Download Column Generation (Gerad 25th Anniversary Series, Volume 5) by Guy Desaulniers, Jacques Desrosiers, Marius M. Solomon PDF

By Guy Desaulniers, Jacques Desrosiers, Marius M. Solomon

Column new release is an insightful evaluation of the cutting-edge in integer programming column iteration and its many functions. the quantity starts off with "A Primer in Column new release" which outlines the speculation and concepts essential to clear up large-scale functional difficulties, illustrated with various examples. different chapters stick with this advent on "Shortest direction issues of source Constraints," "Vehicle Routing challenge with Time Window," "Branch-and-Price Heuristics," "Cutting inventory Problems," every one facing methodological facets of the sector. 3 chapters take care of transportation purposes: "Large-scale types within the Airline Industry," "Robust stock send Routing by means of Column Generation," and "Ship Scheduling with routine Visits and stopover at Separation Requirements." creation is the point of interest of one other 3 chapters: "Combining Column new release and Lagrangian Relaxation," "Dantzig-Wolfe Decomposition for activity store Scheduling," and "Applying Column iteration to computing device Scheduling." the ultimate bankruptcy by means of Fran?ois Vanderbeck, "Implementing combined Integer Column Generation," experiences the best way to set-up the Dantzig-Wolfe reformulation, adapt commonplace MIP innovations to the column iteration context (branching, preprocessing, primal heuristics), and care for particular column new release concerns (initialization, stabilization, column administration strategies).

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Additional resources for Column Generation (Gerad 25th Anniversary Series, Volume 5)

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This is the only reduced cost which exceeds the current optimality gap which equals to 15 — 7 = 8. Arc (3,4) can be permanently discarded from the network and paths 1346 and 13456 will never be generated. Integrality property. Solving the subproblem as an integer program usually helps in closing part of the integrality gap of the master problem (Geoffrion, 1974), except when the subproblem possesses the integrality property. This property means that solutions to the pricing problem are naturally integer when it is solved as a linear program.

Sometimes, these modifications cannot be handled by simply removing some arcs or nodes of the underlying network. In order to specify those constraints, we need some definitions. An elementary path is a path in which all nodes are pairwise different. Contrarily, a cycle is a path {vo^vi^,,, ^ Vp) of length p > 1 having VQ = Vp. We call any cycle of length less than or equal to A: a k-cycle. The following SPPRC variants have been proposed in the literature and defined according to path-structural constraints.

Optimization Theory for Large Systems. Macmillan, London. E. and Desrosiers, J. (2002). Selected topics in column generation. Les Cahiers du GERAD G-2002-64, HEC, Montreal, Canada. Forthcoming in: Operations Research. L. A. (1988). Integer and Combinatorial Optimization. John Wiley &; Sons, Chichester. W. D. (2000). A decomposition-based pricing procedure for large-scale linear programs—An application to the linear multicommodity flow problem. Management Science^ 46(5):693-709. E. (1975). The use of the boxstep method in discrete optimization.

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