A Two-Sided Stable Matching Model of Cloud Manufacturing Tasks and Services considering the Nonlinear Relationship between Satisfaction and Expectations

<table class="table-group" id="tab3"><tr><td><table class="table"><tr><td class="thead-hr" colspan="8"><hr/></td></tr><tr class="thead"><td class="align_left">Satisfaction degree</td><td class="align_center">Cost</td><td class="align_center">Delivery time</td><td class="align_center">Credibility</td><td class="align_center">Satisfaction degree</td><td class="align_center">Cost</td><td class="align_center">Delivery time</td><td class="align_center">Credibility</td></tr><tr><td class="thead-hr" colspan="8"><hr/></td></tr><tr><td class="align_left"><span style="width: 33.9659ptpx;"><svg height="15.608pt" id="M160" style="vertical-align:-3.833899pt" version="1.1" viewbox="-0.0498162 -11.7741 33.9659 15.608" width="33.9659pt" 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="M542 242C542 369 469 429 379 468C370 472 372 496 376 513L416 681L400 691L344 648L219 51C167 69 113 128 113 217C113 324 166 387 266 428L252 459C124 418 23 336 23 202C23 95 90 13 205 -8L182 -132C165 -222 191 -254 209 -261L215 -258L270 -7C415 -4 542 98 542 242ZM469 232C469 126 403 33 279 39L355 409C399 394 469 331 469 232Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.346,-5.741)"><path d="M786 370C786 572 637 650 431 650H137L130 618C217 606 220 603 204 519L129 127C115 48 107 39 26 30L18 0H270C410 0 516 20 609 75C722 140 786 240 786 370ZM683 373C683 178 547 40 323 40C298 40 264 40 241 45C213 51 207 64 220 127L295 545C304 582 309 595 320 601C335 610 367 613 406 613C570 613 683 538 683 373Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,14.381,-5.741)"><path d="M588 236V289H72V236H588Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.569,-5.741)"><path d="M935 263C895 299 821 372 745 456L719 439L824 289H72V236H823L719 87L745 70C821 154 895 227 935 263Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,27.634,-5.741)"><path d="M622 479C622 589 545 650 400 650H146L140 618C229 609 230 602 215 527L135 132C117 43 112 41 27 32L18 0H305L313 32C213 40 205 44 222 132L251 284L324 262H365C484 269 622 333 622 479ZM528 477C528 356 420 305 344 305C300 305 276 314 259 321L303 554C311 597 313 600 331 606C345 611 361 614 379 614C463 614 528 580 528 477Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.02,3.784)"><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><g transform="matrix(.0091,0,0,-0.0091,11.452,3.784)"><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></td><td class="align_center">1.126</td><td class="align_center">1.126</td><td class="align_center">1.001</td><td class="align_center"><span style="width: 33.9659ptpx;"><svg height="15.608pt" id="M161" style="vertical-align:-3.833899pt" version="1.1" viewbox="-0.0498162 -11.7741 33.9659 15.608" width="33.9659pt" 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="M542 242C542 369 469 429 379 468C370 472 372 496 376 513L416 681L400 691L344 648L219 51C167 69 113 128 113 217C113 324 166 387 266 428L252 459C124 418 23 336 23 202C23 95 90 13 205 -8L182 -132C165 -222 191 -254 209 -261L215 -258L270 -7C415 -4 542 98 542 242ZM469 232C469 126 403 33 279 39L355 409C399 394 469 331 469 232Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.346,-5.741)"><path d="M786 370C786 572 637 650 431 650H137L130 618C217 606 220 603 204 519L129 127C115 48 107 39 26 30L18 0H270C410 0 516 20 609 75C722 140 786 240 786 370ZM683 373C683 178 547 40 323 40C298 40 264 40 241 45C213 51 207 64 220 127L295 545C304 582 309 595 320 601C335 610 367 613 406 613C570 613 683 538 683 373Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,14.381,-5.741)"><path d="M588 236V289H72V236H588Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.569,-5.741)"><path d="M935 263C895 299 821 372 745 456L719 439L824 289H72V236H823L719 87L745 70C821 154 895 227 935 263Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,27.634,-5.741)"><path d="M622 479C622 589 545 650 400 650H146L140 618C229 609 230 602 215 527L135 132C117 43 112 41 27 32L18 0H305L313 32C213 40 205 44 222 132L251 284L324 262H365C484 269 622 333 622 479ZM528 477C528 356 420 305 344 305C300 305 276 314 259 321L303 554C311 597 313 600 331 606C345 611 361 614 379 614C463 614 528 580 528 477Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.02,3.784)"><path d="M462 177V227H365V632H320C217 496 116 350 21 208V177H284V109C284 43 280 38 190 31V0H451V31C369 38 365 43 365 108V177H462ZM284 227H88C155 336 218 430 282 519H284V227Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.452,3.784)"><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></td><td class="align_center">1</td><td class="align_center">1</td><td class="align_center">1.001</td></tr><tr><td class="align_left"><span style="width: 33.9659ptpx;"><svg height="15.608pt" id="M162" style="vertical-align:-3.833899pt" version="1.1" viewbox="-0.0498162 -11.7741 33.9659 15.608" width="33.9659pt" 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="M542 242C542 369 469 429 379 468C370 472 372 496 376 513L416 681L400 691L344 648L219 51C167 69 113 128 113 217C113 324 166 387 266 428L252 459C124 418 23 336 23 202C23 95 90 13 205 -8L182 -132C165 -222 191 -254 209 -261L215 -258L270 -7C415 -4 542 98 542 242ZM469 232C469 126 403 33 279 39L355 409C399 394 469 331 469 232Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.346,-5.741)"><path d="M786 370C786 572 637 650 431 650H137L130 618C217 606 220 603 204 519L129 127C115 48 107 39 26 30L18 0H270C410 0 516 20 609 75C722 140 786 240 786 370ZM683 373C683 178 547 40 323 40C298 40 264 40 241 45C213 51 207 64 220 127L295 545C304 582 309 595 320 601C335 610 367 613 406 613C570 613 683 538 683 373Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,14.381,-5.741)"><path d="M588 236V289H72V236H588Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.569,-5.741)"><path d="M935 263C895 299 821 372 745 456L719 439L824 289H72V236H823L719 87L745 70C821 154 895 227 935 263Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,27.634,-5.741)"><path d="M622 479C622 589 545 650 400 650H146L140 618C229 609 230 602 215 527L135 132C117 43 112 41 27 32L18 0H305L313 32C213 40 205 44 222 132L251 284L324 262H365C484 269 622 333 622 479ZM528 477C528 356 420 305 344 305C300 305 276 314 259 321L303 554C311 597 313 600 331 606C345 611 361 614 379 614C463 614 528 580 528 477Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.02,3.784)"><path d="M414 144C384 79 371 75 317 75H135L276 221C367 316 408 376 408 465C408 570 327 635 237 635C179 635 131 609 100 575L42 494L67 471C94 510 138 565 205 565C277 565 321 517 321 435C321 348 258 270 195 195C146 137 88 81 33 26V0H411C423 44 433 88 446 135L414 144Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.452,3.784)"><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></td><td class="align_center">1</td><td class="align_center">1.126</td><td class="align_center">0.998</td><td class="align_center"><span style="width: 33.9659ptpx;"><svg height="15.7176pt" id="M163" style="vertical-align:-3.9435pt" version="1.1" viewbox="-0.0498162 -11.7741 33.9659 15.7176" width="33.9659pt" 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="M542 242C542 369 469 429 379 468C370 472 372 496 376 513L416 681L400 691L344 648L219 51C167 69 113 128 113 217C113 324 166 387 266 428L252 459C124 418 23 336 23 202C23 95 90 13 205 -8L182 -132C165 -222 191 -254 209 -261L215 -258L270 -7C415 -4 542 98 542 242ZM469 232C469 126 403 33 279 39L355 409C399 394 469 331 469 232Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.346,-5.741)"><path d="M786 370C786 572 637 650 431 650H137L130 618C217 606 220 603 204 519L129 127C115 48 107 39 26 30L18 0H270C410 0 516 20 609 75C722 140 786 240 786 370ZM683 373C683 178 547 40 323 40C298 40 264 40 241 45C213 51 207 64 220 127L295 545C304 582 309 595 320 601C335 610 367 613 406 613C570 613 683 538 683 373Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,14.381,-5.741)"><path d="M588 236V289H72V236H588Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.569,-5.741)"><path d="M935 263C895 299 821 372 745 456L719 439L824 289H72V236H823L719 87L745 70C821 154 895 227 935 263Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,27.634,-5.741)"><path d="M622 479C622 589 545 650 400 650H146L140 618C229 609 230 602 215 527L135 132C117 43 112 41 27 32L18 0H305L313 32C213 40 205 44 222 132L251 284L324 262H365C484 269 622 333 622 479ZM528 477C528 356 420 305 344 305C300 305 276 314 259 321L303 554C311 597 313 600 331 606C345 611 361 614 379 614C463 614 528 580 528 477Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.02,3.784)"><path d="M158 548H390L417 615L410 623H122L83 318C105 326 143 337 185 337C296 337 350 275 350 188C350 116 308 42 225 42C164 42 122 74 100 93C90 101 82 99 72 92C60 82 51 68 50 59C48 46 52 38 66 24C82 9 125 -12 172 -12C225 -11 292 15 346 59C408 108 437 166 437 226C437 309 371 397 242 397C214 397 170 382 133 369L158 548Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.452,3.784)"><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></td><td class="align_center">1.126</td><td class="align_center">1.126</td><td class="align_center">1.098</td></tr><tr><td class="align_left"><span style="width: 33.9659ptpx;"><svg height="15.7176pt" id="M164" style="vertical-align:-3.9435pt" version="1.1" viewbox="-0.0498162 -11.7741 33.9659 15.7176" width="33.9659pt" 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="M542 242C542 369 469 429 379 468C370 472 372 496 376 513L416 681L400 691L344 648L219 51C167 69 113 128 113 217C113 324 166 387 266 428L252 459C124 418 23 336 23 202C23 95 90 13 205 -8L182 -132C165 -222 191 -254 209 -261L215 -258L270 -7C415 -4 542 98 542 242ZM469 232C469 126 403 33 279 39L355 409C399 394 469 331 469 232Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.346,-5.741)"><path d="M786 370C786 572 637 650 431 650H137L130 618C217 606 220 603 204 519L129 127C115 48 107 39 26 30L18 0H270C410 0 516 20 609 75C722 140 786 240 786 370ZM683 373C683 178 547 40 323 40C298 40 264 40 241 45C213 51 207 64 220 127L295 545C304 582 309 595 320 601C335 610 367 613 406 613C570 613 683 538 683 373Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,14.381,-5.741)"><path d="M588 236V289H72V236H588Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.569,-5.741)"><path d="M935 263C895 299 821 372 745 456L719 439L824 289H72V236H823L719 87L745 70C821 154 895 227 935 263Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,27.634,-5.741)"><path d="M622 479C622 589 545 650 400 650H146L140 618C229 609 230 602 215 527L135 132C117 43 112 41 27 32L18 0H305L313 32C213 40 205 44 222 132L251 284L324 262H365C484 269 622 333 622 479ZM528 477C528 356 420 305 344 305C300 305 276 314 259 321L303 554C311 597 313 600 331 606C345 611 361 614 379 614C463 614 528 580 528 477Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.02,3.784)"><path d="M290 377C321 398 342 415 358 430C378 450 389 473 389 502C389 578 329 635 238 635H237C184 635 137 610 109 578L64 515L88 493C112 529 154 573 208 573S303 542 303 482C303 409 233 370 141 341L149 308C165 313 190 319 215 319C272 319 341 283 341 193C342 98 292 43 222 43C163 43 122 72 96 94C88 101 79 100 70 94C61 87 47 73 46 60C44 47 48 37 62 23C76 10 118 -12 165 -12C238 -12 430 62 430 223C430 297 379 359 290 375V377Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.452,3.784)"><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></td><td class="align_center">1.173</td><td class="align_center">1.126</td><td class="align_center">0.966</td><td class="align_center"><span style="width: 33.9659ptpx;"><svg height="15.7176pt" id="M165" style="vertical-align:-3.9435pt" version="1.1" viewbox="-0.0498162 -11.7741 33.9659 15.7176" width="33.9659pt" 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="M542 242C542 369 469 429 379 468C370 472 372 496 376 513L416 681L400 691L344 648L219 51C167 69 113 128 113 217C113 324 166 387 266 428L252 459C124 418 23 336 23 202C23 95 90 13 205 -8L182 -132C165 -222 191 -254 209 -261L215 -258L270 -7C415 -4 542 98 542 242ZM469 232C469 126 403 33 279 39L355 409C399 394 469 331 469 232Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.346,-5.741)"><path d="M786 370C786 572 637 650 431 650H137L130 618C217 606 220 603 204 519L129 127C115 48 107 39 26 30L18 0H270C410 0 516 20 609 75C722 140 786 240 786 370ZM683 373C683 178 547 40 323 40C298 40 264 40 241 45C213 51 207 64 220 127L295 545C304 582 309 595 320 601C335 610 367 613 406 613C570 613 683 538 683 373Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,14.381,-5.741)"><path d="M588 236V289H72V236H588Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,18.569,-5.741)"><path d="M935 263C895 299 821 372 745 456L719 439L824 289H72V236H823L719 87L745 70C821 154 895 227 935 263Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,27.634,-5.741)"><path d="M622 479C622 589 545 650 400 650H146L140 618C229 609 230 602 215 527L135 132C117 43 112 41 27 32L18 0H305L313 32C213 40 205 44 222 132L251 284L324 262H365C484 269 622 333 622 479ZM528 477C528 356 420 305 344 305C300 305 276 314 259 321L303 554C311 597 313 600 331 606C345 611 361 614 379 614C463 614 528 580 528 477Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,7.02,3.784)"><path d="M141 347C171 480 264 541 327 570C364 587 403 599 436 605L429 641C389 634 339 622 300 609C191 570 37 458 37 239C37 86 126 -12 245 -12C367 -12 454 89 454 210C454 314 380 397 272 397C252 397 230 390 208 380L141 347ZM231 338C323 338 366 257 366 174C366 108 340 27 263 27C180 27 129 123 129 244C129 268 130 292 135 310C158 323 193 338 231 338Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,11.452,3.784)"><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></td><td class="align_center">1</td><td class="align_center">0</td><td class="align_center">1.047</td></tr><tr class="table-tr"><td colspan="8"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Satisfaction degree of <i>D</i><sub>1</sub>–<i>D</i><sub>6</sub> with <i>P</i><sub>1</sub>.</div>

Complexity

tab3

Table 3

Table 3: A Two-Sided Stable Matching Model of Cloud Manufacturing Tasks and Services considering the Nonlinear Relationship between Satisfaction and Expectations 

Table 3 | A Two-Sided Stable Matching Model of Cloud Manufacturing Tasks and Services considering the Nonlinear Relationship between Satisfaction and Expectations 