Using genetic algorithm for lot sizing and scheduling problem with arbitrary job volumes and distinct job due date considerations

Deyun Wang, Olivier Grunder and Abdellah EL Moudni

International Journal of Systems Science, 2014, vol. 45, issue 8, 1694-1707

Abstract: This paper considers an integrated lot sizing and scheduling problem for a production–distribution environment with arbitrary job volumes and distinct due dates considerations. In the problem, jobs are firstly batch processed on a batching machine at production stage and then delivered to a pre-specified customer at the subsequent delivery stage by a capacitated vehicle. Each job is associated with a distinct due date and a distinct volume, and has to be delivered to the customer before its due date, i.e. delay is not allowed. The processing time of a batch is a constant independent of the jobs it contains. In production, a constant set-up time as well as a constant set-up cost is required before the first job of this batch is processed. In delivery, a constant delivery time as well as a constant delivery cost is needed for each round-trip delivery between the factory and the customer. Moreover, it is supposed that a job that arrives at the customer before its due date will incur a customer inventory cost. The objective is to find a coordinated lot sizing and scheduling scheme such that the total cost is minimised while guaranteeing a certain customer service level. A mixed integer formulation is proposed for this problem, and then a genetic algorithm is developed to solve it. To evaluate the performance of the proposed genetic algorithm, a lower bound on the objective value is established. Computational experiments show that the proposed genetic algorithm performs well on randomly generated problem instances.

Date: 2014
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DOI: 10.1080/00207721.2012.748946

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