In all the linear programming models presented in Chapters 2 through 8, a single objective was either maximized or minimized. However, a company or an organization often has more than one objective, which may relate to something other than profit or cost. In fact, a company may have several criteria, that is, multiple criteria , that it will consider in making a decision instead of just a single objective. For example, in addition to maximizing profit, a company in danger of a labor strike might want to avoid employee layoffs, or a company about to be fined for pollution infractions might want to minimize the emission of pollutants. A company deciding between several potential research and development projects might want to consider the probability of success of each of the projects, the cost and time required for each, and potential profitability in making a selection.
In this chapter we discuss three techniques that can be used to solve problems when they have multiple objectives: goal programming , the analytical hierarchy process , and scoring models . Goal programming is a variation of linear programming in that it considers more than one objective (called goals) in the objective function. Goal programming models are set up in the same general format as linear programming models, with an objective function and linear constraints. The model solutions are very much like the solutions to linear programming models. The format for the analytical hierarchy process and scoring models, however, is quite different from that of linear programming. These methods are based on a comparison of decision alternatives for different criteria that reflects the decision maker's preferences. The result is a mathematical "score" for each alternative that helps the decision maker rank the alternatives in terms of preferability.