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A contractor, Susan Meyer, has to haul gravel to three building sites. She can purchase as much as 18 tons at a gravel pit in the north of the city and 14 tons at one in the south. She needs 10, 5, and 10 tons at sites 1, 2, and 3, respectively. The purchase price per ton at each gravel pit and the hauling cost per ton are given in the table below. Pit North South Hauling Cost per Ton at Site 1 2 3 $100 $160 $180 $140 $190 $110 Price per Ton $300 $420 (a) Susan wishes to determine how much to haul from each pit to each site to minimize the total cost for purchasing and hauling gravel. Formulate this problem as a transportation problem by constructing the appropriate parameter table. (b) Susan now needs to hire the trucks (and their drivers) to do the hauling. Each truck can only be used to haul gravel from a single pit to a single site. In addition to the hauling and gravel costs specified above, there is also a fixed cost of $150 associated with hiring each truck. A truck can haul 5 tons, but it is not required to go full. For each combination of pit and site, there are now two decisions to be made: the number of trucks to be used and the amount of gravel to be hauled. Susan wishes to make those two decisions in order to minimize the total cost for purchasing and hauling gravel. (b1) Formulate an MIP model for this problem. (b2) Use the computer to solve this model.

A contractor, Susan Meyer, has to haul gravel to three building sites. She can purchase as much as 18 tons at a gravel pit in the north of the city and 14 tons at one in the south. She needs 10, 5, and 10 tons at sites 1, 2, and 3, respectively. The purchase price per ton at each gravel pit and the hauling cost per ton are given in the table below. Pit North South Hauling Cost per Ton at Site 1 2 3 $100 $160 $180 $140 $190 $110 Price per Ton $300 $420 (a) Susan wishes to determine how much to haul from each pit to each site to minimize the total cost for purchasing and hauling gravel. Formulate this problem as a transportation problem by constructing the appropriate parameter table. (b) Susan now needs to hire the trucks (and their drivers) to do the hauling. Each truck can only be used to haul gravel from a single pit to a single site. In addition to the hauling and gravel costs specified above, there is also a fixed cost of $150 associated with hiring each truck. A truck can haul 5 tons, but it is not required to go full. For each combination of pit and site, there are now two decisions to be made: the number of trucks to be used and the amount of gravel to be hauled. Susan wishes to make those two decisions in order to minimize the total cost for purchasing and hauling gravel. (b1) Formulate an MIP model for this problem. (b2) Use the computer to solve this model.

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter5: Network Models
Section5.5: Shortest Path Models
Problem 30P
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A contractor, Susan Meyer, has to haul gravel to three building sites. She can purchase as much as 18 tons at a gravel pit in the north of the city and 14 tons at one in the south. She needs 10, 5, and 10 tons at sites 1, 2, and 3, respectively. The purchase price per ton at each gravel pit and the hauling cost per ton are given in the table below. Pit North South Hauling Cost per Ton at Site 1 2 3 $160 $140 $100 $180 $190 $110 Price per Ton $300 $420 (a) Susan wishes to determine how much to haul from each pit to each site to minimize the total cost for purchasing and hauling gravel. Formulate this problem as a transportation problem by constructing the appropriate parameter table. (b) Susan now needs to hire the trucks (and their drivers) to do the hauling. Each truck can only be used to haul gravel from a single pit to a single site. In addition to the hauling and gravel costs specified above, there is also a fixed cost of $150 associated with hiring each truck. A truck can haul 5 tons, but it is not required to go full. For each combination of pit and site, there are now two decisions to be made: the number of trucks to be used and the amount of gravel to be hauled. Susan wishes to make those two decisions in order to minimize the total cost for purchasing and hauling gravel. (b1) Formulate an MIP model for this problem. (b2) Use the computer to solve this model.
Transcribed Image Text:A contractor, Susan Meyer, has to haul gravel to three building sites. She can purchase as much as 18 tons at a gravel pit in the north of the city and 14 tons at one in the south. She needs 10, 5, and 10 tons at sites 1, 2, and 3, respectively. The purchase price per ton at each gravel pit and the hauling cost per ton are given in the table below. Pit North South Hauling Cost per Ton at Site 1 2 3 $160 $140 $100 $180 $190 $110 Price per Ton $300 $420 (a) Susan wishes to determine how much to haul from each pit to each site to minimize the total cost for purchasing and hauling gravel. Formulate this problem as a transportation problem by constructing the appropriate parameter table. (b) Susan now needs to hire the trucks (and their drivers) to do the hauling. Each truck can only be used to haul gravel from a single pit to a single site. In addition to the hauling and gravel costs specified above, there is also a fixed cost of $150 associated with hiring each truck. A truck can haul 5 tons, but it is not required to go full. For each combination of pit and site, there are now two decisions to be made: the number of trucks to be used and the amount of gravel to be hauled. Susan wishes to make those two decisions in order to minimize the total cost for purchasing and hauling gravel. (b1) Formulate an MIP model for this problem. (b2) Use the computer to solve this model.
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