An Integrated Multiechelon Logistics Model with Uncertain Delivery Lead Time and Quality Unreliability

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_center" colspan="4">Manufacturing activities</td></tr><tr class="thead"><td class="align_left">Echelon</td><td class="align_center"><span style="width: 9.83627ptpx;"><svg height="11.927pt" id="M221" style="vertical-align:-3.291101pt" version="1.1" viewbox="-0.0498162 -8.6359 9.83627 11.927" width="9.83627pt" 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="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z" id="g113-81"></path><glyph.data ascent="3473" descent="-2876" 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10C543 39 590 127 606 167L580 181C519 89 459 18 348 18C201 18 122 136 122 287C122 464 244 632 435 632C544 632 602 595 608 472L639 475C643 526 645 581 645 631Z" id="g113-68"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="668" vert-adv-y="668"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,8.619,3.132)"><path d="M781 91L765 118C733 86 702 70 693 70C686 70 685 77 692 106L738 297C772 439 736 451 712 451S675 445 647 431C605 410 526 356 452 257H450L459 294C491 426 459 451 429 451C403 451 386 445 361 431C312 404 239 343 170 253H168L188 333C208 411 205 451 175 451C148 451 85 417 24 346L39 318C57 338 100 374 112 374C120 374 122 372 115 339C91 226 62 112 28 -6L37 -12C59 -4 87 3 114 6C125 68 142 127 154 168C184 227 316 383 372 383C397 383 396 366 381 289C362 192 338 92 312 -6L317 -12C339 -5 367 3 396 6L434 170C468 234 598 383 650 383C668 383 676 369 664 319L609 90C593 23 600 -12 629 -12C654 -12 722 23 781 91Z" id="g50-110"></path><glyph.data ascent="3443" descent="-2856" 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650H132L126 622C211 615 214 609 198 524L121 122C106 42 102 35 23 28L17 0H276L282 28C196 35 191 40 206 122L243 324H597L559 123C544 42 537 35 452 28L446 0H710L716 28C632 35 628 43 643 122L719 524C735 610 741 615 822 622L828 650Z" id="g113-73"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="840" vert-adv-y="840"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,10.075,3.132)"><path d="M781 91L765 118C733 86 702 70 693 70C686 70 685 77 692 106L738 297C772 439 736 451 712 451S675 445 647 431C605 410 526 356 452 257H450L459 294C491 426 459 451 429 451C403 451 386 445 361 431C312 404 239 343 170 253H168L188 333C208 411 205 451 175 451C148 451 85 417 24 346L39 318C57 338 100 374 112 374C120 374 122 372 115 339C91 226 62 112 28 -6L37 -12C59 -4 87 3 114 6C125 68 142 127 154 168C184 227 316 383 372 383C397 383 396 366 381 289C362 192 338 92 312 -6L317 -12C339 -5 367 3 396 6L434 170C468 234 598 383 650 383C668 383 676 369 664 319L609 90C593 23 600 -12 629 -12C654 -12 722 23 781 91Z" id="g50-110"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="805" vert-adv-y="805"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,17.647,3.132)"><path d="M250 606C250 634 233 656 203 656C168 656 146 618 146 593C146 564 169 545 192 545C227 545 250 573 250 606ZM227 95L212 119C187 98 152 71 135 71C129 71 128 78 134 102L207 373C219 418 217 451 194 451C165 451 92 411 30 351L44 326C77 353 106 371 114 371C124 371 121 357 117 341L55 97C32 5 46 -12 70 -12C108 -12 191 51 227 95Z" id="g50-106"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="280" vert-adv-y="280"></glyph.data></g></svg></span></td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left">1</td><td class="align_center">—</td><td class="align_center">—</td><td class="align_center">—</td></tr><tr><td class="align_left">2</td><td class="align_center">200000</td><td class="align_center">280</td><td class="align_center">2.5</td></tr><tr><td class="align_left">3</td><td class="align_center">240000</td><td class="align_center">200</td><td class="align_center">1.9</td></tr><tr><td class="align_left">4</td><td class="align_center">300000</td><td class="align_center">320</td><td class="align_center">1.4</td></tr><tr><td class="align_left">5</td><td class="align_center">350000</td><td class="align_center">360</td><td class="align_center">1.0</td></tr><tr><td class="align_left">6</td><td class="align_center">400000</td><td class="align_center">380</td><td class="align_center">0.9</td></tr><tr><td class="align_left">7</td><td class="align_center">450000</td><td class="align_center">420</td><td class="align_center">0.5</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

The relevant data of manufacturing activities.

Mathematical Problems in Engineering

tab2

Table 2

Table 2: An Integrated Multiechelon Logistics Model with Uncertain Delivery Lead Time and Quality Unreliability 