Optimization of Production-Distribution Problem in Supply Chain Management under Stochastic and Fuzzy Uncertainties

<table class="table-group" id="tab16"><tr><td><table class="table"><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr class="thead"><td class="align_left" rowspan="2">Product</td><td class="align_center" colspan="2">Plant</td></tr><tr class="thead"><td class="align_center"><span style="width: 29.0242ptpx;"><svg height="11.7782pt" id="M519" style="vertical-align:-3.42938pt" version="1.1" viewbox="-0.0498162 -8.34882 29.0242 11.7782" width="29.0242pt" 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="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 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-142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z" id="g113-113"></path></g><g transform="matrix(.013,0,0,-0.013,11.342,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,22.605,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z" id="g113-51"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="3"><hr/></td></tr><tr><td class="align_left"><span style="width: 26.806ptpx;"><svg height="12.0653pt" id="M521" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -8.6359 26.806 12.0653" width="26.806pt" 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="M394 607C394 634 378 655 350 655C315 655 294 620 294 594C294 564 314 546 339 546C372 546 394 574 394 607ZM360 349C373 414 374 448 351 448C321 448 249 404 183 338L197 313C223 336 265 367 276 367C285 367 283 355 275 313C241 129 220 23 189 -102C175 -158 153 -197 124 -197C106 -197 85 -187 70 -177C64 -173 51 -177 44 -183C34 -193 23 -209 23 -228C23 -244 46 -261 67 -261C86 -261 127 -245 181 -197C237 -147 279 -52 303 66L360 349Z" id="g113-107"></path></g><g transform="matrix(.013,0,0,-0.013,9.132,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,20.395,0)"><path d="M384 0V27C293 34 287 42 287 114V635C232 613 172 594 109 583V559L157 557C201 555 205 550 205 499V114C205 42 199 34 109 27V0H384Z" id="g113-50"></path></g></svg></span></td><td class="align_center">6.15</td><td class="align_center">6.02</td></tr><tr><td class="align_left"><span style="width: 26.806ptpx;"><svg height="12.0653pt" id="M522" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -8.6359 26.806 12.0653" width="26.806pt" 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="M394 607C394 634 378 655 350 655C315 655 294 620 294 594C294 564 314 546 339 546C372 546 394 574 394 607ZM360 349C373 414 374 448 351 448C321 448 249 404 183 338L197 313C223 336 265 367 276 367C285 367 283 355 275 313C241 129 220 23 189 -102C175 -158 153 -197 124 -197C106 -197 85 -187 70 -177C64 -173 51 -177 44 -183C34 -193 23 -209 23 -228C23 -244 46 -261 67 -261C86 -261 127 -245 181 -197C237 -147 279 -52 303 66L360 349Z" id="g113-107"></path></g><g transform="matrix(.013,0,0,-0.013,9.132,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,20.395,0)"><path d="M412 140C382 77 369 73 315 73H129L270 222C362 320 402 379 402 466C402 571 322 635 234 635C177 635 130 609 99 576L42 495L64 475C90 514 133 568 201 568C274 568 318 519 318 435C318 349 255 267 193 193C144 135 87 78 32 23V0H405C417 45 427 89 440 131L412 140Z" id="g113-51"></path></g></svg></span></td><td class="align_center">6.92</td><td class="align_center">6.94</td></tr><tr><td class="align_left"><span style="width: 26.806ptpx;"><svg height="12.0653pt" id="M523" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -8.6359 26.806 12.0653" width="26.806pt" 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="M394 607C394 634 378 655 350 655C315 655 294 620 294 594C294 564 314 546 339 546C372 546 394 574 394 607ZM360 349C373 414 374 448 351 448C321 448 249 404 183 338L197 313C223 336 265 367 276 367C285 367 283 355 275 313C241 129 220 23 189 -102C175 -158 153 -197 124 -197C106 -197 85 -187 70 -177C64 -173 51 -177 44 -183C34 -193 23 -209 23 -228C23 -244 46 -261 67 -261C86 -261 127 -245 181 -197C237 -147 279 -52 303 66L360 349Z" id="g113-107"></path></g><g transform="matrix(.013,0,0,-0.013,9.132,0)"><path d="M535 323V373H52V323H535ZM535 138V188H52V138H535Z" id="g117-34"></path></g><g transform="matrix(.013,0,0,-0.013,20.395,0)"><path d="M285 378C315 398 338 416 353 432C373 451 384 474 384 503C384 579 325 635 236 635H235C182 635 136 610 108 579L65 516L85 496C110 533 150 575 205 575C258 575 300 543 300 481C300 407 232 369 141 339L147 310C163 315 188 321 211 321C268 321 338 284 338 192C338 94 288 40 217 40C160 40 119 68 93 91C85 98 77 97 69 91C60 84 47 71 46 58C44 46 48 35 62 22C75 10 116 -12 162 -12C234 -12 424 62 424 224C424 297 373 359 285 376V378Z" id="g113-52"></path></g></svg></span></td><td class="align_center">8.54</td><td class="align_center">6.74</td></tr><tr class="table-tr"><td colspan="3"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

Unit production time of product <svg height="12.0653pt" id="M516" style="vertical-align:-3.4294pt" version="1.1" viewbox="-0.0498162 -8.6359 5.61923 12.0653" width="5.61923pt" 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="M394 607C394 634 378 655 350 655C315 655 294 620 294 594C294 564 314 546 339 546C372 546 394 574 394 607ZM360 349C373 414 374 448 351 448C321 448 249 404 183 338L197 313C223 336 265 367 276 367C285 367 283 355 275 313C241 129 220 23 189 -102C175 -158 153 -197 124 -197C106 -197 85 -187 70 -177C64 -173 51 -177 44 -183C34 -193 23 -209 23 -228C23 -244 46 -261 67 -261C86 -261 127 -245 181 -197C237 -147 279 -52 303 66L360 349Z" id="g113-107"></path></g></svg> in plant <svg height="10.2124pt" id="M517" style="vertical-align:-3.42943pt" version="1.1" viewbox="-0.0498162 -6.78297 7.83752 10.2124" width="7.83752pt" 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="M570 304C570 398 525 448 414 448C385 448 343 445 312 434L329 511L321 518C297 504 262 482 244 460L233 411C195 397 159 381 128 358L135 332C160 347 189 360 224 373L111 -147C97 -210 84 -218 17 -231L13 -257L254 -247L259 -218L233 -216C183 -212 177 -202 189 -142L218 -1C238 -10 266 -12 283 -12C351 3 429 48 483 105C543 168 570 242 570 304ZM482 289C482 161 380 33 304 33C278 33 248 51 233 69L303 396C326 400 352 403 369 403C428 403 482 380 482 289Z" id="g113-113"></path></g></svg> at period <span class="nowrap"><svg height="8.02022pt" id="M518" style="vertical-align:-0.2063999pt" version="1.1" viewbox="-0.0498162 -7.81382 4.54925 8.02022" width="4.54925pt" 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="M324 430H196L233 583L223 592L145 529L120 430H54L29 396L31 388H111L56 126C33 15 54 -12 77 -12C137 -12 214 57 250 95L233 119C208 92 155 59 138 59C126 59 120 70 131 125L186 390L298 394L324 430Z" id="g113-117"></path></g></svg>.</span>

Mathematical Problems in Engineering

tab16

Table 16

Table 16: Optimization of Production-Distribution Problem in Supply Chain Management under Stochastic and Fuzzy Uncertainties 