TY - JOUR

T1 - Lagrangian Relaxation for an Inventory Location Problem with Periodic Inventory Control and Stochastic Capacity Constraints

AU - Araya-Sassi, Claudio

AU - Miranda, Pablo A.

AU - Paredes-Belmar, Germán

N1 - Funding Information:
This research has been supported by Chilean National Science and Technology Foundation (FONDECYT) under Grant 1140811.
Publisher Copyright:
© 2018 Claudio Araya-Sassi et al.

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85056634731&partnerID=8YFLogxK

U2 - 10.1155/2018/8237925

DO - 10.1155/2018/8237925

M3 - Article

AN - SCOPUS:85056634731

VL - 2018

JO - Mathematical Problems in Engineering

JF - Mathematical Problems in Engineering

SN - 1024-123X

M1 - 8237925

ER -