Global Optimization for Stochastic Planning, Scheduling and Design Problems

Abstract

The work addresses the problem of including aspects of uncertainty in process parameters and product demands at the planning, scheduling and design of multiproduct/multipurpose plants operating in either continuous or batch mode. For stochastic linear planning models, it is shown that based on a two-stage stochastic programming formulation, a decomposition based global optimization approach can be developed to obtain the plan with the maximum expected profit by simultaneously considering future feasibility. An equivalent representation is also presented based on the relaxation of demand requirements enabling the consideration of partial order fulfilment while properly penalizing unfilled orders in the objective function. A similar relaxation is shown for the problem of scheduling of continuous multiproduct plants enabling the determination of a robust schedule capable of meeting stochastic demands. In both cases, it is shown that such relaxed reformulations can be solved to global optimality, since despite the presence of stochastic parameters the convexity properties of the original deterministic (i.e. without uncertainty) models are fully preserved. Finally, for the case of batch processes, global solution procedures are derived for the cases of continuous and discrete equipment sizes by exploiting the special structure of the resulting stochastic models. Examples are presented to illustrate the applicability of the proposed techniques.