Decomposition approaches for the efficient solution of short-term scheduling problems

The solution of large-scale scheduling problems involving the production of hundreds different products using a variety of process unit operations are typical for chemical and pharmaceutical companies. These problems however are translated to mathematical models involving a computationally infeasible number of variables and constraints independent of the mathematical modeling approach one choose to follow. In this paper, the continuous-time formulation proposed by Ierapetritou and Floudas (Ind. Eng. Chem. Res. 37 (1998) 4341) is used as a basic scheduling model. A number of different heuristic-based decomposition approaches are presented including time-based decomposition, required production method and resource-based decomposition. Lagrangean relaxation (LR) and Lagrangean decomposition (LD) are then employed that give rise to an upper bound of the original scheduling problem. Finally, an iterative solution framework is proposed that exploits the lower bound obtained through the heuristic-based approaches and the upper bound based on the LR and LD to result in a refined schedule for large-scale scheduling problems. Two examples are used to illustrate the application of the approaches presented and compare their efficiencies. # 2003 Elsevier Science Ltd. All rights reserved.