Operations Research: Linear Optimization
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.