A decomposition method for the simultaneous planning and scheduling of single-stage continuous multiproduct plants

In this paper, we address the problem of simultaneously integrating the planning and scheduling of continuous multiproduct plants that consist of a single processing unit. We present a multiperiod mixed-integer linear programming (MILP) optimization model that is based on a continuous time representation, which becomes computationally very expensive to solve as the length of the planning horizon increases. To circumvent this problem, a rigorous bilevel decomposition algorithm is proposed to reduce the computational cost of the problem. The original simultaneous model is decomposed into an upper level planning problem and a lower level planning and scheduling problem. The upper level determines the potential products to be processed, their production levels, and inventories. The lower level is solved in the reduced space of binary variables and determines production levels, product inventories, and the detailed sequence of products and their corresponding processing times. Integer cuts and logic cuts are proposed to reduce the feasible search space for the binary variables and to tighten the gap between the solutions of the two levels. Numerical examples for problems ranging from 4 to 24 weeks are presented to illustrate the performance of the algorithm and to compare it with a full space solution.