New MILP models for scheduling of multiproduct batch plants under zero-wait policy

Abstract

This paper presents a new mixed-integer linear programming (MILP) model in which makespan is minimized for the multiproduct batch plants. In particular, the zero-wait (ZW) scheduling with transfer and setup times is analyzed. Not only idle times between the successive products but also heads and tails are used to select a possible production sequence with the minimum makespan. To determine the suitable head and tail, new binary variables are defined and aggregated to the assignment constraints of traveling salesman problems (TSPs). Although the number of binary variables increases, the mathematical formulation can yield a very compact MILP model. The effectiveness of the proposed model is demonstrated through several examples. The proposed model is extended to solve the scheduling problems for productions with single product campaigns (SPCs) and mixed product campaigns (MPCs) explained by Birewar and Grossmann (Ind. Eng. Chem. Res. 1989b, 28, 1333). The solutions by the proposed method are compared with the solutions obtained from the rigorous solution method by Birewar and Grossmann, The proposed model is formulated as a compact size and leads to a significant reduction in solution times.