In the past the company has shipped the wood by train. However, because shipping costs have been increasing, the alternative of using ships to make some of the deliveries is being investigated. This alternative would require the company to invest in some ships. Except for these investment costs, the shipping costs in thousands of dollars per million board feet by rail and by water (when feasible) would be the following for each route:
Source | Unit cost by rail Market | Unit cost by ship Market | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | 1 | 2 | 3 | 4 | 5 | |
1 | 61 | 72 | 45 | 55 | 66 | 31 | 38 | 24 | - | 35 |
2 | 69 | 78 | 60 | 49 | 56 | 36 | 43 | 28 | 24 | 31 |
3 | 59 | 66 | 63 | 61 | 47 | - | 33 | 36 | 32 | 26 |
The capital investment (in thousands of dollars) in ships required for each million board feet to be transported annually by ship along each route is given as follows:
Source | Investment for ships Market | ||||
---|---|---|---|---|---|
1 | 2 | 3 | 4 | 5 | |
1 | 275 | 303 | 238 | - | 285 |
2 | 293 | 318 | 270 | 250 | 265 |
3 | - | 283 | 275 | 268 | 240 |
Considering the expected useful life of the ships and the time value of money, the equivalent uniform annual cost of these investments is one-tenth the amount given in the table. The company is able to raise only $6,750,000 to invest in ships. The object is to determine the overall shipping plan that minimizes the total equivalent uniform annual cost while meeting this investment budget and the sales demand at the markets. Formulate the linear programming model for this problem.