Application of Hierarchical Facility Location-Routing Problem with Optimization of an Underground Logistic System: A Case Study in China

<table class="fixed-width table-group" id="tab3"><tr><td><table class="table"><colgroup><col style="width:8.38em"/><col style="width:2.07em"/><col style="width:3.77em"/><col style="width:2.23em"/><col style="width:3.60em"/></colgroup><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left"> </td><td class="align_center" colspan="2"><b>20 nodes</b></td><td class="align_center" colspan="2"><b>30 nodes</b></td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left"><b>model</b></td><td class="align_center"><span style="width: 8.41168ptpx;"><svg height="9.01194pt" id="M189" 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" id="g113-85"></path></g></svg></span></td><td class="align_center"><span style="width: 8.02022ptpx;"><svg height="8.68572pt" id="M190" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 8.02022 8.68572" width="8.02022pt" 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="M584 650H137L131 622C214 614 217 612 200 521L125 127C109 41 101 35 23 28L17 0H288L294 28C201 35 193 42 209 128L242 309H348C440 309 442 300 443 226H471L510 422H482C452 354 449 348 357 348H251L295 575C302 609 304 615 338 615H426C502 615 517 604 526 581C534 560 536 524 537 492L565 494C574 554 583 631 584 650Z" id="g113-71"></path></g></svg></span></td><td class="align_center"><span style="width: 8.41168ptpx;"><svg height="9.01194pt" id="M191" 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" id="g113-85"></path></g></svg></span></td><td class="align_center"><span style="width: 8.02022ptpx;"><svg height="8.68572pt" id="M192" style="vertical-align:-0.0498209pt" version="1.1" viewbox="-0.0498162 -8.6359 8.02022 8.68572" width="8.02022pt" 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="M584 650H137L131 622C214 614 217 612 200 521L125 127C109 41 101 35 23 28L17 0H288L294 28C201 35 193 42 209 128L242 309H348C440 309 442 300 443 226H471L510 422H482C452 354 449 348 357 348H251L295 575C302 609 304 615 338 615H426C502 615 517 604 526 581C534 560 536 524 537 492L565 494C574 554 583 631 584 650Z" id="g113-71"></path></g></svg></span></td></tr><tr><td class="align_left" colspan="5"><hr/></td></tr><tr><td class="align_left"><b>Primary nodes</b></td><td class="align_center">5</td><td class="align_center">5</td><td class="align_center">6</td><td class="align_center">6</td></tr><tr><td class="align_left" colspan="5"><hr/></td></tr><tr><td class="align_left"><b>Secondary nodes</b></td><td class="align_center">15</td><td class="align_center">9</td><td class="align_center">24</td><td class="align_center">14</td></tr><tr><td class="align_left" colspan="5"><hr/></td></tr><tr><td class="align_left"><b>Tertiary nodes</b></td><td class="align_center">0</td><td class="align_center">6</td><td class="align_center">0</td><td class="align_center">14</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Node composition of two algorithms.</div>

Mathematical Problems in Engineering

tab3

Table 3

Table 3: Application of Hierarchical Facility Location-Routing Problem with Optimization of an Underground Logistic System: A Case Study in China 