The green capacitated multi-item lot sizing problem with parallel machines

•We propose a mixed integer programming model for the green capacitated multi-item lot sizing problem with parallel machines.•The mathematical model can support the reduction of carbon emissions for manufacturing companies.•The green lot sizing problem is NP-hard and is therefore difficult to solve....

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Veröffentlicht in:	Computers & operations research Jg. 98; S. 149 - 164
Hauptverfasser:	Wu, Tao, Xiao, Fan, Zhang, Canrong, He, Yan, Liang, Zhe
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	New York Elsevier Ltd 01.10.2018 Pergamon Press Inc
Schlagworte:	Carbon Carbon emissions Column generation Computation Customer satisfaction Emissions control Energy consumptions Green manufacturing Heuristic Integer programming Lagrangian relaxation Linear programming Lot sizing Lower bounds Manufacturing Mixed integer Operations research Parallel processing Problem solving Production planning Studies Green manufacturing Column generation Production planning Lagrangian relaxation Lot sizing Energy consumptions Carbon emissions Heuristic
ISSN:	0305-0548, 1873-765X, 0305-0548
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Abstract	•We propose a mixed integer programming model for the green capacitated multi-item lot sizing problem with parallel machines.•The mathematical model can support the reduction of carbon emissions for manufacturing companies.•The green lot sizing problem is NP-hard and is therefore difficult to solve.•We apply a progressive selection heuristic to find feasible solutions and upper bounds for the problem.•We also apply Lagrangian-relaxation, Dantzig–Wolfe decomposition, and column generation to enhance lower bounds for quantifying the solution quality. Carbon emissions related to energy consumptions from the manufacturing industry have become a substantial part of environmental burdens. To reduce carbon emissions, we introduce carbon emission constraints into the capacitated multi-item lot sizing problem with nonidentical parallel machines. The problem aims to satisfy customer demand for various items over the planning horizon, with an objective to minimize total costs without violating the capacity and carbon emission constraints. We formulate the problem with a mixed integer programming model and propose Lagrangian relaxation and column generation methods to improve lower bounds over the linear programming relaxation. Furthermore, we apply a heuristic named progressive selection to solve the problem and compare the heuristic with other state-of-the-art approaches in the literature. Computational results indicate that the progressive selection heuristic is computationally tractable and can obtain superior results under the same computational resources.
AbstractList	Carbon emissions related to energy consumptions from the manufacturing industry have become a substantial part of environmental burdens. To reduce carbon emissions, we introduce carbon emission constraints into the capacitated multi-item lot sizing problem with nonidentical parallel machines. The problem aims to satisfy customer demand for various items over the planning horizon, with an objective to minimize total costs without violating the capacity and carbon emission constraints. We formulate the problem with a mixed integer programming model and propose Lagrangian relaxation and column generation methods to improve lower bounds over the linear programming relaxation. Furthermore, we apply a heuristic named progressive selection to solve the problem and compare the heuristic with other state-of-the-art approaches in the literature. Computational results indicate that the progressive selection heuristic is computationally tractable and can obtain superior results under the same computational resources. •We propose a mixed integer programming model for the green capacitated multi-item lot sizing problem with parallel machines.•The mathematical model can support the reduction of carbon emissions for manufacturing companies.•The green lot sizing problem is NP-hard and is therefore difficult to solve.•We apply a progressive selection heuristic to find feasible solutions and upper bounds for the problem.•We also apply Lagrangian-relaxation, Dantzig–Wolfe decomposition, and column generation to enhance lower bounds for quantifying the solution quality. Carbon emissions related to energy consumptions from the manufacturing industry have become a substantial part of environmental burdens. To reduce carbon emissions, we introduce carbon emission constraints into the capacitated multi-item lot sizing problem with nonidentical parallel machines. The problem aims to satisfy customer demand for various items over the planning horizon, with an objective to minimize total costs without violating the capacity and carbon emission constraints. We formulate the problem with a mixed integer programming model and propose Lagrangian relaxation and column generation methods to improve lower bounds over the linear programming relaxation. Furthermore, we apply a heuristic named progressive selection to solve the problem and compare the heuristic with other state-of-the-art approaches in the literature. Computational results indicate that the progressive selection heuristic is computationally tractable and can obtain superior results under the same computational resources.
Author	Wu, Tao Xiao, Fan He, Yan Liang, Zhe Zhang, Canrong
Author_xml	– sequence: 1 givenname: Tao orcidid: 0000-0001-7954-485X surname: Wu fullname: Wu, Tao email: danielwu9999@gmail.com, twu1@dow.com organization: Advanced Analytics Department, Dow Chemical, Midland, MI 48642, USA – sequence: 2 givenname: Fan surname: Xiao fullname: Xiao, Fan email: 1631022@tongji.edu.cn organization: School of Economics & Management, Tongji University, Shanghai 200092, China – sequence: 3 givenname: Canrong surname: Zhang fullname: Zhang, Canrong email: crzhang@sz.tsinghua.edu.cn organization: Logistics Engineering and Simulation Laboratory, Graduate School at Shenzhen, Tsinghua University, Shenzhen 518055, China – sequence: 4 givenname: Yan surname: He fullname: He, Yan email: heyan@cqu.edu.cn organization: State Key Laboratory of Mechanical Transmission, Chongqing University, Chongqing 400030, China – sequence: 5 givenname: Zhe surname: Liang fullname: Liang, Zhe email: liangzhe@tongji.edu.cn organization: School of Economics & Management, Tongji University, Shanghai 200092, China
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Keywords	Green manufacturing Column generation Production planning Lagrangian relaxation Lot sizing Energy consumptions Carbon emissions Heuristic
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Snippet	•We propose a mixed integer programming model for the green capacitated multi-item lot sizing problem with parallel machines.•The mathematical model can... Carbon emissions related to energy consumptions from the manufacturing industry have become a substantial part of environmental burdens. To reduce carbon...
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SubjectTerms	Carbon Carbon emissions Column generation Computation Customer satisfaction Emissions control Energy consumptions Green manufacturing Heuristic Integer programming Lagrangian relaxation Linear programming Lot sizing Lower bounds Manufacturing Mixed integer Operations research Parallel processing Problem solving Production planning Studies
Title	The green capacitated multi-item lot sizing problem with parallel machines
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