Multi-commodity variable upper bound flow models
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TL;DR: A polyhedral study of a multi-commodity generalization of variable upper bound flow models is performed and a new family of inequalities is introduced, which generalizes traditional flow cover inequalities to the multi- commodity context.
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About: This article is published in Discrete Optimization. The article was published on 01 Aug 2015. and is currently open access. The article focuses on the topics: Upper and lower bounds & Flow (mathematics).
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Citations
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Valid linear inequalities for fixed charge problems
Manfred Padberg,T.J. van Roy,Laurence A. Wolsey +2 more
- 01 Jan 1985
TL;DR: Two classes of facet-defining linear inequalities of the convex hull of X are derived, and it is shown that the second of these classes gives a complete description of the conveyance when mj = m for all j, and methods to detect violated inequalities are developed.
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•Journal Article
The MCF-separator: detecting and exploiting multi-commodity flow structures in MIPs
TL;DR: The implementation adds a separator to the branch-and-cut libraries of Scip and Cplex and makes use of the complemented mixed integer rounding framework but provides a special purpose aggregation heuristic that exploits the network structure.
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George L. Nemhauser,Laurence A. Wolsey +1 more
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TL;DR: This chapter discusses the Scope of Integer and Combinatorial Optimization, as well as applications of Special-Purpose Algorithms and Matching.
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Supermodularity and Complementarity
Donald M. Topkis
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TL;DR: In this article, the authors introduce the concept of lattices, supermodular functions, and optimal decision models for cooperative games and non-cooperative games, and present a review of the literature.
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Integer and Combinatorial Optimization
Karla Hoffman,Ted K. Ralphs +1 more
- 01 Jan 2013
TL;DR: In today’s changing and competitive industrial environment, the difference between ad hoc planning methods and those that use sophisticated mathematical models to determine an optimal course of action can determine whether or not a company survives.
Bundle-based relaxation methods for multicommodity capacitated fixed charge network design
TL;DR: This study substantiates the fact that bundle methods appear superior to subgradient approches because they converge faster and are more robust relative to different relaxations, problem characteristics, and selection of the initial parameter values and demonstrates that effective lower bounds may be computed efficiently for large-scale instances of the capacitated fixed-charge network design problem.
282
The 0-1 Knapsack problem with a single continuous variable
TL;DR: The polyhedral structure of the knapsack problem with a single continuous variable is investigated, and it is shown that the flow cover inequalities derived for the single node flow set, consisting of arc flows into and out of a single node with binary variable lower and upper bounds on each arc, can be obtained from valid inequalities for the mixed 0-1 knapsacks problem.
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