Simultaneous Batching and Scheduling Using Dynamic Decomposition on a Grid

Scheduling problems arise in many applications in process industries. However, despite various efforts to develop efficient scheduling methods, current approaches cannot be used to solve instances of industrial importance in reasonable time frames. The goal of this paper is the development of a dynamic decomposition scheme that exploits the structure of the problem and is well suited for grid computing. The problem we study is the simultaneous batching and scheduling of multi-stage batch processes. The algorithm first decomposes the original problem into 1-level subproblems based on batching decisions. The subproblems that remain unsolved within a resource limit are then dynamically decomposed into 2-level subproblems based on batch-unit assignment decisions in one stage. The process can be repeated in a dynamic fashion by identifying subproblems that cannot be solved within a given resource limit and decomposing them by batch-unit assignment, until all subproblems are solved. Alternatively, a problem can be decomposed into a number of promising subproblems using an automatic strong branching scheme. Our results show that the proposed method can be used on a grid computer to solve large problems to optimality in reasonable computational time.