A general structure of achievement function for a goal programming model

A key element of a goal programming model is the achievement function; that is, the function that measures the degree of minimisation of the unwanted deviation variables of the goals considered in the model. The three oldest and still most widely used forms of achievement functions are the following: Archimedean, lexicographic and MINMAX. While they are the most common, other newer versions can offer theoretical and practical advantages. These newer forms will be analytically described and interpreted in utility terms throughout this paper. The presentation will end with a very general structure, which encompasses as particular cases basically all the achievement functions proposed in the literature.