Solving the integrated lot-sizing and job-shop scheduling problem

Abstract

Production planning and scheduling are usually performed in a sequential manner, thus generating unfeasibility conflicts. Moreover, solving these problems in complex manufacturing systems (with several products sharing different resources) is very challenging in production management. This paper addresses the solution of multi-item multi-period multi-resource single-level lot-sizing and scheduling problems in general manufacturing systems with job-shop configurations. The mathematical formulation is a generalisation of the one used for the Capacitated Lot-Sizing Problem, including detailed capacity constraints for a fixed sequence of operations. The solution method combines a Lagrangian heuristic, determining a feasible production plan for a fixed sequence of operations, with a sequence improvement method which iteratively feeds the heuristic. Numerical results demonstrate that this approach is efficient and more appropriate than a standard solver for solving complex problems, regarding solution quality and computational requirements.

Keywords:

• production planning
• lot-sizing
• job-shop scheduling
• Lagrangian heuristic
• Tabu Search
• integrated approach

Notes

This work is supported by the National Research Fund, Luxembourg, through IALOM project (C09/IS/14).