Solving a time-space network formulation for the convoy movement problem

Chardaire, P., McKeown, G. P., Verity-Harrison, S. A. and Richardson, S. B. (2005) Solving a time-space network formulation for the convoy movement problem. Operations Research, 53 (2). pp. 219-230. ISSN 0030-364X

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We give a formal specification for a strategic network routing problem known as the convoy movement problem (CMP) and establish that the corresponding feasibility problem is NP-complete. We then introduce an integer programming (IP) model based on the concept of a time-space network and apply a Lagrangian relaxation to this model. We discuss how the dual function may be evaluated using a modified version of Dijkstra’s algorithm suitable to very large, implicitly defined graphs and show how heuristic solutions to the primal problem may be obtained. We present results for a number of instances of the CMP, most of which are based on real-world problems. The number of convoys in these instances varies between 15–25, and their movement time requires up to several thousand time units in networks ranging in size from a few dozen to several thousand vertices and edges. The most difficult instance tested involves 17 long convoys each taking four times the average link travel time to pass through a point in the network. This instance is solved within 3.3% of optimality in less than 3.5 hours of computing time on a Dell Precision 420 dual processor computer. Every other test instance is solved within 2% of the optimal value in less than 20 minutes of computing time.

Item Type: Article
Faculty \ School: Faculty of Science > School of Computing Sciences
Depositing User: Vishal Gautam
Date Deposited: 09 Jun 2011 15:19
Last Modified: 27 Oct 2023 00:39
DOI: 10.1287/opre.1040.0183

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