Alabama Atlantic is a lumber company that has three sources of wood and five markets to be supplied. The annual availability of wood at sources 1, 2, and 3 is 15, 20, and 15 million board feet, respectively. The amount that can be sold annually at markets 1, 2, 3, 4, and 5 is 11, 12, 9, 10, and 8 million board feet, respectively. 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:
Unit Cost by Rail ($1,000s) to Market
Unit Cost by Ship ($1,000s) to Market
Source
1
2
3
4
5
1
2
3
4
5
1
61
71
45
55
66
61
38
24
−
35
2
69
78
60
49
56
36
43
28
24
31
3
59
66
63
61
47
−
33
36
32
23
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
Unit Investment for Ships ($1,000s) to 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 objective is to determine the overall shipping plan that minimizes the total equivalent uniform annual cost (including shipping costs).
You are the head of the management science team that has been assigned the task of determining this shipping plan for each of the following three options.
Option 1: Continue shipping exclusively by rail.
Option 2: Switch to shipping exclusively by water (except where only rail is feasible).
Option 3: Ship by either rail or water, depending on which is less expensive for the particular route.
Present your results for each option. Compare.
Finally, consider the fact that these results are based on current shipping and investment costs, so that the decision on the option to adopt now should take into account management’s projection of how these costs are likely to change in the future. For each option, describe a scenario of future cost changes that would justify adopting that option now.