Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas. Demand forecasts for the coming winter season are Hamilton County, 400 units; Butler County, 200 units; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars) are as follows: From               TO                      Hamilton Butler Clermont Southern Gas 10 20 15 Northwest Gas 12 15 18 REQUIREMENTS Develop a network representation of this problem and Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs. Describe the distribution plan and show the total distribution cost. (First determine initial transportation cost then use LCM). Recent residential and industrial growth in Butler County has the potential for increasing demand by as much as 100 units. Which supplier should Tri-County contract with to supply the additional capacity? (Hint: Use LCM method only).

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter6: Optimization Models With Integer Variables
Section: Chapter Questions
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Tri-County Utilities, Inc., supplies natural gas to customers in a three-county area. The company purchases natural gas from two companies: Southern Gas and Northwest Gas. Demand forecasts for the coming winter season are Hamilton County, 400 units; Butler County, 200 units; and Clermont County, 300 units. Contracts to provide the following quantities have been written: Southern Gas, 500 units; and Northwest Gas, 400 units. Distribution costs for the counties vary, depending upon the location of the suppliers. The distribution costs per unit (in thousands of dollars) are as follows:

From

 

 

          TO                     

Hamilton

Butler

Clermont

Southern Gas

10

20

15

Northwest Gas

12

15

18

REQUIREMENTS

  1. Develop a network representation of this problem and Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs.

  2. Describe the distribution plan and show the total distribution cost. (First determine initial transportation cost then use LCM).

  3. Recent residential and industrial growth in Butler County has the potential for increasing demand by as much as 100 units. Which supplier should Tri-County contract with to supply the additional capacity? (Hint: Use LCM method only).
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ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,