East Coast Trucking provides service from Boston to Miami using regional offices
ID: 3403614 • Letter: E
Question
East Coast Trucking provides service from Boston to Miami using regional offices located in Boston, New York, Philadelphia, Baltimore, Washington, Richmond, Raleigh, Florence, Savannah, Jacksonville, and Tampa. The number of miles between each of the regional offices is provided in the following table:
New York Philadelphia Baltimore Washington Richmond Raleigh Florence Savannah Jacksonville Tampa Miami Boston 211 320 424 459 565 713 884 1056 1196 1399 1669 New York 109 213 248 354 502 673 845 985 1188 1458 Philadelphia 104 139 245 393 564 736 876 1079 1349 Baltimore 35 141 289 460 632 772 975 1245 Washington 106 254 425 597 737 940 1210 Richmond 148 319 491 631 834 1104 Raleigh 171 343 483 686 956 Florence 172 312 515 785 Savannah 140 343 613 Jacksonville 203 473 Tampa 270Explanation / Answer
Tampa. The number of miles between each of the regional offices is provided in the following table.
New York
Philadelphia
Baltimore
Washington
Richmond
Raleigh
Florence
Savannah
Jacksonville
Tampa
Miami
Boston
211
320
424
459
565
713
884
1056
1196
1399
1669
New York
109
213
248
354
502
673
845
985
1188
1458
Philadelphia
104
139
245
393
564
736
876
1079
1349
Baltimore
35
141
289
460
632
772
975
1245
Washington
106
254
425
597
737
940
1210
Richmond
148
319
491
631
834
1104
Raleigh
171
343
483
686
956
Florence
172
312
515
785
Savannah
140
343
613
Jacksonville
203
473
Tampa
270
The company's expansion plans involve constructing service facilities in some of the cities where a regional office is located. Each regional office must be within 400 miles of a service facility. For instance, if a service facility is constructed in Richmond, it can provide service to regional offices located in New York, Philadelphia, Baltimore, Washington, Richmond, Raleigh, and Florence. Management would like to determine the minimum number of service facilities needed and where they should be located.
a. Formulate and solve an integer linear programming model that can be used to determine the minimum number of service facilities needed and their location.
New York
Philadelphia
Baltimore
Washington
Richmond
Raleigh
Florence
Savannah
Jacksonville
Tampa
Miami
Boston
211
320
424
459
565
713
884
1056
1196
1399
1669
New York
109
213
248
354
502
673
845
985
1188
1458
Philadelphia
104
139
245
393
564
736
876
1079
1349
Baltimore
35
141
289
460
632
772
975
1245
Washington
106
254
425
597
737
940
1210
Richmond
148
319
491
631
834
1104
Raleigh
171
343
483
686
956
Florence
172
312
515
785
Savannah
140
343
613
Jacksonville
203
473
Tampa
270
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