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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Vydané v:	Computers & operations research Ročník 124; s. 105068
Hlavní autori:	Wu, Tao, Shi, Zhongshun, Liang, Zhe, Zhang, Xiaoning, Zhang, Canrong
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	New York Elsevier Ltd 01.12.2020 Pergamon Press Inc
Predmet:	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
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Abstract	•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.
AbstractList	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. •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.
ArticleNumber	105068
Author	Shi, Zhongshun Wu, Tao Liang, Zhe Zhang, Canrong Zhang, Xiaoning
Author_xml	– sequence: 1 givenname: Tao orcidid: 0000-0001-7954-485X surname: Wu fullname: Wu, Tao email: danielwu9999@gmail.com organization: School of Economics & Management, Tongji University, Shanghai 200092, China – sequence: 2 givenname: Zhongshun surname: Shi fullname: Shi, Zhongshun email: tzshi@utk.edu organization: Department of Industrial and Systems Engineering, University of Tennessee Knoxville, Knoxville, TN 37996, USA – sequence: 3 givenname: Zhe orcidid: 0000-0001-5774-2791 surname: Liang fullname: Liang, Zhe email: liangzhe@tongji.edu.cn organization: School of Economics & Management, Tongji University, Shanghai 200092, China – sequence: 4 givenname: Xiaoning surname: Zhang fullname: Zhang, Xiaoning email: cexzhang@tongji.edu.cn organization: School of Economics & Management, Tongji University, Shanghai 200092, China – sequence: 5 givenname: Canrong surname: Zhang fullname: Zhang, Canrong email: crzhang@sz.tsinghua.edu.cn organization: Logistics Engineering and Simulation Laboratory, Shenzhen International Graduate School, Tsinghua University, Shenzhen 518055, China
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Keywords	Facility location Lot-sizing Column generation Production planning Mixed integer programming Item decomposition Production distribution
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Snippet	•We propose two mathematical models for the facility location and production planning problem.•Item Dantzig-Wolfe decomposition is proposed to improve lower... There are several mathematical models proposed for the facility location and production planning problem in the literature. However, some of these models...
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SubjectTerms	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
Title	Dantzig-Wolfe decomposition for the facility location and production planning problem
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