Title: Production and delivery scheduling problem with delivery times and costs dependent on batch-size

Authors: Olivier Grunder; Zakaria Hammoudan; Abdellah El Moudni

Addresses: Université Bourgogne Franche-Comté, Université de Technologie de Belfort-Montbéliard, IRTES EA7274, F-90010 Belfort, France ' Université Bourgogne Franche-Comté, Université de Technologie de Belfort-Montbéliard, IRTES EA7274, F-90010 Belfort, France ' Université Bourgogne Franche-Comté, Université de Technologie de Belfort-Montbéliard, IRTES EA7274, F-90010 Belfort, France

Abstract: In this paper, we study a real-industrial case of an integrated lot sizing and delivery scheduling problem with multi-capacitated transporters, distinct due dates considerations and batch-size-dependent delivery times and costs. The objective is to find a coordinated lot sizing and scheduling scheme so that the total cost is minimised while guaranteeing a certain service level at the manufacturers. A mathematical formulation of the problem is given as a nonlinear model in a general way. We prove dominance properties among the solutions of the problem and propose two solving methods. The first one is a generalised dynamic programming scheme to solve this problem in the case of homogeneous and heterogeneous transporters, and the second one is a mixed integer programming formulation proposed to evaluate the performance of the dynamic programming method. Computational experiments show that the proposed approach is very efficient for solving from small to medium-sized instances, especially for the identical transporter case.

Keywords: automotive manufacturing; coordinated scheduling; production; distribution; dynamic programming; mixed integer programming; MIP; delivery times; costs dependent; batch sizes; multi-capacitated transporters; due dates; lot sizing; service levels; automobile industry; nonlinear modelling.

DOI: 10.1504/IJLSM.2016.076891

International Journal of Logistics Systems and Management, 2016 Vol.24 No.3, pp.333 - 355

Received: 17 Mar 2015
Accepted: 16 May 2015
Published online: 06 Jun 2016 *

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