A parametric programming approach to supply chains problems
In this work, a parametric programming based approach is proposed to the hierarchical plant selection problem. Based on recently proposed multi-parametric programming algorithms (Dua et al., 2002; Dua and Pistikopoulos, 2000), multi-level programming problems can be solved without disassembling the multi-level nature of them, since the rational reaction sets can be computed in advance and thereby the leader can choose the global optimum. Moreover, since the rational reaction set is computed through the Basic Sensitivity Theorem (Fiacco, 1983), the behaviour of the follower will be given by an affine function of the leader's variables. Consequently, in the upper level no extra numerical complexity is introduced. The advantage of this technique is that the parametric nature of the leader's problem is preserved and allows for possible comparisons between global optima. The underlying mathematical theory and a illustrating example are provided.