Short-term scheduling in multi-stage batch plants through Lagrangean decomposition.

Abstract

In this work, a continuous-time Mixed-Integer Linear Programming (MILP) model for the short-term scheduling in multi-stage batch plants is used. The MILP model accounts for ready unit times, release order times, sequence-dependent changeovers, transfer times between adjacent processing stages and different intermediates storage policies. A Lagrangean decomposition technique (Conejo et al., 2002) is applied to the MILP model in order to facilitate the resolution of real-world industrial cases. The proposed decomposition technique is thoroughly examined.

An industrial case study of a multi-product multi-stage pharmaceuticals batch plant is addressed in order to demonstrate the performance and the advantages of the proposed decomposition scheme. The pharmaceutical plant under study consists of 17 processing equipments. The numerous (30 to 50) final products require 5 to 6 processing stages. Sequence-dependent changeovers are permitted in most stages. It is noteworthy that changeovers are usually of the same order of magnitude or even larger than the processing times. The main optimization goal is the minimization of the makespan. Results obtained are discussed highlighting the advantages and the special characteristics of the proposed scheduling model.