Problem: Applichem wants to allocate the capacity of its worldwide manufacturing plants to fulfill its customer demand. Applichem makes a product, R, which is used by plastic molding companies around the world. R sells for $1/lb. Its plants are located in Gary, Indiana, Windsor, Ontario, Frankfurt, Germany, Mexico City, Caracus, Venezula, and Osaka, Japan. Its current strategy is to make and ship R as shown in the table below (x 100,000 lbs)
|
From/To
|
Mexico
|
Canada
|
Venezula
|
Europe
|
United States
|
Japan
|
|
Mexico City
|
3.0
|
|
6.3
|
|
|
|
|
Windsor
|
|
2.6
|
|
|
|
|
|
Caracus
|
|
|
4.1
|
|
|
|
|
Frankfurt
|
|
|
5.6
|
20.0
|
12.4
|
|
|
Gary
|
|
|
|
|
14.0
|
|
|
Japan
|
|
|
|
|
|
4.0
|
Plant Production Costs and Capacity are shown in the table below:
|
Plant
|
Cost/1000lbs
|
Capacity (100,000 lbs)
|
|
Mexico City
|
95.01
|
22.0
|
|
Windsor
|
97.35
|
3.7
|
|
Caracas
|
116.34
|
4.5
|
|
Frankfurt
|
76.69
|
47.0
|
|
Gary
|
102.93
|
18.5
|
|
Osaka
|
153.80
|
5.0
|
The current Transportation Cost ($/1000 lb), Import Duties, and current customer Demand are shown in the table below:
|
Plant/Country
|
Mexico
|
Canada
|
Venezuela
|
Europe
|
United States
|
Japan
|
|
Mexico City
|
0
|
11.40
|
7.00
|
11.00
|
11.00
|
14.00
|
|
Windsor
|
11.00
|
0
|
9.00
|
11.50
|
6.00
|
13.00
|
|
Caracas
|
7.00
|
10.00
|
0
|
13.00
|
10.40
|
14.30
|
|
Frankfurt
|
10.00
|
11.50
|
12.50
|
0
|
11.20
|
13.30
|
|
Gary
|
10.00
|
6.00
|
11.00
|
10.00
|
0
|
12.50
|
|
Osaka
|
14.00
|
13.00
|
12.50
|
14.20
|
13.00
|
0
|
|
Demand
(100,000 lbs)
|
3.0
|
2.6
|
16.0
|
20.0
|
26.4
|
11.9
|
|
Import Duty
|
|
|
50%
|
9.5%
|
4.5%
|
6%
|
Your boss has asked you to look at this and suggest improvements to increase profit.
a. What is the current cost being incurred and profit earned?
b. Build a LP model to represent the situation. Hint you need a variable for product shipped from each plant to each destination, for the total produced at each plant and the total received in each country.
c. Solve the LP model using POM/QM and develop your recommendation.