] unitCosts = {4, 4, 2, 2, 6, 1, 3, 2, 3};</div><div class="line"><a name="l00033"></a><span class="lineno"> 33</span> </div><div class="line"><a name="l00034"></a><span class="lineno"> 34</span>  <span class="comment">// Define an array of supplies at each node.</span></div><div class="line"><a name="l00035"></a><span class="lineno"> 35</span>  <span class="keywordtype">int</span>[] supplies = {20, 0, 0, -5, -15};</div><div class="line"><a name="l00036"></a><span class="lineno"> 36</span>  <span class="comment">// [END data]</span></div><div class="line"><a name="l00037"></a><span class="lineno"> 37</span> </div><div class="line"><a name="l00038"></a><span class="lineno"> 38</span>  <span class="comment">// [START constraints]</span></div><div class="line"><a name="l00039"></a><span class="lineno"> 39</span>  <span class="comment">// Instantiate a SimpleMinCostFlow solver.</span></div><div class="line"><a name="l00040"></a><span class="lineno"> 40</span>  MinCostFlow minCostFlow = <span class="keyword">new</span> MinCostFlow();</div><div class="line"><a name="l00041"></a><span class="lineno"> 41</span> </div><div class="line"><a name="l00042"></a><span class="lineno"> 42</span>  <span class="comment">// Add each arc.</span></div><div class="line"><a name="l00043"></a><span class="lineno"> 43</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < startNodes.Length; ++i)</div><div class="line"><a name="l00044"></a><span class="lineno"> 44</span>  {</div><div class="line"><a name="l00045"></a><span class="lineno"> 45</span>  <span class="keywordtype">int</span> arc = minCostFlow.AddArcWithCapacityAndUnitCost(startNodes[i], endNodes[i],</div><div class="line"><a name="l00046"></a><span class="lineno"> 46</span>  capacities[i], unitCosts[i]);</div><div class="line"><a name="l00047"></a><span class="lineno"> 47</span>  <span class="keywordflow">if</span> (arc != i) <span class="keywordflow">throw</span> <span class="keyword">new</span> Exception(<span class="stringliteral">"Internal error"</span>);</div><div class="line"><a name="l00048"></a><span class="lineno"> 48</span>  }</div><div class="line"><a name="l00049"></a><span class="lineno"> 49</span> </div><div class="line"><a name="l00050"></a><span class="lineno"> 50</span>  <span class="comment">// Add node supplies.</span></div><div class="line"><a name="l00051"></a><span class="lineno"> 51</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < supplies.Length; ++i)</div><div class="line"><a name="l00052"></a><span class="lineno"> 52</span>  {</div><div class="line"><a name="l00053"></a><span class="lineno"> 53</span>  minCostFlow.SetNodeSupply(i, supplies[i]);</div><div class="line"><a name="l00054"></a><span class="lineno"> 54</span>  }</div><div class="line"><a name="l00055"></a><span class="lineno"> 55</span> </div><div class="line"><a name="l00056"></a><span class="lineno"> 56</span>  <span class="comment">// [END constraints]</span></div><div class="line"><a name="l00057"></a><span class="lineno"> 57</span> </div><div class="line"><a name="l00058"></a><span class="lineno"> 58</span>  <span class="comment">// [START solve]</span></div><div class="line"><a name="l00059"></a><span class="lineno"> 59</span>  <span class="comment">// Find the min cost flow.</span></div><div class="line"><a name="l00060"></a><span class="lineno"> 60</span>  MinCostFlow.Status solveStatus = minCostFlow.Solve();</div><div class="line"><a name="l00061"></a><span class="lineno"> 61</span>  <span class="comment">// [END solve]</span></div><div class="line"><a name="l00062"></a><span class="lineno"> 62</span> </div><div class="line"><a name="l00063"></a><span class="lineno"> 63</span>  <span class="comment">// [START print_solution]</span></div><div class="line"><a name="l00064"></a><span class="lineno"> 64</span>  <span class="keywordflow">if</span> (solveStatus == MinCostFlow.Status.OPTIMAL)</div><div class="line"><a name="l00065"></a><span class="lineno"> 65</span>  {</div><div class="line"><a name="l00066"></a><span class="lineno"> 66</span>  Console.WriteLine(<span class="stringliteral">"Minimum cost: "</span> + minCostFlow.OptimalCost());</div><div class="line"><a name="l00067"></a><span class="lineno"> 67</span>  Console.WriteLine(<span class="stringliteral">""</span>);</div><div class="line"><a name="l00068"></a><span class="lineno"> 68</span>  Console.WriteLine(<span class="stringliteral">" Edge Flow / Capacity Cost"</span>);</div><div class="line"><a name="l00069"></a><span class="lineno"> 69</span>  <span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = 0; i < minCostFlow.NumArcs(); ++i)</div><div class="line"><a name="l00070"></a><span class="lineno"> 70</span>  {</div><div class="line"><a name="l00071"></a><span class="lineno"> 71</span>  <span class="keywordtype">long</span> cost = minCostFlow.Flow(i) * minCostFlow.UnitCost(i);</div><div class="line"><a name="l00072"></a><span class="lineno"> 72</span>  Console.WriteLine(minCostFlow.Tail(i) + <span class="stringliteral">" -> "</span> +</div><div class="line"><a name="l00073"></a><span class="lineno"> 73</span>  minCostFlow.Head(i) + <span class="stringliteral">" "</span> +</div><div class="line"><a name="l00074"></a><span class="lineno"> 74</span>  <span class="keywordtype">string</span>.Format(<span class="stringliteral">"{0,3}"</span>, minCostFlow.Flow(i)) + <span class="stringliteral">" / "</span> +</div><div class="line"><a name="l00075"></a><span class="lineno"> 75</span>  <span class="keywordtype">string</span>.Format (<span class="stringliteral">"{0,3}"</span>, minCostFlow.Capacity(i)) + <span class="stringliteral">" "</span> +</div><div class="line"><a name="l00076"></a><span class="lineno"> 76</span>  <span class="keywordtype">string</span>.Format (<span class="stringliteral">"{0,3}"</span>, cost));</div><div class="line"><a name="l00077"></a><span class="lineno"> 77</span>  }</div><div class="line"><a name="l00078"></a><span class="lineno"> 78</span>  }</div><div class="line"><a name="l00079"></a><span class="lineno"> 79</span>  <span class="keywordflow">else</span></div><div class="line"><a name="l00080"></a><span class="lineno"> 80</span>  {</div><div class="line"><a name="l00081"></a><span class="lineno"> 81</span>  Console.WriteLine(<span class="stringliteral">"Solving the min cost flow problem failed. Solver status: "</span> +</div><div class="line"><a name="l00082"></a><span class="lineno"> 82</span>  solveStatus);</div><div class="line"><a name="l00083"></a><span class="lineno"> 83</span>  }</div><div class="line"><a name="l00084"></a><span class="lineno"> 84</span>  <span class="comment">// [END print_solution]</span></div><div class="line"><a name="l00085"></a><span class="lineno"> 85</span>  }</div><div class="line"><a name="l00086"></a><span class="lineno"> 86</span> }</div><div class="line"><a name="l00087"></a><span class="lineno"> 87</span> <span class="comment">// [END program]</span></div><div class="ttc" id="classSimpleMinCostFlowProgram_html"><div class="ttname"><a href="classSimpleMinCostFlowProgram.html">SimpleMinCostFlowProgram</a></div><div class="ttdef"><b>Definition:</b> <a href="SimpleMinCostFlowProgram_8cs_source.html#l00019">SimpleMinCostFlowProgram.cs:19</a></div></div>
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<div class="ttc" id="namespaceGoogle_html"><div class="ttname"><a href="namespaceGoogle.html">Google</a></div><div class="ttdef"><b>Definition:</b> <a href="RoutingEnums_8pb_8cs_source.html#l00012">RoutingEnums.pb.cs:12</a></div></div>
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<div class="ttc" id="namespaceGoogle_1_1OrTools_html"><div class="ttname"><a href="namespaceGoogle_1_1OrTools.html">Google.OrTools</a></div><div class="ttdef"><b>Definition:</b> <a href="RoutingEnums_8pb_8cs_source.html#l00012">RoutingEnums.pb.cs:12</a></div></div>
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