A Supply Chain-Logistics Super-Network Equilibrium Model for Urban Logistics Facility Network Optimization

<table class="fixed-width table-group" id="tab12"><tr><td><table class="table"><colgroup><col style="width:5.21em"/><col style="width:5.02em"/><col style="width:5.15em"/><col style="width:5.02em"/><col style="width:5.15em"/></colgroup><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2"><span style="width: 15.6807ptpx;"><svg height="18.4396pt" id="M136" style="vertical-align:-6.1814pt" version="1.1" viewbox="-0.0498162 -12.2582 15.6807 18.4396" width="15.6807pt" 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="M474 429L457 433C435 440 389 448 367 448C348 448 323 446 309 443C266 434 195 406 148 366C78 307 23 210 23 101C23 35 55 -12 92 -12C118 -12 146 1 196 35C247 70 311 130 346 173H348L281 -148C268 -211 256 -221 208 -229L191 -232L187 -257L433 -245L437 -219L411 -216C357 -210 350 -205 362 -140L427 207C447 315 461 381 474 429ZM387 387C379 337 363 262 355 236C318 180 201 57 142 57C126 57 112 81 112 128C112 205 150 321 220 376C244 395 280 403 312 403C345 403 370 396 387 387Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.383,-5.741)"><path d="M509 90L493 118C465 91 427 70 418 70S409 77 415 103L469 327C494 429 466 451 436 451C412 451 387 444 356 427C307 400 222 342 160 264H158L246 667C253 701 252 710 243 710C228 710 169 680 87 673L83 644H117C155 644 160 640 149 588L24 -4L32 -12C57 -4 86 4 108 9L143 187C198 275 324 386 375 386C394 386 399 367 385 311L331 87C315 22 322 -12 351 -12C387 -12 452 24 509 90Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.318,3.784)"><path d="M400 606C400 634 383 656 353 656C316 656 294 620 294 593C294 564 317 545 343 545C375 545 400 573 400 606ZM366 351C379 413 381 451 356 451C323 451 251 408 183 341L199 313C223 335 267 365 277 365C285 365 284 354 277 312C245 132 222 27 193 -100C182 -148 160 -188 131 -188C113 -188 90 -178 75 -170C64 -164 55 -168 48 -175C38 -185 24 -203 24 -222S48 -257 71 -257C89 -257 131 -241 186 -192C243 -141 286 -46 310 74L366 351Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,10.396,3.784)"><path d="M485 418C485 434 469 451 441 451C389 451 312 387 255 335C221 304 194 278 159 242H157L259 678C264 698 264 710 255 710C242 710 183 681 96 673L90 643L128 642C165 641 171 640 162 602L24 -5L31 -12C51 -4 81 4 110 9L145 181C154 195 180 220 205 242C233 170 263 106 291 53C318 1 335 -12 360 -12C383 -12 425 0 483 82L463 105C437 79 411 57 400 57C388 57 378 68 355 110C329 156 288 244 268 298C299 333 355 376 405 376C426 376 440 373 448 368C453 365 465 368 468 373C477 386 485 405 485 418Z"></path></g></svg></span></td><td class="align_center" colspan="2">retailer 1</td><td class="align_center" colspan="2">retailer 2</td></tr><tr class="thead"><td class="align_center">product 1</td><td class="align_center">product 2</td><td class="align_center">product 1</td><td class="align_center">product 2</td></tr><tr><td class="thead-hr" colspan="5"><hr/></td></tr><tr><td class="align_left">supplier 1</td><td class="align_center">5.62</td><td class="align_center">11.28</td><td class="align_center">5.62</td><td class="align_center">11.28</td></tr><tr><td class="align_left">supplier 2</td><td class="align_center">5.62</td><td class="align_center">0</td><td class="align_center">5.62</td><td class="align_center">0</td></tr><tr class="table-tr"><td colspan="5"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>The shipments between suppliers and retailers.</div>

Mathematical Problems in Engineering

tab12

Table 12

Table 12: A Supply Chain-Logistics Super-Network Equilibrium Model for Urban Logistics Facility Network Optimization 