Minimizing costs can be costly (Q965878)

Summary: A quite common practice, even in academic literature, is to simplify a decision problem and model it as a cost-minimizing problem. In fact, some type of models has been standardized to minimization problems, like quadratic assignment problems (QAPs), where a maximization formulation would be treated as a ``generalized'' QAP and not solvable by many of the specially designed softwares for QAP. Ignoring revenues when modeling a decision problem works only if costs can be separated from the decisions influencing revenues. More often than we think this is not the case, and minimizing costs will not lead to maximized profit. This will be demonstrated using spreadsheets to solve a small example. The example is also used to demonstrate other pitfalls in network models: the inability to generally balance the problem or allocate costs in advance, and the tendency to anticipate a specific type of solution and thereby make constraints too limiting when formulating the problem.