Formulate an integer linear program that can be used to determine the minimum number of service facilities needed and their locations.

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 the regional offices is provided in the following table:

The company’s expansion plans involve constructing service facilities in some of the cities where regional offices are 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 an integer linear program that can be used to determine the minimum number of service facilities needed and their locations.

b. Solve the integer linear program formulated in part (a). How many service facilities are required, and where should they be located?

c. Suppose that each service facility can provide service only to regional offices within 300 miles. Re-solve the integer linear program with the 300-mile requirement. How many service facilities are required and where should they be located?

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