The Transportation Model

This module is used to solve transportation problems. Of course, this module can be used to solve other problems such as assignment problems and production planning problems.

Data

The transportation problem is structured according to the number of origins in the problem and the number of destinations.

Objective function. While minimization is the usual objective in transportation, either minimize or maximize can be chosen at the time that the data set is created or as usual at the edit screen through the objective box above the data set.

Consider the following example. Our initial data screen for this 5 by 6 sample problem follows.

Notice that a STEP button appears on the toolbar ..

Objective. The objective function can be changed in the usual option method.

Shipping costs. The main body of information is the shipping cost from each origin to each destination.

Supplies. The column on the far right contains the supply at each origin.

Demands. The demand row contains the demand at each destination.

Starting method. Four options are available in the method drop-down box. They are:

1.	Any method (the software actually uses Vogel's approximation method)

2.	Northwest corner method.

3.	Vogel's approximation method.

4.	Minimum cost method. (Also known as the intuitive method)

The optimal cost is, of course, independent of the initial method, as is the optimal shipping schedule when there are no alternative solutions.

Solution

A solution to the sample problem follows. The main solution screen shows the shipments that are to be made and contains the total cost in the upper-left corner. If a dummy row or column needs to be added, it will appear in this table.

Total cost or profit. The total cost or profit appears in the upper left corner.

Marginal costs

A table of marginal costs is available.

Stepping

We consider the same problem but change the solution method to Northwest corner. The first table appears as below.

Notice that some of the numbers are enclosed in parentheses while others are not. (On the screen the numbers also display in two different colors.) The numbers without a sign represent the shipments, while the numbers with a sign represent the marginal costs. The largest (absolute value) marginal cost is -98 in the cell Jenkintown to Dummy (which is the current cell selected by the software). Also notice that the total cost, which is $31,087, is displayed at the top of the table. You do not have to use the entering cell suggested by the software. You can use the direction keys to change the entering cell.

Repeating this process five more times brings us to the screen displayed next. In this screen there is a message after the cost indicating that the solution is optimal and we need to press FINISH. Everything after this is as before if we press a key one more time. That is, we can display the shipments, the marginal costs, or both in one table.