We saw that the “natural” way to model SureStep’s backlogging model, with IF functions, leads to a nonsmooth model that Solver has difficulty handling.

Another version of the problem is also difficult for Solver. Suppose SureStep wants to meet all demand on time (no backlogging), but it wants to keep its employment level as constant across time as possible.

To induce this, it charges a cost of $1000 each month on the absolute difference between the beginning number of workers and the number after hiring and firing—that is, the absolute difference between the values in rows 17 and 20 of the original spreadsheet model. Implement this extra cost in the model in the

“natural” way, using the ABS function. Using demands of 6000, 8000, 5000, and 3000, see how well Solver does in trying to solve this nonsmooth model. Try several initial solutions, and see whether Solver gets the same optimal solution from each of them.