Global Optimization In Multiproduct and Multipurpose Batch Design Under Uncertainty

Abstract

This paper addresses the design of multiproduct and multipurpose batch plants with uncertainty in both product demands and in processing parameters. The uncertain demands may be described by any continuous/discrete probability distribution. Uncertain processing parameters are handled in a scenario-based approach. Through the relaxation of the feasibility requirement, the design problem with a fixed number of pieces of equipment per stage is formulated as a single large-scale nonconvex optimization problem. This problem is solved using a branch and bound technique in which a convex relaxation of the original nonconvex problem is solved to provide a lower bound on the global solution. Several different expressions for the tight convex lower bounding functions are proposed. Using these expressions, a tight lower bound on the global optimum solution can be obtained at each iteration. The ffBB algorithm (Androulakis et al. (1995)) is subsequently employed to refine the upper and lower bound..