GLOBAL OPTIMIZATION IN MULTIPRODUCT AND MULTIPURPOSE BATCH DESIGN UNDER UNCERTAINTY

This paper addresses the design of multiproduct and multipurpose batch plants with uncertainty in both product demands and processing parame ters. The uncertain demands may be described by any continuous/discret e probability distribution. Uncertain processing parameters are handle d in a scenario-based approach. Through the relaxation of the feasibil ity requirement, the design problem with a fixed number of pieces of e quipment per stage is formulated as a single large-scale nonconvex opt imization problem. This problem is solved using a branch and bound tec hnique in which a convex relaxation of the original nonconvex problem is solved to provide a lower bound on the global solution. Several dif ferent expressions for the tight convex lower bounding functions are p roposed. Using these expressions, a tight lower bound on the global op timum solution can be obtained at each iteration. The alpha BB algorit hm is subsequently employed to refine the upper and lower bounds and c onverge to the global solution. The tight lower bounds and the efficie ncy of the proposed approach is demonstrated in several example proble ms. These case studies correspond to large-scale global optimization p roblems with nonconvex constraints ranging in number from 25 to 3750, variables ranging from 30 to 15636 and nonconvex terms ranging from 50 to 15000. It is shown that such large-scale multiproduct and multipur pose batch design problems can be solved to global optimality with rea sonable computational effort.