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...

Celý popis

Uloženo v:
Podrobná bibliografie
Vydáno v:European journal of operational research Ročník 256; číslo 2; s. 487 - 499
Hlavní autoři: Ogbe, Emmanuel, Li, Xiang
Médium: Journal Article
Jazyk:angličtina
Vydáno: Amsterdam Elsevier B.V 16.01.2017
Elsevier Sequoia S.A
Témata:
Benders decomposition
Cross decomposition
Dantzig–Wolfe decomposition
Decomposition
Integer programming
Linear programming
Mixed-integer linear programming
Stochastic models
Stochastic programming
Studies
Supply chains
Cross decomposition
Benders decomposition
Dantzig–Wolfe decomposition
Mixed-integer linear programming
Stochastic programming
ISSN:0377-2217, 1872-6860
On-line přístup:Získat plný text
Tagy: Přidat tag
Žádné tagy, Buďte první, kdo vytvoří štítek k tomuto záznamu!
Popis
Shrnutí:•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.
Bibliografie:SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 14
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2016.08.005