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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. 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.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section6.5: Set-covering And Location-assignment Models
Problem 35P
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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. 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: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.
(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
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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(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
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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