Developing a Model for the University Course Timetabling Problem: A Case Study

<table class="table-group" id="tab17"><tr><td><table class="table"><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr class="thead"><td class="align_left">Objective function</td><td class="align_center">Z1</td><td class="align_center">Z2</td><td class="align_center">Z3</td></tr><tr><td class="thead-hr" colspan="4"><hr/></td></tr><tr><td class="align_left"><span style="width: 12.2503ptpx;"><svg height="13.8634pt" id="M76" style="vertical-align:-3.8339pt" version="1.1" viewbox="-0.0498162 -10.0295 12.2503 13.8634" width="12.2503pt" 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="M410 152L393 124C355 58 321 44 251 44H187C264 179 330 297 407 428L398 442H153C114 441 100 447 92 463H70C60 419 44 357 30 308L60 295L77 328C106 384 130 399 197 399C214 399 232 399 249 399C173 265 106 147 24 16L37 0H392C404 31 420 82 439 138L410 152Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.807,-5.741)"><path d="M499 152C501 180 492 209 480 228C432 233 403 235 357 256C403 278 432 279 480 284C492 303 504 328 499 359C477 375 447 382 424 380C396 342 380 317 338 288C342 339 356 364 376 408C366 429 350 451 320 463C295 451 274 429 265 408C284 364 297 339 301 288C259 317 244 341 216 380C193 382 166 379 141 359C139 332 148 303 160 284C208 279 237 277 283 256C237 234 208 233 160 228C148 209 136 184 141 152C163 137 193 130 216 132C244 170 260 195 302 224C298 173 284 148 265 104C274 83 290 61 320 49C345 61 366 83 376 104C356 148 343 173 339 224C381 195 396 171 424 132C447 130 474 133 499 152Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.807,3.784)"><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">15</td><td class="align_center">63</td><td class="align_center">146</td></tr><tr><td class="align_left"><span style="width: 12.2503ptpx;"><svg height="13.8634pt" id="M77" style="vertical-align:-3.8339pt" version="1.1" viewbox="-0.0498162 -10.0295 12.2503 13.8634" width="12.2503pt" 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="M410 152L393 124C355 58 321 44 251 44H187C264 179 330 297 407 428L398 442H153C114 441 100 447 92 463H70C60 419 44 357 30 308L60 295L77 328C106 384 130 399 197 399C214 399 232 399 249 399C173 265 106 147 24 16L37 0H392C404 31 420 82 439 138L410 152Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.807,-5.741)"><path d="M499 152C501 180 492 209 480 228C432 233 403 235 357 256C403 278 432 279 480 284C492 303 504 328 499 359C477 375 447 382 424 380C396 342 380 317 338 288C342 339 356 364 376 408C366 429 350 451 320 463C295 451 274 429 265 408C284 364 297 339 301 288C259 317 244 341 216 380C193 382 166 379 141 359C139 332 148 303 160 284C208 279 237 277 283 256C237 234 208 233 160 228C148 209 136 184 141 152C163 137 193 130 216 132C244 170 260 195 302 224C298 173 284 148 265 104C274 83 290 61 320 49C345 61 366 83 376 104C356 148 343 173 339 224C381 195 396 171 424 132C447 130 474 133 499 152Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.807,3.784)"><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></svg></span></td><td class="align_center">501.6</td><td class="align_center">456</td><td class="align_center">726.15</td></tr><tr><td class="align_left"><span style="width: 12.2503ptpx;"><svg height="13.973pt" id="M78" style="vertical-align:-3.9435pt" version="1.1" viewbox="-0.0498162 -10.0295 12.2503 13.973" width="12.2503pt" 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="M410 152L393 124C355 58 321 44 251 44H187C264 179 330 297 407 428L398 442H153C114 441 100 447 92 463H70C60 419 44 357 30 308L60 295L77 328C106 384 130 399 197 399C214 399 232 399 249 399C173 265 106 147 24 16L37 0H392C404 31 420 82 439 138L410 152Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.807,-5.741)"><path d="M499 152C501 180 492 209 480 228C432 233 403 235 357 256C403 278 432 279 480 284C492 303 504 328 499 359C477 375 447 382 424 380C396 342 380 317 338 288C342 339 356 364 376 408C366 429 350 451 320 463C295 451 274 429 265 408C284 364 297 339 301 288C259 317 244 341 216 380C193 382 166 379 141 359C139 332 148 303 160 284C208 279 237 277 283 256C237 234 208 233 160 228C148 209 136 184 141 152C163 137 193 130 216 132C244 170 260 195 302 224C298 173 284 148 265 104C274 83 290 61 320 49C345 61 366 83 376 104C356 148 343 173 339 224C381 195 396 171 424 132C447 130 474 133 499 152Z"></path></g><g transform="matrix(.0091,0,0,-0.0091,5.807,3.784)"><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></svg></span></td><td class="align_center">366.66</td><td class="align_center">336.268</td><td class="align_center">315</td></tr><tr class="table-tr"><td colspan="4"><hr class="tbody-hr"/></td></tr></table></td></tr></table>

<div>Payoff table for three objective functions.</div>

Complexity

tab17

Table 17

Table 17: Developing a Model for the University Course Timetabling Problem: A Case Study 