Multiobjective Programming

Abstract

In the mathematical optimization problems discussed so far, we have assumed that there was a single objective function. This may be valid in some circumstances (e.g., when a well-established company attempts to maximize its profit), it will be unsatisfactory in others. In particular, when there is more than a single stakeholder as is the case in virtually all public decision making problems, or more than a single concern exists. Typical concerns include some often interrelated measures such as profits, costs, revenues, market shares, and return on investment, but can also include other issues such as risk, pollution, the loss of property values, and other criteria. The former, sometimes referred to as “private objectives” tend to be easily measured, while the latter, also referred to as “public objectives,” are typically difficult to measure. For instance, pollution is almost always an expression that combines different pollutants that are not difficult to measure individually, while modeling their aggregation is certainly problematic. For simplicity, we will assume throughout this chapter that r issues of concern have been identified and agreed upon by all decision makers, and that these concerns can be expressed by means of a quantitative measure.