Lagrangian relaxation for an inventory location problem with periodic inventory control and stochastic capacity constraints
type: Item
instance of: scholarly article
title: Lagrangian relaxation for an inventory location problem with periodic inventory control and stochastic capacity constraints
zbMATH Open document ID: 1427.90007
DOI: 10.1155/2018/8237925
author: Claudio Araya-Sassi
author: Pablo A. Miranda
author: Germán Paredes-Belmar
published in: Mathematical Problems in Engineering
publication date: 2019-02-08T00:00:00Z
review text: Summary: We studied a joint inventory location problem assuming a periodic review for inventory control. A single plant supplies a set of products to multiple warehouses and they serve a set of customers or retailers. The problem consists in determining which potential warehouses should be opened and which retailers should be served by the selected warehouses as well as their reorder points and order sizes while minimizing the total costs. The problem is a Mixed Integer Nonlinear Programming (MINLP) model, which is nonconvex in terms of stochastic capacity constraints and the objective function. We propose a solution approach based on a Lagrangian relaxation and the subgradient method. The decomposition approach considers the relaxation of different sets of constraints, including customer assignment, warehouse demand, and variance constraints. In addition, we develop a Lagrangian heuristic to determine a feasible solution at each iteration of the subgradient method. The proposed Lagrangian relaxation algorithm provides low duality gaps and near-optimal solutions with competitive computational times. It also shows significant impacts of the selected inventory control policy into total system costs and network configuration, when it is compared with different review period values.
Mathematics Subject Classification ID: 90B05
Mathematics Subject Classification ID: 90B80
zbMATH DE Number: 7019573
describes a project that uses: SITATION
describes a project that uses: MOD-DIST
describes a project that uses: MENU-OKF
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2018/8237925
OpenAlex ID: W2894990380
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Wikidata QID: Q129122361
description: scientific article; zbMATH DE number 7019573