ormulate 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 and 0

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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.
Boston
New York
Philadelphia
Baltimore
Washington
Richmond
Raleigh
Florence
Savannah
Jacksonville
Tampa
Miami
New York Philadelphia Baltimore Washington Richmond Raleigh Florence Savannah Jacksonville Tampa Miami
1
565
2
3
4
5
ஈ
NOGE
7
8
9
11
211
320
109
424
213
104
459
248
139
35
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
1,079
975 1,245
834
940 1,210
686
515
1,458
343
1,349
203
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: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. Boston New York Philadelphia Baltimore Washington Richmond Raleigh Florence Savannah Jacksonville Tampa Miami New York Philadelphia Baltimore Washington Richmond Raleigh Florence Savannah Jacksonville Tampa Miami 1 565 2 3 4 5 ஈ NOGE 7 8 9 11 211 320 109 424 213 104 459 248 139 35 354 245 141 106 713 502 393 289 254 148 884 673 564 460 425 319 171 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 1,079 975 1,245 834 940 1,210 686 515 1,458 343 1,349 203 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.
(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
X11 X2 X3 X4 X5, X61X71 X8 X9 X10 X11 X12 = 0, 1
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 X11 X2 X3 X4 X5, X61X71 X8 X9 X10 X11 X12 = 0, 1
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