A new cross decomposition method for stochastic mixed-integer linear programming
•A new cross decomposition method combining two classical decomposition methods.•A Phase I procedure introduced for warm starting the solution procedure.•Two different algorithms for the proposed cross decomposition method.•The method outperforms Benders decomposition when the number of scenarios is...
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| Vydáno v: | European journal of operational research Ročník 256; číslo 2; s. 487 - 499 |
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| Hlavní autoři: | , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Amsterdam
Elsevier B.V
16.01.2017
Elsevier Sequoia S.A |
| Témata: | |
| ISSN: | 0377-2217, 1872-6860 |
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| Abstract | •A new cross decomposition method combining two classical decomposition methods.•A Phase I procedure introduced for warm starting the solution procedure.•Two different algorithms for the proposed cross decomposition method.•The method outperforms Benders decomposition when the number of scenarios is large.
Two-stage stochastic mixed-integer linear programming (MILP) problems can arise naturally from a variety of process design and operation problems. These problems, with a scenario based formulation, lead to large-scale MILPs that are well structured. When first-stage variables are mixed-integer and second-stage variables are continuous, these MILPs can be solved efficiently by classical decomposition methods, such as Dantzig/Wolfe decomposition (DWD), Lagrangian decomposition, and Benders decomposition (BD), or a cross decomposition strategy that combines some of the classical decomposition methods. This paper proposes a new cross decomposition method, where BD and DWD are combined in a unified framework to improve the solution of scenario based two-stage stochastic MILPs. This method alternates between DWD iterations and BD iterations, where DWD restricted master problems and BD primal problems yield a sequence of upper bounds, and BD relaxed master problems yield a sequence of lower bounds. The method terminates finitely to an optimal solution or an indication of the infeasibility of the original problem. Case study of two different supply chain systems, a bioproduct supply chain and an industrial chemical supply chain, show that the proposed cross decomposition method has significant computational advantage over BD and the monolith approach, when the number of scenarios is large. |
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| AbstractList | Two-stage stochastic mixed-integer linear programming (MILP) problems can arise naturally from a variety of process design and operation problems. These problems, with a scenario based formulation, lead to large-scale MILPs that are well structured. When first-stage variables are mixed-integer and second-stage variables are continuous, these MILPs can be solved efficiently by classical decomposition methods, such as Dantzig/Wolfe decomposition (DWD), Lagrangian decomposition, and Benders decomposition (BD), or a cross decomposition strategy that combines some of the classical decomposition methods. This paper proposes a new cross decomposition method, where BD and DWD are combined in a unified framework to improve the solution of scenario based two-stage stochastic MILPs. This method alternates between DWD iterations and BD iterations, where DWD restricted master problems and BD primal problems yield a sequence of upper bounds, and BD relaxed master problems yield a sequence of lower bounds. The method terminates finitely to an optimal solution or an indication of the infeasibility of the original problem. Case study of two different supply chain systems, a bioproduct supply chain and an industrial chemical supply chain, show that the proposed cross decomposition method has significant computational advantage over BD and the monolith approach, when the number of scenarios is large. •A new cross decomposition method combining two classical decomposition methods.•A Phase I procedure introduced for warm starting the solution procedure.•Two different algorithms for the proposed cross decomposition method.•The method outperforms Benders decomposition when the number of scenarios is large. Two-stage stochastic mixed-integer linear programming (MILP) problems can arise naturally from a variety of process design and operation problems. These problems, with a scenario based formulation, lead to large-scale MILPs that are well structured. When first-stage variables are mixed-integer and second-stage variables are continuous, these MILPs can be solved efficiently by classical decomposition methods, such as Dantzig/Wolfe decomposition (DWD), Lagrangian decomposition, and Benders decomposition (BD), or a cross decomposition strategy that combines some of the classical decomposition methods. This paper proposes a new cross decomposition method, where BD and DWD are combined in a unified framework to improve the solution of scenario based two-stage stochastic MILPs. This method alternates between DWD iterations and BD iterations, where DWD restricted master problems and BD primal problems yield a sequence of upper bounds, and BD relaxed master problems yield a sequence of lower bounds. The method terminates finitely to an optimal solution or an indication of the infeasibility of the original problem. Case study of two different supply chain systems, a bioproduct supply chain and an industrial chemical supply chain, show that the proposed cross decomposition method has significant computational advantage over BD and the monolith approach, when the number of scenarios is large. |
| Author | Ogbe, Emmanuel Li, Xiang |
| Author_xml | – sequence: 1 givenname: Emmanuel surname: Ogbe fullname: Ogbe, Emmanuel – sequence: 2 givenname: Xiang surname: Li fullname: Li, Xiang email: xiang.li@queensu.ca |
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| Snippet | •A new cross decomposition method combining two classical decomposition methods.•A Phase I procedure introduced for warm starting the solution procedure.•Two... Two-stage stochastic mixed-integer linear programming (MILP) problems can arise naturally from a variety of process design and operation problems. These... |
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| SubjectTerms | Benders decomposition Cross decomposition Dantzig–Wolfe decomposition Decomposition Integer programming Linear programming Mixed-integer linear programming Stochastic models Stochastic programming Studies Supply chains |
| Title | A new cross decomposition method for stochastic mixed-integer linear programming |
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