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05 Nov You are the vehicle dispatcher for a delivery service that serves a mix of easy’ customers who are quite pleasant when the driver arrives and hard’ customers who are difficult to manag

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You are the vehicle dispatcher for a delivery service that serves a mix of ‘easy’ customers who are quite pleasant when the driver arrives and ‘hard’ customers who are difficult to manage. In order to keep the drivers happy, you never assign a driver to visit two hard customers in a row. Thus, for each driver, given a set of ‘easy’ and ‘hard’ customers to visit, your goal is to minimize the travel time to visit all customers, starting and returning from the company depot, satisfying the constraint that a hard customer visit cannot be followed by another hard customer.

This problem can be infeasible if the number of hard customers is greater than the number of easy customers. Let’s assume that this is sometimes the case. As dispatcher, you have decided to relax the constraint that a hard customer visit cannot be followed by another hard customer. Rather, you want to minimize the number of times this happens and minimize the route travel length.

  • It may not be possible to minimize both terms at once; how would you find a good compromise?
  • Formulate the Hard/Easy Customer Traveling Salesman Problem (TSP) with the two term objective function terms. Define any new notation you introduce and explain your formulation in words and present mathematically.
  • Develop a heuristic to solve the problem. Clearly present your heuristic.
  • Solve the instances posted in the excel file. Solutions should include the visit sequence of nodes and the tour length and # of times a hard customer follows another hard customer for each instance. Your solution should be included on the tab “Sample solution” in the data spreadsheet.

Instance 1

nodes 17
1 Easy 0 633 257 91 412 150 80 134 259 505 353 324 70 211 268 246 121
2 Easy 633 0 390 661 227 488 572 530 555 289 282 638 567 466 420 745 518
3 Hard 257 390 0 228 169 112 196 154 372 262 110 437 191 74 53 472 142
4 Hard 91 661 228 0 383 120 77 105 175 476 324 240 27 182 239 237 84
5 Easy 412 227 169 383 0 267 351 309 338 196 61 421 346 243 199 528 297
6 Hard 150 488 112 120 267 0 63 34 264 360 208 329 83 105 123 364 35
7 Hard 80 572 196 77 351 63 0 29 232 444 292 297 47 150 207 332 29
8 Easy 134 530 154 105 309 34 29 0 249 402 250 314 68 108 165 349 36
9 Hard 259 555 372 175 338 264 232 249 0 495 352 95 189 326 383 202 236
10 Hard 505 289 262 476 196 360 444 402 495 0 154 578 439 336 240 685 390
11 Easy 353 282 110 324 61 208 292 250 352 154 0 435 287 184 140 542 238
12 Hard 324 638 437 240 421 329 297 314 95 578 435 0 254 391 448 157 301
13 Hard 70 567 191 27 346 83 47 68 189 439 287 254 0 145 202 289 55
14 Easy 211 466 74 182 243 105 150 108 326 336 184 391 145 0 57 426 96
15 Easy 268 420 53 239 199 123 207 165 383 240 140 448 202 57 0 483 153
16 Hard 246 745 472 237 528 364 332 349 202 685 542 157 289 426 483 0 336
17 Hard 121 518 142 84 297 35 29 36 236 390 238 301 55 96 153 336 0

Instance 2

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nodes 26
1 Easy 0 83 93 129 133 139 151 169 135 114 110 98 99 95 81 152 159 181 172 185 147 157 185 220 127 181
2 Easy 83 0 40 53 62 64 91 116 93 84 95 98 89 68 67 127 156 175 152 165 160 180 223 268 179 197
3 Hard 93 40 0 42 42 49 59 81 54 44 58 64 54 31 36 86 117 135 112 125 124 147 193 241 157 161
4 Hard 129 53 42 0 11 11 46 72 65 70 88 100 89 66 76 102 142 156 127 139 155 180 228 278 197 190
5 Hard 133 62 42 11 0 9 35 61 55 62 82 95 84 62 74 93 133 146 117 128 148 173 222 272 194 182
6 Easy 139 64 49 11 9 0 39 65 63 71 90 103 92 71 82 100 141 153 124 135 156 181 230 280 202 190
7 Hard 151 91 59 46 35 39 0 26 34 52 71 88 77 63 78 66 110 119 88 98 130 156 206 257 188 160
8 Easy 169 116 81 72 61 65 26 0 37 59 75 92 83 76 91 54 98 103 70 78 122 148 198 250 188 148
9 Easy 135 93 54 65 55 63 34 37 0 22 39 56 47 40 55 37 78 91 62 74 96 122 172 223 155 128
10 Hard 114 84 44 70 62 71 52 59 22 0 20 36 26 20 34 43 74 91 68 82 86 111 160 210 136 121
11 Hard 110 95 58 88 82 90 71 75 39 20 0 18 11 27 32 42 61 80 64 77 68 92 140 190 116 103
12 Easy 98 98 64 100 95 103 88 92 56 36 18 0 11 34 31 56 63 85 75 87 62 83 129 178 100 99
13 Hard 99 89 54 89 84 92 77 83 47 26 11 11 0 23 24 53 68 89 74 87 71 93 140 189 111 107
14 Hard 95 68 31 66 62 71 63 76 40 20 27 34 23 0 15 62 87 106 87 100 93 116 163 212 132 130
15 Easy 81 67 36 76 74 82 78 91 55 34 32 31 24 15 0 73 92 112 96 109 93 113 158 205 122 130
16 Hard 152 127 86 102 93 100 66 54 37 43 42 56 53 62 73 0 44 54 26 39 68 94 144 196 139 95
17 Easy 159 156 117 142 133 141 110 98 78