Compromise Programming and Utility Functions

Proposed in the last decades of the twentieth century, the Compromise Programming (CP) model assumes that the decision maker looks for a compromise between objectives of different character, financial, ethical or others. As described by CP, the decision maker has in mind an ideal point, which is a basket containing the best feasible level of each objective. This ideal is a utopian infeasible basket of reference because all the best objectives cannot be simultaneously reached. Given an efficient frontier of baskets, the CP satisfying solution is to choose the basket closer to the ideal. More precisely, the CP solution is obtained by minimizing the distance between a frontier basket and the ideal. Distances are not necessarily measured by the Euclidean quadratic metric but by a conventional metric between one and infinity. Moreover, the distance in CP is not a purely geometric notion but a composite measure in which the geometric components are multiplied by the decision maker’s preference weights for each objective. Years later the CP proposal, a linkage between CP and utility theory was investigated. Finally, Linear–quadratic composite metric looks for a compromise between aggressive (large risky acnievements) and conservative (balanced solutions) objectives.