Using genetic algorithm for lot sizing and scheduling problem with arbitrary job volumes and distinct job due date considerations |
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Authors: | Deyun Wang Abdellah EL Moudni |
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Affiliation: | Université de Technologie de Belfort-Montbéliard, Institut de Recherche sur les Transports, l'Energie et la Société - laboratoire Systèmes et Transports (IRTES-SET), Belfort Cedex, France |
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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. |
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Keywords: | scheduling production distribution genetic algorithm lower bound |
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