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 ofmiles between each of the regional offices and the numbers associated with each city are provided in the following table.BostonNew YorkPhiladelphiaBaltimoreWashingtonRichmondRaleighFlorenceSavannahJacksonvilleTampaMiamiNew York Philadelphia Baltimore Washington Richmond Raleigh Florence Savannah Jacksonville Tampa Miami15652345ஈNOGE78911211320109424213104459248139353542451411067135023932892541488846735644604253191711,0568457366325974913431721,1969858767727376314833121401,399 1,6691,1881,079975 1,245834940 1,2106865151,4583431,3492031,104956785613473270The 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 isconstructed 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 facilitiesneeded 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 0otherwise.)Mins.t.BostonNew YorkPhiladelphiaBaltimoreWashingtonRichmondRaleighFlorenceSavannahJacksonvilleTampaMiamiX11 X2 X3 X4 X5, X61X71 X8 X9 X10 X11 X12 = 0, 1

A linear program model is a mathematical model with a linear objective function a set of linear…

Answered: ormulate an integer linear program that…

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 34P

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The Midlands Field Produce Company contracts with potato farmers in Colorado, Minnesota, North Dakota, and Wisconsin for monthly potato shipments. Midlands picks up the potatoes at the farms and ships mostly by truck (and sometimes by rail) to its sorting and distribution centers in Ohio, Missouri, and Iowa. At these centers the potatoes are cleaned, rejects are discarded, and the potatoes are sorted according to size and quality. They are then shipped to combination plants and distribution centers in Virginia, Pennsylvania, Georgia, and Texas, where the company produces a variety of potato products and distributes bags of potatoes to stores. Exceptions are the Ohio distribution center, which will accept potatoes only from farms in Minnesota, North Dakota, and Wisconsin, and the Texas plant, which won’t accept shipments from Ohio because of disagreements over delivery schedules and quality issues. Following are summaries of the shipping costs from the farms to the distribution centers…
Cars-to-Dealers Logistics Inc. is the exclusive logistics provider for the Summit Motor Co. and has responsibilityfor transporting cars from Summit’s 3 manufacturing plants in Toledo, OH; Charlotte, NC and Savannah, GA tothe 7 regional dealer locations as in the tables provided in your dataset. To do this, Cars-to-Dealers uses threetransshipment facilities and all cars in the distribution network pass through these transshipment facilities.Dataset also contains the information about the capacities of each of these transshipment facilities, the demandrequirement at each of the regional dealer locations and the unit cost to ship one car between the variouslocations.In addition to supply of cars (manufacturers) and demand for cars (dealers) there are two types of constraintsfor each transshipment facility:1. Balance flow constraints: dictate that all cars flowing into a transshipment facility should also flow out of thetransshipment facility – i.e. no inventory of cars should remain at…
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PharmaCo wants to determine how to deploy sales representatives across its Western U.S. region to support a new drug for obesity. Sales representatives will be located in a "home city", which they serve, in addition to cities with feasible commuting distance, with the objective that all cities must be served by at least one sales representative. The feasible connections between each city in the region are listed below (1 indicates a feasible connection, potential home cities are shown in columns, and cities served in rows): Potential Rep Home City Served? Albuquerque El Paso Denver Phoenix San Diego Los Angeles San Francisco Portland Seattle Las Vegas Salt Lake City Albuquerque 1 1 1 1 0 0 0 0 0 0 0 El Paso 1 1 0 1 0 0 0 0 0 0 0 Denver 1 0 1 1 0 0 0 0 0 0 1 Phoenix 1 1 1 1 1 1 0 0 0 1 1 San Diego 0 0 0 1 1 1 1 0 0 1 0…
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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