Dynamic Pricing of Ride-Hailing Platforms considering Service Quality and Supply Capacity under Demand Fluctuation

<table class="table-group" id="tab2"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left">Market demand situations</td><td class="align_center">Cases</td><td class="align_center"><i>T</i>’s conditions</td><td class="align_center"><span style="width: 27.7091ptpx;"><svg height="12.3706pt" id="M142" style="vertical-align:-2.2681pt" version="1.1" viewbox="-0.0498162 -10.1025 27.7091 12.3706" width="27.7091pt" 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="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,8.026,-5.741)"><path d="M486 158C486 177 478 202 466 220C413 228 386 236 336 262C386 288 413 297 466 304C478 323 486 347 485 366C470 376 444 381 422 380C389 338 368 319 321 288C323 345 329 372 349 422C339 442 322 461 305 470C289 461 271 442 262 422C281 372 287 345 290 288C243 319 222 338 189 380C167 381 142 376 125 366C125 347 133 322 145 304C198 296 225 288 275 262C225 236 198 227 145 220C133 201 125 177 126 158C141 148 167 143 189 144C222 186 243 205 290 236C288 179 282 152 262 102C272 82 289 63 306 54C322 63 340 82 350 102C330 152 324 179 321 236C368 205 390 186 422 144C444 143 470 148 486 158Z"></path></g><g transform="matrix(.013,0,0,-0.013,14.105,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z"></path></g><g transform="matrix(.013,0,0,-0.013,18.603,0)"><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"></path></g><g transform="matrix(.013,0,0,-0.013,23.036,0)"><path d="M275 270C275 450 212 609 64 710L45 686C145 604 203 442 203 270S147 -63 45 -147L64 -170C213 -68 275 89 275 270Z"></path></g></svg></span></td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left" rowspan="4"><i>a</i> &gt; 0</td><td class="align_center" rowspan="2"><i>c</i> = 0</td><td class="align_center"><i>T</i> ≦ <i>T</i><sub>th</sub></td><td class="align_center">↓</td></tr><tr><td class="align_center"><i>T</i> &gt; <i>T</i><sub>th</sub></td><td class="align_center">↓ ⟶</td></tr><tr><td class="align_center" rowspan="2"><i>c</i> ≠ 0</td><td class="align_center"><i>T</i> ≦ <i>t</i><sub>1</sub></td><td class="align_center">↓</td></tr><tr><td class="align_center"><i>T</i> &gt; <i>t</i><sub>1</sub></td><td class="align_center">↓ ↑</td></tr><tr><td class="align_left" rowspan="3"><i>a</i> &lt; 0</td><td class="align_center"><span style="width: 54.639ptpx;"><svg height="12.248pt" id="M143" style="vertical-align:-0.3499002pt" version="1.1" viewbox="-0.0498162 -11.8981 54.639 12.248" width="54.639pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><rect height="0.65243" width="8.05108" x="0" y="-11.1958"></rect><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z"></path></g><g transform="matrix(.013,0,0,-0.013,11.683,0)"><path d="M567 230V280H69V230H567Z"></path></g><g transform="matrix(.013,0,0,-0.013,17.459,0)"><path d="M901 255C861 290 790 361 716 442L694 427L796 280H69V230H796L694 83L716 68C790 149 861 220 901 255Z"></path></g><g transform="matrix(.013,0,0,-0.013,33.57,0)"><path d="M535 230V280H323V490H265V280H52V230H265V-3H323V230H535Z"></path></g><g transform="matrix(.013,0,0,-0.013,41.201,0)"><path d="M983 225C983 348 891 448 766 448C646 448 579 377 521 276C458 383 382 448 256 448C165 448 37 373 37 208C37 98 119 -12 256 -12C375 -12 440 60 498 161C561 53 639 -12 766 -12C865 -12 983 64 983 225ZM478 196C428 106 365 21 266 21C183 21 129 114 129 240C129 353 183 415 244 415C352 415 420 301 478 196ZM889 204C889 66 838 21 776 21C666 21 598 135 540 241C590 331 655 415 754 415C842 415 889 320 889 204Z"></path></g></svg></span></td><td class="align_left"> </td><td class="align_center">↑</td></tr><tr><td class="align_center" rowspan="2"><svg height="11.9479pt" id="M144" style="vertical-align:-0.04979992pt" version="1.1" viewbox="-0.0498162 -11.8981 8.15071 11.9479" width="8.15071pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><rect height="0.65243" width="8.05108" x="0" y="-11.1958"></rect><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M600 480C600 590 528 650 384 650H143L137 622C222 614 225 607 210 531L130 127C113 41 106 36 23 28L17 0H294L300 28C204 36 195 42 212 127L243 284L314 263C327 263 339 263 352 264C465 271 600 337 600 480ZM508 481C508 351 402 304 329 304C289 304 265 311 250 317L295 559C302 594 310 606 323 611C335 616 350 619 367 619C455 619 508 573 508 481Z"></path></g></svg> is a constant</td><td class="align_center"><i>T</i> ≦ <i>t</i><sub>2</sub></td><td class="align_center">↑</td></tr><tr><td class="align_center"><i>T</i> &gt; <i>t</i><sub>2</sub></td><td class="align_center">↑ ⟶</td></tr><tr><td class="align_left"><i>a</i> = 0</td><td class="align_left"> </td><td class="align_left"> </td><td class="align_center">⟶</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>The optimal dynamic price changes with <i>t</i>.</div>

Mathematical Problems in Engineering

tab2

Table 2

Table 2: Dynamic Pricing of Ride-Hailing Platforms considering Service Quality and Supply Capacity under Demand Fluctuation 