A manufacturer of printing inks, has five manufacturing plants worldwide. Their locations and capacities are shown in the tables below. The cost of producing 1 ton of ink at each facility in shown in Table 2 and the production costs are in the local currency of the country where the plant is located. The major markets for the inks are North America, South America, Europe, Japan, and the rest of Asia. Table 1 shows the following information: Demand at each market; Transportation costs from each plant to each market in U.S. dollars; Management must come up with a production plan. Answer the questions below. For each case, be sure to fully define the mathematical model (notation, objective function, and constraints). Make sure your results are clear. If the exchange rates are expected as shown in Table 3, and no plant can run below 50 percent of capacity, how much should each plant produce and which markets should each plant supply? If there are no limits on the amount produced in a plant, how much should each plant produce? Can adding 10 tons of capacity in any plant reduce costs? Table 1. Demand and transportation cost in us dollars N. Amer. S. America Europe Japan Asia US 600 1200 1300 2000 1700 Germany 1300 1400 600 1400 1300 Japan 2000 2100 1400 300 900 Brazil 1200 800 1400 2100 2100 India 2200 2300 1300 1000 800 Demand 270 190 200 120 100 Table 2. Production cost and capacity at each plant Plant Capacity (Tons/Year) Production cost per ton US 185 10000 dollars Germany 475 15000 marks Japan 50 1,800,000 yen Brazil 200 13,000 real India 80 400,000 rupees Table 3. Exchange Rates US Mark Yen Real Rupee US 1 1.993 107.7 1.78 43.55 Mark 0.502 1 54.07 0.89 21.83 Yen 0.0093 0.0185 1 0.016 0.405 Real 0.562 1.124 60.65 1 24.52 Rupee 0.023 0.046 2.47 0.041 1
A manufacturer of printing inks, has five manufacturing plants worldwide. Their locations and capacities are shown in the tables below. The cost of producing 1 ton of ink at each facility in shown in Table 2 and the production costs are in the local currency of the country where the plant is located. The major markets for the inks are North America, South America, Europe, Japan, and the rest of Asia. Table 1 shows the following information:
- Demand at each market;
- Transportation costs from each plant to each market in U.S. dollars;
Management must come up with a production plan. Answer the questions below. For each case, be sure to fully define the mathematical model (notation, objective function, and constraints). Make sure your results are clear.
- If the exchange rates are expected as shown in Table 3, and no plant can run below 50 percent of capacity, how much should each plant produce and which markets should each plant supply?
- If there are no limits on the amount produced in a plant, how much should each plant produce?
- Can adding 10 tons of capacity in any plant reduce costs?
Table 1. Demand and transportation cost in us dollars
|
N. Amer. |
S. America |
Europe |
Japan |
Asia |
|
|
US |
600 |
1200 |
1300 |
2000 |
1700 |
|
Germany |
1300 |
1400 |
600 |
1400 |
1300 |
|
Japan |
2000 |
2100 |
1400 |
300 |
900 |
|
Brazil |
1200 |
800 |
1400 |
2100 |
2100 |
|
India |
2200 |
2300 |
1300 |
1000 |
800 |
|
Demand |
270 |
190 |
200 |
120 |
100 |
Table 2. Production cost and capacity at each plant
|
Plant |
Capacity (Tons/Year) |
Production cost per ton |
|
|
US |
185 |
10000 |
dollars |
|
Germany |
475 |
15000 |
marks |
|
Japan |
50 |
1,800,000 |
yen |
|
Brazil |
200 |
13,000 |
real |
|
India |
80 |
400,000 |
rupees |
Table 3. Exchange Rates
|
US |
Mark |
Yen |
Real |
Rupee |
|
|
US |
1 |
1.993 |
107.7 |
1.78 |
43.55 |
|
Mark |
0.502 |
1 |
54.07 |
0.89 |
21.83 |
|
Yen |
0.0093 |
0.0185 |
1 |
0.016 |
0.405 |
|
Real |
0.562 |
1.124 |
60.65 |
1 |
24.52 |
|
Rupee |
0.023 |
0.046 |
2.47 |
0.041 |
1 |
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