Approximation to Multistage Stochastic Optimization in Multiperiod Batch Plant Scheduling under Demand Uncertainty

Abstract We consider the problem of scheduling under demand uncertainty a multiproduct batch plant represented through the State Task Network. Given a scheduling horizon consisting of several time-periods in which product demands are placed, the objective is to select a schedule that maximizes the expected profit. We present a multistage stochastic Mixed Integer Linear Programming (MILP) model, wherein certain decisions are made irrespective of the realization of the uncertain parameters, and some decisions are taken upon realization of the uncertainty. To overcome the computational expense associated with the solution of the large-scale stochastic multistage MILP for large problems, we examine an approximation strategy based on the solution of a series of a two-stage models within a shrinking horizon approach. Computational results indicate that the proposed approximation strategy provides an expected profit within a few percent of the multistage stochastic MILP in a fraction of the computation time, and provides significant improvement in the expected profit over similar deterministic approaches.