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, Tampa, and Miami. The number of miles between each of the regional offices and the numbers associated with each city are provided in the following table. New York Philadelphia Baltimore Jacksonville Tampa Miami 320 1,196 1,399 1,669 1,188 1,458 1,079 1,349 Boston New York Philadelphia Baltimore Washington Richmond Raleigh Florence Savannah Jacksonville Tampa Miami A G 123 In Is 4 G n a 47 G G 211 109 424 213 104 Washington 459 248 139 35 Richmond Raleigh Florence Savannah 565 713 884 354 245 141 106 502 393 254 148 673 425 319 171 1,056 845 736 632 597 491 343 172 985 772 737 631 312 140 975 940 515 1,245 834 1,104 956 343 203 1,210 785 613 473 270 The company's expansion plans involve constructing service facilities in some of the cities where a regional office is located, such that each regional office is within 400 miles of at least one 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.
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, Tampa, and Miami. The number of miles between each of the regional offices and the numbers associated with each city are provided in the following table. New York Philadelphia Baltimore Jacksonville Tampa Miami 320 1,196 1,399 1,669 1,188 1,458 1,079 1,349 Boston New York Philadelphia Baltimore Washington Richmond Raleigh Florence Savannah Jacksonville Tampa Miami A G 123 In Is 4 G n a 47 G G 211 109 424 213 104 Washington 459 248 139 35 Richmond Raleigh Florence Savannah 565 713 884 354 245 141 106 502 393 254 148 673 425 319 171 1,056 845 736 632 597 491 343 172 985 772 737 631 312 140 975 940 515 1,245 834 1,104 956 343 203 1,210 785 613 473 270 The company's expansion plans involve constructing service facilities in some of the cities where a regional office is located, such that each regional office is within 400 miles of at least one 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.
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6th Edition
ISBN:9781337406659
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Transcribed Image Text: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, Tampa, and Miami. The number of miles between each of the regional offices and the numbers associated with each city are provided in the following table.
New York Philadelphia Baltimore Washington Richmond Raleigh Florence Savannah Jacksonville Tampa Miami
Boston
New York
Philadelphia
Baltimore
Washington
Richmond
Raleigh
Florence
Savannah
Jacksonville
Tampa
Miami
4
2
3
4
5
6
8
La
1
1
1
211
320
109
424
213
104
459
248
139
35
565
354
245
141
106
713
502
393
289
254
148
884
673
564
460
425
319
171
1,056
845
736
632
597
491
343
172
1,196
985
876
772
737
631
483
312
140
1,399 1,669
1,188 1,458
1,079
975 1,245
940
834
686
515
343
1,349
203
1,210
1,104
956
785
613
473
270
The company's expansion plans involve constructing service facilities in some of the cities where a regional office is located, such that each regional office is within 400 miles of at least one 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.
Transcribed Image Text:(a) Formulate an integer linear program that can be used to determine the minimum number of service facilities needed and their location. (Let x; be the 0-1 variable, which is 1 if a service facility is constructed in city i, and 0 otherwise.)
Min
s.t.
Boston
New York
Philadelphia
Baltimore
Washington
Richmond
Raleigh
Florence
Savannah
Jacksonville
Tampa
Miami
X1 X2 X3 X4 X5, X61 X7, X8, X9, X10 X11 X12 = 0, 1
(b) Solve the linear program formulated in part (a). How many service facilities are required?
Where should they be located? (Select all that apply.)
Boston
New York
Philadelphia
Baltimore
Washington
Richmond
Raleigh
Florence
Savannah
Jacksonville
Tampa
Miami
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Transcribed Image Text:(c) Suppose that each service facility can only provide service to regional offices within 300 miles. How many service facilities are required?
Where should they be located? (Select all that apply.)
Boston
New York
Philadelphia
Baltimore
Washington
Richmond
Raleigh
Florence
Savannah
Jacksonville
Tampa
Miami
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