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A multi-stage stochastic integer programming approach for a multi-echelon lot-sizing problem with returns and lost sales

By Franco Quezada, Céline Gicquel, Safia Kedad-Sidhoum and Dong Quan Vu

Abstract

International audienceWe consider an uncapacitated multi-item multi-echelon lot-sizing problem within a remanufacturing system involving three production echelons: disassembly, refurbishing and reassembly. We seek to plan the production activities on this system over a multi-period horizon. We consider a stochastic environment, in which the input data of the optimization problem are subject to uncertainty. We propose a multi-stage stochastic integer programming approach relying on scenario trees to represent the uncertain information structure and develop a branch-and-cut algorithm in order to solve the resulting mixed-integer linear program to optimality. This algorithm relies on a new set of tree inequalities obtained by combining valid inequalities previously known for each individual scenario of the scenario tree. These inequalities are used within a cutting-plane generation procedure based on a heuristic resolution of the corresponding separation problem. Computational experiments carried out on randomly generated instances show that the proposed branch-and-cut algorithm performs well as compared to the use of a stand-alone mathematical solver. Finally, rolling horizon simulations are carried out to assess the practical performance of the multi-stage stochastic planning model with respect to a deterministic model and a two-stage stochastic planning model

Topics: Stochastic lot-sizing, remanufacturing system, lost sales, multi-stage stochastic integer programming, scenario tree, valid inequalities, branch-and-cut algorithm, [INFO]Computer Science [cs], [INFO.INFO-RO]Computer Science [cs]/Operations Research [cs.RO]
Publisher: 'Elsevier BV'
Year: 2020
DOI identifier: 10.1016/j.cor.2019.104865
OAI identifier: oai:HAL:hal-02470310v1
Provided by: HAL-CentraleSupelec
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