Multi-period lot sizing and job shop scheduling with compressible process times for multilevel product structures

Abstract

This paper presents mathematical modelling of joint lot sizing and scheduling problem in job shop environment under a set of working conditions. The main feature of the problem is to deal with flexible machines able to change their working speeds, known as process compressibility. Furthermore, produced items should be assembled together to make final products. In other words, the products have a multilevel structure, shown with bill of materials. As the problem is proved to be strongly NP-hard, it is solved by a memetic algorithm here. Computational experiences on the data of ‘Mega Motor’ company are reported. Also, further experiences on random test data confirm the performance of the proposed method with less than 5.02% optimality gap while solving the problems in very shorter times than CPLEX 12.0.

Keywords:

• lot sizing
• scheduling
• process compressibility
• job shop
• multi-level