A Genetic Algorithm for a Two-Machine Flowshop with a Limited Waiting Time Constraint and Sequence-Dependent Setup Times

<table class="table-group" id="tab5"><tr><td><table class="table"><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left"><span style="width: 8.41168ptpx;"><svg height="9.01194pt" id="M186" style="vertical-align:-0.04981995pt" version="1.1" viewbox="-0.0498162 -8.96212 8.41168 9.01194" width="8.41168pt" 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="M620 675H597C578 656 570 650 541 650H144C112 650 104 653 94 675H72C59 618 42 552 23 493L53 491C71 534 88 564 105 585C124 608 144 615 238 615H290L197 121C182 40 174 34 88 28L82 0H361L367 28C275 34 266 38 281 121L374 615H441C522 615 543 608 553 583C562 560 566 531 565 493L597 494C603 551 612 629 620 675Z"></path></g></svg></span></td><td class="align_center"><span style="width: 38.7064ptpx;"><svg height="8.8423pt" id="M187" style="vertical-align:-0.2064009pt" version="1.1" viewbox="-0.0498162 -8.6359 38.7064 8.8423" width="38.7064pt" 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="M610 18C585 26 567 34 540 68C517 97 499 128 476 171C452 215 425 276 413 304C496 332 570 394 570 494C570 555 545 595 509 619S419 650 364 650H139L133 622C216 615 219 612 203 527L129 132C112 40 105 36 23 28L17 0H279L285 28C199 34 194 40 211 132L239 284H284C320 284 334 275 351 236C374 182 394 140 420 93C459 23 495 -1 592 -8H600L610 18ZM480 485C480 424 449 372 403 342C374 323 338 316 293 316H245L291 562C296 589 301 601 311 608S337 618 358 618C432 618 480 575 480 485Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.783,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,23.046,0)"><path d="M241 635C89 635 35 457 35 312C35 153 89 -12 240 -12C390 -12 443 166 443 312C443 466 390 635 241 635ZM238 602C329 602 354 454 354 312C354 172 330 22 240 22C152 22 124 173 124 313S148 602 238 602Z"></path></g><g transform="matrix(.013,0,0,-0.013,29.286,0)"><path d="M113 -12C146 -12 170 11 170 46C170 78 146 103 114 103S58 78 58 46C58 11 82 -12 113 -12Z"></path></g><g transform="matrix(.013,0,0,-0.013,32.25,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z"></path></g></svg></span></td><td class="align_center">0.5</td><td class="align_center">0.8</td><td class="align_center">Average</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left">0.2</td><td class="align_center">1435.14</td><td class="align_center">1580.84</td><td class="align_center">2313.12</td><td class="align_center">1776.37</td></tr><tr><td class="align_left">0.4</td><td class="align_center">2172.74</td><td class="align_center">2473.35</td><td class="align_center">880.95</td><td class="align_center">1842.35</td></tr><tr><td class="align_left">0.6</td><td class="align_center">905.23</td><td class="align_center">255.19</td><td class="align_center">759.17</td><td class="align_center">639.86</td></tr><tr><td class="align_left">Average</td><td class="align_center">1504.37</td><td class="align_center">1436.46</td><td class="align_center">1317.75</td><td class="align_center">1419.53</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Effect of due date parameters on the performance of CPLEX.</div>

Mathematical Problems in Engineering

tab5

Table 5

Table 5: A Genetic Algorithm for a Two-Machine Flowshop with a Limited Waiting Time Constraint and Sequence-Dependent Setup Times 