DSS Inc. is an electronics company with production facilities located in Atlanta, Boston, and Chicago. Components produced at these facilities may be shipped to the firm's regional warehouses that are located in Edison and Fargo. From the warehouses the firm supplies retail outlets located in Houston, Indianapolis, and Jacksonville.
The capacity of each production facility is presented below:
|
Atlanta
|
Boston
|
Chicago
|
|
800
|
500
|
700
|
The firm must meet the demands specified below for each retail outlet:
|
Houston
|
Indianapolis
|
Jacksonville
|
|
900
|
600
|
500
|
The transportation cost per unit from each facility to each warehouse is specified below:
|
|
Atlanta
|
Boston
|
Chicago
|
|
Edison
|
6
|
1
|
3
|
|
Fargo
|
4
|
8
|
1
|
The transportation cost per unit from each warehouse to each retail outlet is specified below:
|
|
Houston
|
Indianapolis
|
Jacksonville
|
|
Edison
|
8
|
3
|
4
|
|
Fargo
|
2
|
3
|
8
|
The firm has to determine an optimal transshipment plan that minimizes total transportation cost while meeting the demands in each retail outlet and not exceeding the capacity at each production facility.
Formulate the transshipment problem as a Linear-programming model and develop a decision support systems prototype to determine the optimal transshipment plan.
In the analysis so far we have ignored the cost of operating each warehouse. If a warehouse is operated, a fixed cost must be incurred. If a warehouse is not operated, the fixed cost can be avoided but no transshipment can occur through that warehouse.
Determine the optimal plan (where the total cost of transportation and warehouse operation is minimized) if the fixed cost for warehouse operation is as given below:
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|
Cost
|
|
Edison
|
$10,000
|
|
Fargo
|
$5,000
|