Continuous time representation in batch/semicontinuous process scheduling: Randomized heuristics approach

Abstract

This paper address the short-term scheduling problem for multipurpose/multiproduct batch and semicontinuous processing systems. The nonuniform time discretization model (NUDM) of Reklaitis and Mockus (1995b), under which binary variables are used to represent occurrence of start and stop events for the various recipe tasks, is extended to accommodate sequence dependent changeovers, non-dedicated storage, and semicontinuous tasks. Since the short term scheduling problem of large batch/semicontinuous plants may be expensive to solve because of its high combinatorial complexity, we adapt and test a bayesian approach to discrete optimization, namely the randomized heuristics technique of Mockus et al (1994). Under this approach, instead of solving the original problem with its large number of binary variables, one solves low a dimensionality heuristics calibration problem which has embedded in it a heuristic solver to the discrete optimization problem. Although any of a number of heuristics suitable for a specific class of problems can be employed within this framework, three different heuristics are tested in this work: simulated annealing, a general polynomial scheme, and a specialized heuristics tailored to the batch scheduling problem structure. The proposed framework readily lends itself to parallelization. Computational comparisons are also reported to solutions obtained via an existing uniform discretization based MILP formulation. It is shown that for test problems proposed formulation and bayesian solution approach consistently outperforms the UDM formulation solved via conventional branch and bound based solution techniques. The results suggest that the NUDM/bayesian approach shows considerable promise for the solution of a class of large and realistic batch scheduling problems.