A Column Generation Algorithm for the Resource-Constrained Order Acceptance and Scheduling on Unrelated Parallel Machines

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="8"><hr/></td></tr><tr class="thead"><td class="align_center" colspan="2">Parameter (factor)</td><td class="align_center"><i>NP</i></td><td class="align_center"><i>F</i></td><td class="align_center"><i>CR</i></td><td class="align_center"><span style="width: 37.0481ptpx;"><svg height="11.9316pt" id="M54" style="vertical-align:-3.2957pt" version="1.1" viewbox="-0.0498162 -8.6359 37.0481 11.9316" width="37.0481pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M405 650H141L135 622C222 616 230 610 215 535L133 116C118 41 113 33 29 28L23 0H289L295 28C209 33 205 40 219 116L298 535C312 609 317 616 399 622L405 650Z"></path></g><g transform="matrix(.013,0,0,-0.013,5.567,0)"><path d="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 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629Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,40.259,3.132)"><path d="M722 297H451L442 267C561 257 561 253 547 182L531 98C521 44 465 24 390 24C228 24 130 134 130 296C130 482 252 628 465 628C592 628 657 579 656 458L692 461C695 540 699 605 702 631C664 642 590 667 492 667C203 667 24 502 24 285C24 93 170 -17 368 -17C464 -17 543 11 617 28C613 43 612 68 620 106L635 182C649 255 652 258 716 268L722 297Z"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="8"><hr/></td></tr><tr><td class="align_left" rowspan="5">Level</td><td class="align_center">1</td><td class="align_center">10</td><td class="align_center">0.2</td><td class="align_center">0.25</td><td class="align_center">100</td><td class="align_center">10</td><td class="align_center">5</td></tr><tr><td class="align_center">2</td><td class="align_center">15</td><td class="align_center">0.4</td><td class="align_center">0.50</td><td class="align_center">200</td><td class="align_center">25</td><td class="align_center">10</td></tr><tr><td class="align_center">3</td><td class="align_center">20</td><td class="align_center">0.6</td><td class="align_center">0.75</td><td class="align_center">300</td><td class="align_center">50</td><td class="align_center">20</td></tr><tr><td class="align_center">4</td><td class="align_center">25</td><td class="align_center">0.8</td><td class="align_center">0.95</td><td class="align_center">400</td><td class="align_center">75</td><td class="align_center">30</td></tr><tr><td class="align_center">5</td><td class="align_center">30</td><td class="align_center">1</td><td class="align_center">1</td><td class="align_center">500</td><td class="align_center">100</td><td class="align_center">40</td></tr><tr class="table-tr"><td colspan="8"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Mathematical Problems in Engineering

tab2

Table 2

Table 2: A Column Generation Algorithm for the Resource-Constrained Order Acceptance and Scheduling on Unrelated Parallel Machines 