Shipping Wood to Market

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:

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:

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).

Please read the case and answer the following questions:

1. What are the problems Shipping Wood to Market is facing if there are? Be specific about the problems.

2. If you are the head of the OR team that has been assigned the task of determining this shipping plan, how could consider to solve this problem. Be specific and provide couple of different scenarios for the solution (At least three scenarios you need to provide).

3. If you were in charge of this company, which scenarios that you provide do you select?

Please justify your recommendation by solving these scenarios. Obtain optimization model for each scenarios by specifying the variables.

4. Consider the fact that these results are based on current shipping and investment costs, so the decision on the option to adopt now should take into account managements 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.

Make sure you add a cover page, number the pages, and include all sources in the bibliography section at the end of your assignment.

\begin{tabular}{c|ccccc|ccccc} \hline & \multicolumn{4}{|c|}{\begin{tabular}{c} Unit Cost by Rail (\$1,000's) \\ Market \end{tabular}} & \multicolumn{5}{c}{ Unit Cost by Ship (\$1,000's) } \\ Source & 1 & 2 & 3 & 4 & 5 & 1 & 2 & 3 & 4 & 5 \\ \cline { 2 - 12 } & & & & & & & & 35 \\ 1 & 61 & 72 & 45 & 55 & 66 & 31 & 38 & 24 & - & 31 \\ 2 & 69 & 78 & 60 & 49 & 56 & 36 & 43 & 28 & 24 & 31 \\ 3 & 59 & 66 & 63 & 61 & 47 & - & 33 & 36 & 32 & 26 \\ \hline \end{tabular} \begin{tabular}{c|ccccr} \hline & \multicolumn{5}{|c}{\begin{tabular}{c} Investment for Ships (\$1,000's) \\ Market \end{tabular}} \\ \cline { 2 - 6 } Source & 1 & 2 & 3 & 4 & 5 \\ \hline \multirow{2}{*}{\begin{tabular}{c} \\ \cline { 2 - 6 } \end{tabular}} & 275 & 303 & 238 & - & 285 \\ 3 & 293 & 318 & 270 & 250 & 265 \\ \hline \end{tabular}