A slot-based formulation for single-stage multiproduct batch plants with multiple orders per product

Multiple orders per product with different due dates are natural in multiproduct batch plants. Existing approaches for scheduling short-term operations in such plants invariably treat each order as if it were a distinct product, convert orders into batches first, and then schedule batches using predecessor-successor variables. A novel mixed-integer linear programming (MILP) model that deals explicitly with multiple orders per product decides both product batches and their schedule in one formulation and uses slots is presented for single-stage batch plants with parallel, nonidentical units. The model is compared thoroughly with existing ones using four illustrative examples. As shown in an example, our model gives better and faster solutions than the current two-step approach. Both our general model and the one reduced for the special case of a single order per product consistently outperform other models by using fewer variables and constraints and by reducing nodes, iterations, and solution times by substantial factors. This paper shows that MILP models with big-M constraints suffer from an erratic dependence on M. Such models cannot be compared based on just one value of M and surely not based on different values of M, a fact overlooked in the literature so far. In contrast to other models, our model is relatively more robust with respect to M and is even free of M for the makespan objective. Last, slot-based models may be superior alternatives to predecessor-successor models for the present problem.