Batch selection, assignment and sequencing in multi-stage multi-product processes

The scheduling of multi-product, multi-stage batch processes is industrially important because it allows us to utilize resources that are shared among competing products in an optimal manner. Previously proposed methods consider problems where the number and size of batches is known a priori. In many instances, however, the selection and sizing (batching) of batches is or should be an optimization decision. To address this class of problems we develop a novel mixed-integer linear programming (MILP) formulation that involves three levels of discrete decisions: selection of batches, assignment of batches to units and sequencing of batches in each unit. Continuous decision variables include sizing and timing of batches. We consider various objective functions: minimization of makespan, earliness, lateness and production cost, as well as maximization of profit, an objective not addressed by previous multi-stage scheduling methods. To enhance the solution of the proposed MILP model we propose symmetry breaking constraints, develop a preprocessing algorithm for the generation of constraints that reduce the number of feasible solutions, and fix sequencing variables based upon time window information. The model enables the optimization of batch selection, assignment and sequencing decisions simultaneously and is shown to yield solutions that are better than those obtained by existing sequential optimization methods.