SHIPPING WOOD TO MARKET

Alabama Atlantic is a lumber company that has three sources of wood and five mar¬kets 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 mar¬kets 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 ship¬ping costs have been increasing, the alternative of using ships to make some of the de¬liveries 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 dol¬lars per million board feet by rail and by water (when feasible) would be the follow¬ing for each route:

Source Unit Cost by Rail ($1,000's) 
Market Unit Cost by Ship ($1,000's) Market

1 2 5 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 ($1,000's)
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 to¬tal equivalent uniform annual cost (including shipping costs).
You are the head of the OR 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 in-vestment costs, so that the decision on the option to adopt now should take into ac¬count 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 adopt¬ing that option now.