Dantzig-Wolfe decomposition for the facility location and production planning problem

•We propose two mathematical models for the facility location and production planning problem.•Item Dantzig-Wolfe decomposition is proposed to improve lower bounds of the studied problem.•We analyze the relationship between these models and Dantzig-Wolfe decomposition reformulations.•The effectivene...

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Bibliographic Details
Published in:Computers & operations research Vol. 124; p. 105068
Main Authors: Wu, Tao, Shi, Zhongshun, Liang, Zhe, Zhang, Xiaoning, Zhang, Canrong
Format: Journal Article
Language:English
Published: New York Elsevier Ltd 01.12.2020
Pergamon Press Inc
Subjects:
Benchmarks
Column generation
Customers
Dantzig-Wolfe decomposition
Decomposition
Facility location
Item decomposition
Linear programming
Lot-sizing
Lower bounds
Mathematical models
Mixed integer programming
Operations research
Production distribution
Production planning
Facility location
Lot-sizing
Column generation
Production planning
Mixed integer programming
Item decomposition
Production distribution
ISSN:0305-0548, 0305-0548
Online Access:Get full text
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Summary:•We propose two mathematical models for the facility location and production planning problem.•Item Dantzig-Wolfe decomposition is proposed to improve lower bounds of the studied problem.•We analyze the relationship between these models and Dantzig-Wolfe decomposition reformulations.•The effectiveness of the item Dantzig-Wolfe decomposition method is verified by computational tests. There are several mathematical models proposed for the facility location and production planning problem in the literature. However, some of these models disregard what products each customer has ordered and neglect critical production-related constraints and setup decisions while some others do not well define the connection cost between customers and facilities. In this study, we propose two mathematical models to overcome the disadvantages aforementioned, along with their reformulations by item decomposition to improve lower bounds. We demonstrate that the pricing subproblems of the item decomposition are related to uncapacitated lot-sizing problems with the Wagner-Whitin property. This property is employed to enhance the performance of column generation for the item decomposition. Our computational results show that this item decomposition method can improve lower bounds over other classical lower bounding techniques, such as linear programming relaxation and model reformulation. Additionally, we implement the proposed item decomposition method to other benchmark problems in the literature and observe that our proposed method can improve the benchmark solutions with a statistical significance.
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ISSN:0305-0548
0305-0548
DOI:10.1016/j.cor.2020.105068