Resource Allocation and Duality

Abstract

The ultimate aim of multiple criteria decision analysis (MCDA) is to provide a device for combining the analytical phase and the judgmental phase of multiple criteria decision making (MCDM). As we have discussed in preceding chapters, MCDM has two phases: analytical and judgmental. Mathematical optimization can effectively be executed in the analytical phase and decision analysis can be properly used in the judgmental phase. However, there exists a decision gap between these two phases, which should be bridged with some devices; this is the intrinsic property of MCDM. In the multiobjective mathematical programming techniques discussed in Chapters 2 to 4, the judgmental phase is reduced to assess the marginal rates of substitution among objectives, and is inserted externally into the solution algorithm without any concern about construction of the preference functions of DM. In the decision analysis discussed in Chapters 5 to 8, the judgmental phase is exclusively treated in construction of the preference functions of DM without any concern about mathematical optimization processes. In both of these approaches, the subjective evaluation processes in MCDM are definitely separated from the mathematical optimization processes for obtaining Pareto optimal solutions. We are concerned with constructing a proper device which can more effectively combine both phases of MCDM. This device can primarily be based on duality of mathematical programming.