The (minimizing) achievement function of the traditional goal programming (GP) model has five basic forms: ni, pi, (ni+pi), (ni−pi), and (pi−ni), where ni and pi are nonnegative under and over achievement variables in the ith goal-constraint. This paper proposes and justifies three new objective-function forms: −ni, −pi, and (ni+pi) and presents an algorithm for solving the ensuing nonconvex program. We also introduce the intuitive concepts of the supposed indifference satisfactory interval (SISI), and the supposed indifference dissatisfactory interval (SIDI). We believe that these concepts will help the decision maker understand the different objective-function forms.
