Multistage Stochastic Optimization with Recourse in Batch Plant Scheduling

Batch processes are the prevalent mode of production for the manufacture of many types of chemicals products, particularly those production processes or the demand patterns are likely to change. During the last decade, the problems of short-term batch plant scheduling became very important in industrial plant operations, and quantities of work have been done on them, in which three types of time domain representations (discrete-time, continuous-time, event point) and two kinds of batch process representations (state-task network (STN), resource-task network (RTN)) have been proposed. Most of the work has been assumed as deterministic approaches. However, in real plants, parameters such as raw material availability, costs, processing times, and market requirements vary with respect to time and are often subject to unexpected deviations, therefore, the consideration of these uncertain factors in scheduling becomes of great importance in preserving plant feasibility and viability during operations.

There has been increasing interest in the development of probabilistic models to copy explicitly with uncertainties. Straub and Grossmann proposed the idea of the stochastic flexibility index to evaluate the effect of uncertainty quantitatively. Ierapetritou and Pistikopoulos presented a two-stage stochastic programming formulation for the batch plant design and operations. Sand et al. proposed an algorithm to approximate the performance of an ideal online scheduler for a multi-product batch plant. Balasubramanian and Grossmann proposed an approximation strategy based on the solution of a series of a two-stage model within a shrinking-horizon approach to reduce problem sizes and computational time.

In this work, efforts were made on the multistage batch plants scheduling under demand uncertainty and recourse strategy was employed to obtain the optimal schedule. The multiperiod problem was firstly reformulated as a two-period problem and optimized by the strategy of the stochastic programming with recourse. An initial feasible solution was obtained and can be introduced to the original multistage problem to improve the first stage decision. Similarly, the scheduling problem can be solved in a reduced scope with resource until the whole scheduling was achieved. An example will be presented to illustrate the validity and effectiveness of the proposed approach.

Keywords: multistage, scheduling, recourse