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An enhanced L-Shaped method for optimizing periodic-review inventory control problems modeled via two-stage stochastic programming

Fabricio Oliveira(fabricio.oliveira***at***puc-rio.br)
Felipe Placido(felipe_placido***at***outlook.com)

Abstract: This paper presents the development of an enhanced L-Shaped method applied to an inventory management problem that considers a replenishment control system based on the periodic review (R,S) policy. We consider single-item one-echelon problems with uncertain demands and partial backorder that are modeled using two-stage stochastic programming. To enable the consideration of large-scale problems, the classical single-cut L-Shaped method and its extended multi-cut form were initially applied. Preliminary computational results indicated that the classical L-Shaped method outperformed its multi-cut counterpart, even though the former required more iterations to converge to the optimal solution. This observation inspired the development of the techniques presented for enhancing the L-Shape method in this context, which consist of the combination of a novel acceleration technique with an efficient formulation and valid inequalities for the proposed model. Numerical experiments suggest that the proposed approach significantly reduced the computational time required to solve large-scale problems.

Keywords: Stochastic programming; Inventory control; Uncertain demand; Partial backordering; L-Shaped method;

Category 1: Applications -- OR and Management Sciences (Production and Logistics )

Category 2: Stochastic Programming

Citation:

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Entry Submitted: 07/07/2017
Entry Accepted: 07/07/2017
Entry Last Modified: 07/07/2017

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