Path-Reduced Costs for Eliminating Arcs in Routing and Scheduling

Authors:
Stefan Irnich;Guy Desaulniers;Jacques Desrosiers;Ahmed Hadjar
Affiliations:
Operations Research and Supply Chain Management, RWTH Aachen University, D-52056 Aachen, Germany;Ecole Polytechnique de Montréal and GERAD, Montréal, Québec H3C 3A7, Canada;HEC Montreal and GERAD, Montréal, Québec H3T 2A7, Canada;Kronos Canadian Systems Inc., Montréal, Québec H3V 1H8, Canada
Venue:
INFORMS Journal on Computing
Year:
2010

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Abstract

In many branch-and-price algorithms, the column generation pricing problem consists of computing feasible paths in a network. In this paper, we show how, in this context, path-reduced costs can be used to remove some arcs from the underlying network without compromising optimality, and we introduce a bidirectional search technique to compute these reduced costs. This arc elimination method can lead to a substantial speedup of the pricing process and the overall branch-and-price algorithm. Special attention is given to variants of shortest-path problems with resource constraints. Computational results obtained for the vehicle routing problem with time windows show the efficiency of the proposed method.