Comments on Romero C, Tamiz M and Jones DF (1998). Goal programming, compromise programming and reference point method formulations: linkages and utility interpretations

The techniques of Goal Programming (GP) and the Reference Point Method (RPM) form the well known multicriteria decision making (MCDM) methodologies. The approaches have a clear common root: they use a certain target point in the criterion (attribute) space to model a decision maker’s (DM) preferences. This point within GP is a vector of aspiration levels which represent the most desired values for several criteria (attributes). The aspiration levels either can or cannot be achieved. Within RPM the target point is a vector of reference levels to be used in an interactive way by the DM. The RPM approach can be expressed in the GP modelling framework of deviational variables and lexicographic optimisation. However, the RPM models differ from typical GP formulations due to the use of negative weights and additional regularisation of the minmax aggregation. Both these elements are important to guarantee the efficiency of solutions. In the September 1998 issue of this journal, Romero et al have proposed some simplified models. Their claims that the models generate efficient solutions are unproven. Simple counterexamples show that these claims are unjustified. Recall that Romero et al assume all the criteria be maximised and they use the following notation for the techniques under examination: