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

Franco Quezada(franco.quezada***at***lip6.fr)
CÚline Gicquel(gicquel***at***lri.fr)
Safia Kedad-Sidhoum(safia.kedad_sidhoum***at***cnam.fr)
Quan Dong(dongquan.math***at***gmail.com)

Abstract: We 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 stochastic planning model with respect to the deterministic model.

Keywords: Stochastic lot-sizing, remanufacturing system, lost sales, multi-stage stochastic integer programming, scenario tree, valid inequalities, branch-and-cut algorithm

Category 1: Applications -- OR and Management Sciences

Category 2: Applications -- OR and Management Sciences (Production and Logistics )

Category 3: Combinatorial Optimization (Branch and Cut Algorithms )

Citation:

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Entry Submitted: 08/31/2018
Entry Accepted: 08/31/2018
Entry Last Modified: 08/31/2018

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