The Effect of Welding on the One-Dimensional Cutting-Stock Problem: The Case of Fixed Firefighting Systems in the Construction Industry

<table class="fixed-width table-group" id="tab1"><tr><td><table class="table"><colgroup><col style="width:9.81em"/><col style="width:8.88em"/></colgroup><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td class="align_center" colspan="2">Stock size (<span class="nowrap"><svg height="11.8174pt" id="M1" style="vertical-align:-3.1815pt" version="1.1" viewbox="-0.0498162 -8.6359 11.1398 11.8174" width="11.1398pt" 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="M449 634C442 637 425 643 405 650C376 660 341 666 307 666C181 666 98 590 98 485C98 400 170 343 215 310L246 288C307 243 343 204 343 147C343 67 291 18 219 18C104 18 61 124 51 202L23 199C28 124 27 71 27 47C47 22 122 -16 204 -16C324 -16 428 60 428 174C428 256 379 309 307 360L276 382C223 419 179 455 179 516C179 576 221 632 293 632C379 632 410 564 418 487L448 490C446 536 446 592 449 634Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.071,3.132)"><path d="M389 0V32C297 38 291 46 291 118V635C234 613 175 595 109 583V556L161 554C203 552 207 547 207 497V118C207 46 201 38 110 32V0H389Z"></path></g></svg>,</span> in mm)</td></tr><tr class="thead"><td class="align_center" colspan="2">6000</td></tr><tr class="thead"><td class="align_center">Pipe sizes (<span class="nowrap"><svg height="9.25202pt" id="M2" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 7.98334 9.25202" width="7.98334pt" 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="M352 391C352 416 319 448 267 448C236 448 173 423 147 400C107 364 96 332 96 304C96 248 143 210 193 181C241 153 258 124 258 100C258 72 232 38 184 38C151 38 107 66 81 108C77 114 64 116 55 111C34 99 23 84 23 65C23 29 81 -12 134 -12C220 -12 325 61 325 141C325 184 297 215 234 256C194 282 161 309 161 346C161 380 188 401 217 401C255 401 279 380 301 353C308 344 313 341 325 347C341 355 352 371 352 391Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,4.81,3.132)"><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"></path></g></svg>,</span> in mm)</td><td class="align_center">Pipe quantities (<span class="nowrap"><svg height="9.25202pt" id="M3" style="vertical-align:-3.29111pt" version="1.1" viewbox="-0.0498162 -5.96091 9.64053 9.25202" width="9.64053pt" 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="M495 86L479 114C446 82 419 66 409 66C401 66 401 72 406 97C420 166 436 231 453 297C489 435 454 448 428 448C406 448 384 439 354 422C305 394 222 327 161 247H159L183 345C200 415 194 448 173 448C143 448 82 410 23 351L38 325C64 349 95 371 105 371C111 371 116 365 109 336L25 -4L31 -12C50 -4 77 3 107 9C119 69 132 122 145 168C197 254 321 381 370 381C387 381 393 374 378 305L329 95C309 17 320 -12 345 -12C372 -12 430 19 495 86Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,6.461,3.132)"><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"></path></g></svg>)</span></td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td class="align_center">2000</td><td class="align_center">1</td></tr><tr><td class="align_center">4000</td><td class="align_center">1</td></tr><tr><td class="align_center">4500</td><td class="align_center">4</td></tr><tr><td class="align_center">4660</td><td class="align_center">2</td></tr><tr><td class="align_center">4680</td><td class="align_center">11</td></tr><tr><td class="align_center">5000</td><td class="align_center">1</td></tr><tr><td class="align_center">5096</td><td class="align_center">1</td></tr><tr><td class="align_center">5250</td><td class="align_center">1</td></tr><tr><td class="align_center">5260</td><td class="align_center">1</td></tr><tr><td class="align_center">5500</td><td class="align_center">1</td></tr><tr><td class="align_center">5660</td><td class="align_center">1</td></tr><tr><td class="align_center">6000</td><td class="align_center">2</td></tr><tr><td class="align_center">7000</td><td class="align_center">2</td></tr><tr><td class="align_center">7200</td><td class="align_center">2</td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Illustrative pipe sizes and quantities for the case of a Hungarian manufacturer of fixed firefighting systems.</div>

Advances in Operations Research

tab1

Table 1

Table 1: The Effect of Welding on the One-Dimensional Cutting-Stock Problem: The Case of Fixed Firefighting Systems in the Construction Industry 