Assignment:
Problem
The Western Paper Company manufactures paper at two factories (F1 and F2) on the West Coast. Their products are shipped by rail to a pair of depots (D1 and D2), one in the Midwest and one in the South. At the depots, the products are repackaged and sent by truck to three regional warehouses (W1, W2, and W3) around the country, in response to replenishment orders.
Each of the factories has a known monthly production capacity, and the three regional warehouses have placed their demands for next month. The following tables summarize the data that have been collected for this planning problem:
|
From Factory
|
To Distribution Center
|
Capacity
|
|
D1
|
D2
|
|
F1
|
$1.28
|
$1.36
|
2500
|
|
F2
|
$1.33
|
$1.38
|
2500
|
|
F3
|
$1.68
|
$1.55
|
2500
|
|
From DC
|
To Warehouse
|
|
W1
|
W2
|
W3
|
W4
|
W5
|
|
D1
|
$0.60
|
$0.42
|
$0.32
|
$0.44
|
$0.68
|
|
D2
|
$0.57
|
$0.30
|
$0.40
|
$0.38
|
$0.72
|
|
Requirement
|
1200
|
1300
|
1400
|
1500
|
1600
|
Knowing the costs of transporting goods from factories to DCs and from DCs to warehouses, Western Paper is interested in scheduling its material flow at the minimum possible cost.
a. Formulate this problem as a linear programming problem. Define all variables clearly and express objective and all constraints in terms of these variables.
b. Solve this problem and clearly show the values of the decision variables and the objective.
c. Suppose that distribution center D2 has a capacity constraint of 2000 units. How will this affect the solution that you find in (b)? Be specific and answer the question completely.