<ahref="scheduling__cuts_8h.html">Go to the documentation of this file.</a><divclass="fragment"><divclass="line"><aid="l00001"name="l00001"></a><spanclass="lineno"> 1</span><spanclass="comment">// Copyright 2010-2021 Google LLC</span></div>
<divclass="line"><aid="l00002"name="l00002"></a><spanclass="lineno"> 2</span><spanclass="comment">// Licensed under the Apache License, Version 2.0 (the "License");</span></div>
<divclass="line"><aid="l00003"name="l00003"></a><spanclass="lineno"> 3</span><spanclass="comment">// you may not use this file except in compliance with the License.</span></div>
<divclass="line"><aid="l00004"name="l00004"></a><spanclass="lineno"> 4</span><spanclass="comment">// You may obtain a copy of the License at</span></div>
<divclass="line"><aid="l00008"name="l00008"></a><spanclass="lineno"> 8</span><spanclass="comment">// Unless required by applicable law or agreed to in writing, software</span></div>
<divclass="line"><aid="l00009"name="l00009"></a><spanclass="lineno"> 9</span><spanclass="comment">// distributed under the License is distributed on an "AS IS" BASIS,</span></div>
<divclass="line"><aid="l00010"name="l00010"></a><spanclass="lineno"> 10</span><spanclass="comment">// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.</span></div>
<divclass="line"><aid="l00011"name="l00011"></a><spanclass="lineno"> 11</span><spanclass="comment">// See the License for the specific language governing permissions and</span></div>
<divclass="line"><aid="l00012"name="l00012"></a><spanclass="lineno"> 12</span><spanclass="comment">// limitations under the License.</span></div>
<divclass="line"><aid="l00035"name="l00035"></a><spanclass="lineno"> 35</span><spanclass="comment">// For a given set of intervals and demands, we compute the energy of</span></div>
<divclass="line"><aid="l00036"name="l00036"></a><spanclass="lineno"> 36</span><spanclass="comment">// each task and make sure their sum fits in the span of the intervals * its</span></div>
<divclass="line"><aid="l00039"name="l00039"></a><spanclass="lineno"> 39</span><spanclass="comment">// If an interval is optional, it contributes</span></div>
<divclass="line"><aid="l00043"name="l00043"></a><spanclass="lineno"> 43</span><spanclass="comment">// If an interval is performed, we use the linear energy formulation (if</span></div>
<divclass="line"><aid="l00044"name="l00044"></a><spanclass="lineno"> 44</span><spanclass="comment">// defined, that is if different from a constant -1), or the McCormick</span></div>
<divclass="line"><aid="l00045"name="l00045"></a><spanclass="lineno"> 45</span><spanclass="comment">// relaxation of the product size * demand if not defined.</span></div>
<divclass="line"><aid="l00047"name="l00047"></a><spanclass="lineno"> 47</span><spanclass="comment">// The maximum energy is capacity * span of intervals at level 0.</span></div>
<divclass="line"><aid="l00054"name="l00054"></a><spanclass="lineno"> 54</span><spanclass="comment">// For a given set of intervals and demands, we first compute the mandatory part</span></div>
<divclass="line"><aid="l00055"name="l00055"></a><spanclass="lineno"> 55</span><spanclass="comment">// of the interval as [start_max , end_min]. We use this to calculate mandatory</span></div>
<divclass="line"><aid="l00056"name="l00056"></a><spanclass="lineno"> 56</span><spanclass="comment">// demands for each start_max time points for eligible intervals.</span></div>
<divclass="line"><aid="l00057"name="l00057"></a><spanclass="lineno"> 57</span><spanclass="comment">// Since the sum of these mandatory demands must be smaller or equal to the</span></div>
<divclass="line"><aid="l00058"name="l00058"></a><spanclass="lineno"> 58</span><spanclass="comment">// capacity, we create a cut representing that.</span></div>
<divclass="line"><aid="l00060"name="l00060"></a><spanclass="lineno"> 60</span><spanclass="comment">// If an interval is optional, it contributes min_demand * presence_literal</span></div>
<divclass="line"><aid="l00061"name="l00061"></a><spanclass="lineno"> 61</span><spanclass="comment">// amount of demand to the mandatory demands sum. So the final cut is generated</span></div>
<divclass="line"><aid="l00062"name="l00062"></a><spanclass="lineno"> 62</span><spanclass="comment">// as follows:</span></div>
<divclass="line"><aid="l00063"name="l00063"></a><spanclass="lineno"> 63</span><spanclass="comment">// sum(demands of always present intervals)</span></div>
<divclass="line"><aid="l00070"name="l00070"></a><spanclass="lineno"> 70</span><spanclass="comment">// Completion time cuts for the cumulative constraint. It is a simple relaxation</span></div>
<divclass="line"><aid="l00071"name="l00071"></a><spanclass="lineno"> 71</span><spanclass="comment">// where we replace a cumulative task with demand k and duration d by a</span></div>
<divclass="line"><aid="l00072"name="l00072"></a><spanclass="lineno"> 72</span><spanclass="comment">// no_overlap task with duration d * k / capacity_max.</span></div>
<divclass="line"><aid="l00079"name="l00079"></a><spanclass="lineno"> 79</span><spanclass="comment">// For a given set of intervals in a cumulative constraint, we detect violated</span></div>
<divclass="line"><aid="l00080"name="l00080"></a><spanclass="lineno"> 80</span><spanclass="comment">// mandatory precedences and create a cut for these.</span></div>
<divclass="line"><aid="l00086"name="l00086"></a><spanclass="lineno"> 86</span><spanclass="comment">// Completion time cuts for the no_overlap_2d constraint. It actually generates</span></div>
<divclass="line"><aid="l00087"name="l00087"></a><spanclass="lineno"> 87</span><spanclass="comment">// the completion time cumulative cuts in both axis.</span></div>
<divclass="line"><aid="l00092"name="l00092"></a><spanclass="lineno"> 92</span><spanclass="comment">// Energetic cuts for the no_overlap_2d constraint.</span></div>
<divclass="line"><aid="l00094"name="l00094"></a><spanclass="lineno"> 94</span><spanclass="comment">// For a given set of rectangles, we compute the area of each rectangle</span></div>
<divclass="line"><aid="l00095"name="l00095"></a><spanclass="lineno"> 95</span><spanclass="comment">// and make sure their sum is less than the area of the bounding interval.</span></div>
<divclass="line"><aid="l00097"name="l00097"></a><spanclass="lineno"> 97</span><spanclass="comment">// If an interval is optional, it contributes</span></div>
<divclass="line"><aid="l00101"name="l00101"></a><spanclass="lineno"> 101</span><spanclass="comment">// If an interval is performed, we use the linear area formulation (if</span></div>
<divclass="line"><aid="l00102"name="l00102"></a><spanclass="lineno"> 102</span><spanclass="comment">// possible), or the McCormick relaxation of the size_x * size_y.</span></div>
<divclass="line"><aid="l00104"name="l00104"></a><spanclass="lineno"> 104</span><spanclass="comment">// The maximum area is the area of the bounding rectangle of each intervals</span></div>
<divclass="line"><aid="l00105"name="l00105"></a><spanclass="lineno"> 105</span><spanclass="comment">// at level 0.</span></div>
<divclass="line"><aid="l00110"name="l00110"></a><spanclass="lineno"> 110</span><spanclass="comment">// For a given set of intervals, we first compute the min and max of all</span></div>
<divclass="line"><aid="l00111"name="l00111"></a><spanclass="lineno"> 111</span><spanclass="comment">// intervals. Then we create a cut that indicates that all intervals must fit</span></div>
<divclass="line"><aid="l00112"name="l00112"></a><spanclass="lineno"> 112</span><spanclass="comment">// in that span.</span></div>
<divclass="line"><aid="l00114"name="l00114"></a><spanclass="lineno"> 114</span><spanclass="comment">// If an interval is optional, it contributes min_size * presence_literal</span></div>
<divclass="line"><aid="l00115"name="l00115"></a><spanclass="lineno"> 115</span><spanclass="comment">// amount of demand to the mandatory demands sum. So the final cut is generated</span></div>
<divclass="line"><aid="l00116"name="l00116"></a><spanclass="lineno"> 116</span><spanclass="comment">// as follows:</span></div>
<divclass="line"><aid="l00117"name="l00117"></a><spanclass="lineno"> 117</span><spanclass="comment">// sum(sizes of always present intervals)</span></div>
<divclass="line"><aid="l00118"name="l00118"></a><spanclass="lineno"> 118</span><spanclass="comment">// + sum(presence_literal * min_of_size) <= span of all intervals.</span></div>
<divclass="line"><aid="l00122"name="l00122"></a><spanclass="lineno"> 122</span><spanclass="comment">// For a given set of intervals in a no_overlap constraint, we detect violated</span></div>
<divclass="line"><aid="l00123"name="l00123"></a><spanclass="lineno"> 123</span><spanclass="comment">// mandatory precedences and create a cut for these.</span></div>
<divclass="line"><aid="l00127"name="l00127"></a><spanclass="lineno"> 127</span><spanclass="comment">// For a given set of intervals in a no_overlap constraint, we detect violated</span></div>
<divclass="line"><aid="l00128"name="l00128"></a><spanclass="lineno"> 128</span><spanclass="comment">// area based cuts from Queyranne 93 [see note in the code] and create a cut for</span></div>
<divclass="ttc"id="anamespaceoperations__research_html"><divclass="ttname"><ahref="namespaceoperations__research.html">operations_research</a></div><divclass="ttdoc">Collection of objects used to extend the Constraint Solver library.</div><divclass="ttdef"><b>Definition:</b><ahref="dense__doubly__linked__list_8h_source.html#l00021">dense_doubly_linked_list.h:21</a></div></div>
