Pricing Decisions of a Supply Chain with Multichannel Retailer under Fairness Concerns

<div>The impact of <svg height="12.7178pt" id="M263" style="vertical-align:-3.42947pt" version="1.1" viewbox="-0.0498162 -9.28833 7.68094 12.7178" width="7.68094pt" 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="M558 587C558 666 497 712 432 712C379 712 330 691 284 650C212 586 178 508 148 348L71 -65C49 -185 35 -229 23 -235L27 -261C49 -259 101 -251 124 -224C131 -216 138 -178 159 -24C171 66 197 200 227 356C264 550 295 668 393 668C443 668 479 632 479 575C479 516 446 458 383 418C361 404 344 398 318 397L296 350C395 338 460 281 460 192C460 110 411 40 300 40C258 40 215 55 192 69L181 51C191 18 222 -16 266 -16C308 -16 351 1 397 26C471 67 545 142 545 221C545 315 486 365 401 395C469 437 558 498 558 587Z"></path></g></svg> on <span class="nowrap"><svg height="17.0081pt" id="M264" style="vertical-align:-3.961801pt" version="1.1" viewbox="-0.0498162 -13.0463 19.5403 17.0081" width="19.5403pt" 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="M703 650H36V622C118 616 126 607 126 526V124C126 45 117 34 40 28V0H297V28C219 34 211 44 211 124V581C211 609 214 613 245 613H494C521 613 527 610 527 583V124C527 45 519 34 434 28V0H700V28C620 34 612 44 612 124V526C612 605 620 616 703 622V650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.594,-5.741)"><path d="M257 449C165 449 37 374 37 209C37 98 119 -12 256 -12C355 -12 473 65 473 226C473 349 381 449 257 449ZM244 416C333 416 380 320 380 204C380 67 329 21 267 21C184 21 130 115 130 241C130 354 184 416 244 416Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,14.252,-9.852)"><path d="M503 164C503 183 495 209 482 228C429 236 402 243 352 269C402 295 428 304 482 311C494 330 503 355 502 376C485 385 459 391 436 390C403 347 383 328 336 298C338 354 343 381 365 431C353 451 337 471 318 481C302 471 283 451 273 431C293 381 300 354 303 298C255 328 235 346 202 389C179 390 153 385 135 374C135 355 143 329 156 310C210 302 236 295 286 269C236 243 210 234 156 227C144 208 135 183 136 162C153 153 180 147 202 148C235 191 255 210 303 240C300 184 295 157 274 107C285 87 301 67 320 57C337 67 355 87 365 107C345 157 339 184 336 240C383 210 404 192 436 149C460 148 485 153 503 164Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.594,3.784)"><path d="M614 175C564 76 510 21 408 21C256 21 146 149 146 336C146 488 235 629 402 629C510 629 570 586 597 480L626 488C620 541 614 582 606 638C578 643 510 665 429 665C206 665 44 527 44 316C44 157 153 -15 402 -15C474 -15 558 5 586 11C604 45 629 119 643 165L614 175Z"></path></g></svg>,</span> <span class="nowrap"><svg height="17.0081pt" id="M265" style="vertical-align:-3.961801pt" version="1.1" viewbox="-0.0498162 -13.0463 18.2341 17.0081" width="18.2341pt" 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="M703 650H36V622C118 616 126 607 126 526V124C126 45 117 34 40 28V0H297V28C219 34 211 44 211 124V581C211 609 214 613 245 613H494C521 613 527 610 527 583V124C527 45 519 34 434 28V0H700V28C620 34 612 44 612 124V526C612 605 620 616 703 622V650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.594,-5.741)"><path d="M319 325C317 349 306 409 297 431C277 440 250 449 209 449C117 449 57 389 57 319C57 243 122 209 182 182C232 159 261 135 261 91C261 48 227 21 190 21C130 21 85 79 68 145L41 140C41 104 51 36 58 22C75 7 121 -12 172 -12C252 -12 337 35 337 126C337 195 286 231 210 262C166 281 126 304 126 348C126 388 152 417 191 417C240 417 274 378 294 318L319 325Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,12.946,-9.852)"><path d="M503 164C503 183 495 209 482 228C429 236 402 243 352 269C402 295 428 304 482 311C494 330 503 355 502 376C485 385 459 391 436 390C403 347 383 328 336 298C338 354 343 381 365 431C353 451 337 471 318 481C302 471 283 451 273 431C293 381 300 354 303 298C255 328 235 346 202 389C179 390 153 385 135 374C135 355 143 329 156 310C210 302 236 295 286 269C236 243 210 234 156 227C144 208 135 183 136 162C153 153 180 147 202 148C235 191 255 210 303 240C300 184 295 157 274 107C285 87 301 67 320 57C337 67 355 87 365 107C345 157 339 184 336 240C383 210 404 192 436 149C460 148 485 153 503 164Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.594,3.784)"><path d="M614 175C564 76 510 21 408 21C256 21 146 149 146 336C146 488 235 629 402 629C510 629 570 586 597 480L626 488C620 541 614 582 606 638C578 643 510 665 429 665C206 665 44 527 44 316C44 157 153 -15 402 -15C474 -15 558 5 586 11C604 45 629 119 643 165L614 175Z"></path></g></svg>,</span> and <span class="nowrap"><svg height="17.0081pt" id="M266" style="vertical-align:-3.961801pt" version="1.1" viewbox="-0.0498162 -13.0463 22.8925 17.0081" width="22.8925pt" 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="M703 650H36V622C118 616 126 607 126 526V124C126 45 117 34 40 28V0H297V28C219 34 211 44 211 124V581C211 609 214 613 245 613H494C521 613 527 610 527 583V124C527 45 519 34 434 28V0H700V28C620 34 612 44 612 124V526C612 605 620 616 703 622V650Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.594,-5.741)"><path d="M257 449C165 449 37 374 37 209C37 98 119 -12 256 -12C355 -12 473 65 473 226C473 349 381 449 257 449ZM244 416C333 416 380 320 380 204C380 67 329 21 267 21C184 21 130 115 130 241C130 354 184 416 244 416Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,14.235,-5.741)"><path d="M319 325C317 349 306 409 297 431C277 440 250 449 209 449C117 449 57 389 57 319C57 243 122 209 182 182C232 159 261 135 261 91C261 48 227 21 190 21C130 21 85 79 68 145L41 140C41 104 51 36 58 22C75 7 121 -12 172 -12C252 -12 337 35 337 126C337 195 286 231 210 262C166 281 126 304 126 348C126 388 152 417 191 417C240 417 274 378 294 318L319 325Z"></path></g><g transform="matrix(.0065,0,0,-0.0065,17.605,-9.852)"><path d="M503 164C503 183 495 209 482 228C429 236 402 243 352 269C402 295 428 304 482 311C494 330 503 355 502 376C485 385 459 391 436 390C403 347 383 328 336 298C338 354 343 381 365 431C353 451 337 471 318 481C302 471 283 451 273 431C293 381 300 354 303 298C255 328 235 346 202 389C179 390 153 385 135 374C135 355 143 329 156 310C210 302 236 295 286 269C236 243 210 234 156 227C144 208 135 183 136 162C153 153 180 147 202 148C235 191 255 210 303 240C300 184 295 157 274 107C285 87 301 67 320 57C337 67 355 87 365 107C345 157 339 184 336 240C383 210 404 192 436 149C460 148 485 153 503 164Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,9.594,3.784)"><path d="M614 175C564 76 510 21 408 21C256 21 146 149 146 336C146 488 235 629 402 629C510 629 570 586 597 480L626 488C620 541 614 582 606 638C578 643 510 665 429 665C206 665 44 527 44 316C44 157 153 -15 402 -15C474 -15 558 5 586 11C604 45 629 119 643 165L614 175Z"></path></g></svg>.</span></div>

Mathematical Problems in Engineering

fig4

Figure 4

Figure 4: Pricing Decisions of a Supply Chain with Multichannel Retailer under Fairness Concerns 