Valid inequalities for Lagrangian relaxation in an inventory location problem with stochastic capacity

Pablo A. Miranda; Rodrigo A. Garrido

doi:10.1016/j.tre.2006.04.002

Valid inequalities for Lagrangian relaxation in an inventory location problem with stochastic capacity

Pablo A. Miranda, Rodrigo A. Garrido

Engineering School

Research output: Contribution to journal › Article › peer-review

72 Citations (Scopus)

Abstract

We developed an efficient heuristic to solve a joint location-distribution-inventory model for a three layered supply chain. A firm must locate distribution centers to supply a commodity to spatially distributed retailers with stochastic demand. The solution approach is based on Lagrangian relaxation, improved with validity constraints derived from the finite set of all possible combinations of mean demand and variance. The optimal solution's lower bound is found through the optimal solution of the dual problem. The dual gap gives a threshold to the heuristic's error. The heuristic was applied to 98 instances with an average error threshold of 3%.

Original language	English
Pages (from-to)	47-65
Number of pages	19
Journal	Transportation Research Part E: Logistics and Transportation Review
Volume	44
Issue number	1
DOIs	https://doi.org/10.1016/j.tre.2006.04.002
Publication status	Published - 1 Jan 2008

Keywords

Distribution network design
Facility location problems
Inventory-location models
Lagrangian relaxation
Valid inequalities

ASJC Scopus subject areas

Business and International Management
Civil and Structural Engineering
Transportation

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10.1016/j.tre.2006.04.002

Cite this

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AB - We developed an efficient heuristic to solve a joint location-distribution-inventory model for a three layered supply chain. A firm must locate distribution centers to supply a commodity to spatially distributed retailers with stochastic demand. The solution approach is based on Lagrangian relaxation, improved with validity constraints derived from the finite set of all possible combinations of mean demand and variance. The optimal solution's lower bound is found through the optimal solution of the dual problem. The dual gap gives a threshold to the heuristic's error. The heuristic was applied to 98 instances with an average error threshold of 3%.

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KW - Facility location problems

KW - Inventory-location models

KW - Lagrangian relaxation

KW - Valid inequalities

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Valid inequalities for Lagrangian relaxation in an inventory location problem with stochastic capacity

Abstract

Keywords

ASJC Scopus subject areas

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