The K&L Designs workbook contains the Sensitivity Reports for both the original problem formulation  (Example 13.19) and the alternative model (Example 13.20). Explain the differences in these reports from a practical perspective. In other words, which model provides more useful information to managers and why?

Data from Example 13.20

In the K&L Designs problem, we simply have to ensure that demand is satisfied. We can do this by guaranteeing that the cumulative production in each quarter is at least as great as the cumulative demand. This is expressed by the following constraints: 

The differences between the left- and right-hand sides of these constraints are the ending inventories for each period (and we need to keep track of these amounts because inventory has a cost associated with it). Thus, we use the following objective function: 

Of course, this function can be simplified algebraically by combining like terms. Although these two models look very different, they are mathematically equivalent and will produce the same solution. Figure 13.32 shows a spreadsheet implementation of this alternate model (available in the worksheet Alternate Model in the K&L Designs workbook), and Figure 13.33 shows the Solver model. Both have the same optimal solution.

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PA = 150 PA + PW = 550 PA+PW + PS 600 PA, PW, Ps= 0