Freight car dispatching with generalized flows

Engels, Birgit and Schrader, Rainer (2015) Freight car dispatching with generalized flows.
Published in: Networks Vol. 66 (1). pp. 33-39. ISSN 1097-0037

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In the freight car dispatching problem empty freight cars have to be assigned to known demands respecting a given time horizon and certain constraints. The goal is to minimize the resulting transportation costs. One of the constraints is that customers can specify the type of cars they want. It is possible, however, that cars of certain types can be substituted by other cars, either in a 1-to-1 fashion or at different exchange rates. We show that these substitutions make the dispatching problem hard to solve and hard to approximate. We model the dispatching problem as an integral generalized transportation problem on a bipartite graph. Using rounding techniques, the LP-relaxation can be transformed to a transportation schedule violating some of the constraints slightly. Under an additional assumption on the cost function we fix this violation and derive a $4$-approximation of the problem.

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Deposit Information:
ZAIK Number: zaik2011-618
Depositing User: Rainer Schrader
Date Deposited: 03 Apr 2014 12:16
Last Modified: 03 Nov 2015 13:00

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