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Transportation modelling  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   Develop a network representation of this problem. 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).

Transportation modelling  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   Develop a network representation of this problem. 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).

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter9: Decision Making Under Uncertainty
Section: Chapter Questions
Problem 46P
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Transportation modelling 

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

 

  1. Develop a network representation of this problem.
  2. Develop a linear programming model that can be used to determine the plan that will minimize total distribution costs.
  3. Describe the distribution plan and show the total distribution cost. (First determine initial transportation cost then use LCM).
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  1. 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?

      Amount Cost
    Southern - Hamilton fill in the blank 38 $fill in the blank 39
    Southern - Butler fill in the blank 40 fill in the blank 41
    Southern - Clermont fill in the blank 42 fill in the blank 43
    Northwest - Hamilton fill in the blank 44 fill in the blank 45
    Northwest - Butler fill in the blank 46 fill in the blank 47
    Northwest - Clermont fill in the blank 48 fill in the blank 49
    Total Cost   $fill in the blank 50

    From the new solution we see that Tri-County should contract with 
     
     Gas for the additional 100 units.
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