Combining minsum and minmax. A goal programming approach.

A number of methods for multiple-objective optimization problems (MOP) give as solution to MOP the set of optimal solutions for some single-objective optimization problems associated with it. Well-known examples of these single-objective optimization problems are the minsum and the minmax. In this note, we propose a new parametric single-objective optimization problem associated with MOP by means of Goal Programming ideas. We show that the minsum and minmax are particular instances, so we are somehow combining minsum and minmax by means of a parameter. Moreover, such parameter has a clear meaning in the value space. Applications of this parametric problem to classical models in Locational Analysis are discussed.