Integrated Yard Space Allocation and Yard Crane Deployment Problem in Resource-Limited Container Terminals

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="9"><hr/></td></tr><tr class="thead"><td class="align_left">Parameters</td><td class="align_center"><span style="width: 23.0572ptpx;"><svg height="14.9569pt" id="M110" style="vertical-align:-3.429399pt" version="1.1" viewbox="-0.0498162 -11.5275 23.0572 14.9569" width="23.0572pt" 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="M538 96L524 119C492 88 454 63 446 63C439 63 434 70 440 101C463 223 491 341 518 448H508L433 422L401 276C355 192 240 56 188 56C163 56 154 89 163 133C184 233 207 338 235 443L230 448L152 424L58 17C40 -60 23 -143 23 -185C23 -241 42 -261 63 -261C92 -261 117 -241 125 -227L124 -221C109 -209 89 -165 89 -103C89 -55 96 -13 105 26H107C121 -3 134 -12 151 -12C172 -12 194 -5 221 16C279 61 330 124 384 194H386C381 159 377 141 368 105C343 3 363 -12 383 -12C416 -12 486 35 538 96Z" id="g113-234"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="555" vert-adv-y="555"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.216,-5.741)"><path d="M810 0V30C751 35 744 40 744 106V296C744 396 694 451 614 451C583 451 558 438 537 425C512 409 485 391 454 368C434 420 390 451 342 451C309 451 285 439 260 424C228 405 206 387 185 372V453C141 434 90 421 43 413V386C102 378 105 373 105 309V106C105 41 96 35 29 30V0H243V30C194 35 185 41 185 106V335C216 360 256 389 297 389C357 389 384 348 384 275V106C384 41 374 35 312 30V0H530V30C475 35 465 41 465 104V294C465 313 464 324 463 336C502 367 539 389 576 389C637 389 663 346 663 274V109C663 41 653 35 593 30V0H810Z" id="g58-107"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="834" vert-adv-y="834"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,14.806,-5.741)"><path d="M138 535C169 535 191 560 191 589C191 620 168 644 139 644S85 620 85 589C85 560 110 535 138 535ZM257 0V30C192 35 185 43 185 109V453C142 435 94 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transform="matrix(.013,0,0,-0.013,0,0)"><path d="M538 96L524 119C492 88 454 63 446 63C439 63 434 70 440 101C463 223 491 341 518 448H508L433 422L401 276C355 192 240 56 188 56C163 56 154 89 163 133C184 233 207 338 235 443L230 448L152 424L58 17C40 -60 23 -143 23 -185C23 -241 42 -261 63 -261C92 -261 117 -241 125 -227L124 -221C109 -209 89 -165 89 -103C89 -55 96 -13 105 26H107C121 -3 134 -12 151 -12C172 -12 194 -5 221 16C279 61 330 124 384 194H386C381 159 377 141 368 105C343 3 363 -12 383 -12C416 -12 486 35 538 96Z" id="g113-234"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="555" vert-adv-y="555"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,7.216,-5.741)"><path d="M810 0V30C751 35 744 40 744 106V296C744 396 694 451 614 451C583 451 558 438 537 425C512 409 485 391 454 368C434 420 390 451 342 451C309 451 285 439 260 424C228 405 206 387 185 372V453C141 434 90 421 43 413V386C102 378 105 373 105 309V106C105 41 96 35 29 30V0H243V30C194 35 185 41 185 106V335C216 360 256 389 297 389C357 389 384 348 384 275V106C384 41 374 35 312 30V0H530V30C475 35 465 41 465 104V294C465 313 464 324 463 336C502 367 539 389 576 389C637 389 663 346 663 274V109C663 41 653 35 593 30V0H810Z" id="g58-107"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="834" vert-adv-y="834"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,14.778,-5.741)"><path d="M442 39L431 68C420 63 406 57 394 57C377 57 359 71 359 118V301C359 353 349 393 314 424C291 443 261 451 230 451C171 438 107 401 79 381C59 366 46 355 46 340C46 316 72 295 91 295C106 295 117 303 122 319C131 350 139 371 152 384C163 397 178 404 197 404C246 404 281 365 281 293V278C260 262 186 232 124 213C69 194 41 161 41 112C41 47 92 -12 163 -12C195 -12 243 25 283 51C288 35 293 22 308 7C319 -4 339 -12 354 -12L442 39ZM281 87C262 68 226 51 199 51C169 51 129 74 129 126C129 162 151 181 190 198C211 208 259 229 281 240V87Z" id="g58-95"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="449" vert-adv-y="449"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,18.864,-5.741)"><path d="M482 0V30C420 38 407 48 370 103L273 248C308 299 331 332 352 357C387 397 401 404 463 409V439H277V409C318 405 324 400 307 369C290 337 270 307 251 279L194 367C175 396 180 402 220 409V439H18V409C74 401 87 395 117 349L204 213C173 168 147 130 119 95C78 46 67 38 5 30V0H195V30C144 38 143 47 162 79C181 112 202 149 225 181L297 70C314 43 307 35 264 30V0H482Z" id="g58-118"></path><glyph.data ascent="1007" descent="-369" horiz-adv-x="481" vert-adv-y="481"></glyph.data></g></svg></span></td><td class="align_center"><span style="width: 11.71ptpx;"><svg height="12.4646pt" id="M112" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -12.2582 11.71 12.4646" width="11.71pt" 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="M494 514C482 587 419 712 303 712C238 712 174 667 174 603C174 561 205 514 249 449C219 438 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vert-adv-y="478"></glyph.data></g></svg></span></td><td class="align_center"><span style="width: 11.2442ptpx;"><svg height="10.1628pt" id="M113" style="vertical-align:-0.2064095pt" version="1.1" viewbox="-0.0498162 -9.95639 11.2442 10.1628" width="11.2442pt" 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="M494 514C482 587 419 712 303 712C238 712 174 667 174 603C174 561 205 514 249 449C219 438 187 422 162 407C93 366 23 283 23 177C23 69 87 -12 190 -12C244 -12 288 5 328 33C406 87 444 170 444 249C444 329 404 391 331 475C265 550 222 605 222 627C222 647 238 657 267 657C355 657 421 585 484 499L494 514ZM359 234C359 143 319 30 219 30C172 30 114 75 114 178C114 275 163 343 195 378C212 397 241 415 269 425C305 382 359 313 359 234Z" id="g113-226"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="517" vert-adv-y="517"></glyph.data></g><g transform="matrix(.0091,0,0,-0.0091,6.722,-5.741)"><path d="M397 380C406 395 404 411 396 425S369 451 350 451C302 451 239 372 192 294H189L199 338C214 407 207 451 180 451C152 451 83 405 30 345L48 318C87 354 117 372 125 372S135 362 127 324L55 -5L61 -12C87 -5 117 3 139 5C154 87 168 162 179 207C198 250 240 310 260 332C281 355 297 366 307 366C321 366 333 360 347 346C351 342 360 342 369 348C379 355 389 366 397 380Z" id="g50-115"></path><glyph.data ascent="3443" descent="-2856" horiz-adv-x="427" vert-adv-y="427"></glyph.data></g></svg></span></td><td class="align_center"><span style="width: 7.69399ptpx;"><svg height="9.39034pt" id="M114" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 7.69399 9.39034" width="7.69399pt" 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="M559 271C559 395 493 448 433 448C370 448 304 394 275 297C259 245 235 121 219 37C157 54 113 110 113 201C113 310 180 386 276 429L265 457C131 410 23 326 23 186C23 83 86 5 211 -10C180 -159 167 -220 158 -252L165 -261C198 -255 236 -246 251 -218L287 -5C421 9 559 119 559 271ZM484 273C484 144 400 40 293 33L352 331C364 389 382 406 405 406C431 406 484 370 484 273Z" id="g113-253"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="582" vert-adv-y="582"></glyph.data></g></svg></span></td><td class="align_center"><span style="width: 7.13289ptpx;"><svg height="9.39034pt" id="M115" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -5.96091 7.13289 9.39034" width="7.13289pt" 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="M516 277C516 378 460 448 376 448C335 448 288 434 240 401C158 345 127 277 107 159C53 -161 38 -221 23 -247L28 -261C43 -260 95 -250 114 -226C122 -216 129 -199 146 -75C152 -29 157 0 164 31C182 9 206 -12 237 -12C267 -12 325 8 376 46C451 102 516 179 516 277ZM432 259C432 134 366 40 259 40C236 40 204 48 171 76L195 203C219 327 253 400 326 400C398 400 432 336 432 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7.81142ptpx;"><svg height="6.1673pt" id="M117" style="vertical-align:-0.2063904pt" version="1.1" viewbox="-0.0498162 -5.96091 7.81142 6.1673" width="7.81142pt" 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="M574 449L545 460C526 432 516 430 487 430C404 430 311 435 226 435C104 435 56 379 25 341L43 318C81 354 121 372 181 372C161 246 87 53 23 3L30 -12C48 -12 88 -4 113 11C157 75 207 248 232 371L386 367L326 109C321 86 318 66 318 50C318 4 339 -12 366 -12C410 -12 461 21 505 69L492 96C467 79 434 60 418 60C406 60 400 78 411 147C422 217 439 300 457 366C487 366 524 367 536 370C547 385 558 408 574 449Z" id="g113-238"></path><glyph.data ascent="3473" descent="-2876" horiz-adv-x="591" vert-adv-y="591"></glyph.data></g></svg></span></td></tr><tr><td class="thead-hr" colspan="9"><hr/></td></tr><tr><td class="align_left">Value</td><td class="align_center">2</td><td class="align_center">3</td><td class="align_center">2</td><td class="align_center">6</td><td class="align_center">15</td><td class="align_center">2.4</td><td class="align_center">0.5</td><td class="align_center">200</td></tr><tr class="table-tr"><td colspan="9"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Configuration parameters of yard crane and intertruck.

Scientific Programming

tab2

Table 2

Table 2: Integrated Yard Space Allocation and Yard Crane Deployment Problem in Resource-Limited Container Terminals 