The ABC Company is a fully integrated company that both produces goods and sells them at the retail outlets. After production, the goods are stored in the company's two warehouses until needed by the retail outlets. Trucks are used to transport the goods from the two plants to the warehouses and then from the warehouses to the three retail outlets.
Using units of full truckloads, Table 1.below shows each plant's monthly output, its shipping cost per truckload sent to each warehouse, and the maximum amount that it can ship per month to each warehouse.
Table 1.
Unit Shipping
|
|
Unit Shipping Cost
|
Shipping Capacity
|
|
|
From/to
|
Warehouse 1
|
Warehouse 2
|
Warehouse 1
|
Warehouse 2
|
output
|
|
Plant 1
|
$ 425
|
$ 560
|
125
|
150
|
200
|
|
Plant 2
|
$ 510
|
$ 600
|
175
|
200
|
300
|
For each retail outlet, Table 2.below shows the shipping cost per truckload from each warehouse, and the maximum amount that can be shipped per month from each warehouse.
The monthly demand for each retail outlets are 150, 200, and 150.
Table 2.
|
Unit cost Shipping
|
Shipping capacity
|
|
From/To
|
Retail outlet 1
|
Retail outlet
2
|
Retail outlet
3
|
Retail outlet
1
|
Retail outlet
2
|
Retail outlet
3
|
|
Warehouse 1
|
$470
|
$505
|
$490
|
100
|
150
|
100
|
|
Warehouse 2
|
$390
|
$410
|
$440
|
125
|
150
|
75
|
Management now wants to determine a distribution plan that specifies the number of truckloads shipped per month from each plant to each warehouse and from each warehouse to each retail outlet that will minimize the total shipping cost.
1. Draw a network that depicts the company's distribution network. Identify the supply nodes, transshipment notes, and demand nodes on the network.
2. Formulate the network model for this problem as a minimum cost flow problem.
a. What are the decision variables?
b. What are the constraints?
c. What is the goal?
d. What are the necessary assumptions of the network model?
e. Solve and interpret results
f. Identify the binding constraints (limiting factors).
3. Critique the limitations of framing the problem as a network model and minimum cost flow problem.
4. What changes to the model would you recommend? What factors were not accounted for? What other factors should be considered?