## Transportation problem (setup help)

A brief overview of the problem:

A wood company is trying to minimize the cost of shipping wood from three sources to five markets. Traditionally they sent their product exclusively by rail, but now management is considering ships as a method of transportation. There are only two locations that they can only send by rail, but the rest can be shipped by ship.

Table 1-a-b)

Note: the 3 sources on the far left column and the 5 markets on the top row. The cells are filled in with the cost for that particular route.

a) Cost chart for rail service

b) Cost chart for ship service

Moreover, the company does not own any ships, so they have to invest in ships.

Table 2)

Note: the 3 sources are on the far left column and the 5 markets are on the top row. The cells are filled in with the cost for that particular route.

Investment cost chart for ships.

Now, the problem says the equivalent uniform annual cost the investments is 1/10 the amount given in the Table 2.

Problem: Determine the overall shipping plan that minimizes the total equivalent uniform annual cost for the following option.

Option 3: Ship either rail of water, depending on which is less expensive for the particular route.

My thoughts:

Since there are three tables and we are only concerned with the equivalent uniform annual investment, I need to divide the investment cost's in table 3 by 10 and then add the resulting cell values (costs) to the corresponding cells (shipping costs) in table b. So now I have two tables (table a and table b) to look at. Also, I would just enter in the rail cost from table a in the cells that shipping by ship is not possible, rather than a big M, since I already have the rail cost.

So, I was thinking of constructing a new cost table for which every cell corresponds to the min(cell entry in table a, cell entry in table b). This would create a new table with the same supply and demand. From here, I would just carry out the usual transportation problem procedure.

Am I over simplifying things, or is the how I should approach them problem?

Thank you