Lagrangian Relaxation for an Inventory Location Problem with Periodic Inventory Control and Stochastic Capacity Constraints

Resultado de la investigación: Article

Resumen

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.

Idioma originalEnglish
Número de artículo8237925
PublicaciónMathematical Problems in Engineering
Volumen2018
DOI
EstadoPublished - 1 ene 2018

Huella dactilar

Lagrangian Relaxation
Inventory control
Inventory Control
Capacity Constraints
Warehouses
Location Problem
Subgradient Method
Customers
Periodic Review
Duality Gap
Mixed Integer Nonlinear Programming
Costs
Control Policy
Programming Model
Nonlinear Model
Nonlinear programming
Assignment
Objective function
Optimal Solution
Heuristics

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Citar esto

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abstract = "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.",
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