Simultaneous planning and scheduling of single-stage multi-product continuous plants with parallel lines

In this paper we present a multi-period mixed integer linear programming model for the simultaneous planning and scheduling of single-stage multi-product continuous plants with parallel units. While effective for short time horizons, the proposed scheduling model becomes computationally expensive to solve for long time horizons. In order to address this problem, we propose a bi-level decomposition algorithm in which the original problem is decomposed into an upper level planning and a lower level scheduling problem. For the representation of the upper level, we propose an MILP model which is based on a relaxation of the original model, but accounts for the effects of scheduling by incorporating sequencing constraints, which results in very tight upper bounds. In the lower level the simultaneous planning and scheduling model is solved for a subset of products predicted by the upper level. These sub-problems are solved iteratively until the upper and lower bounds converge. A number of examples are presented that show that the planning model can often obtain the optimal schedule in one single iteration.