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

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

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Article ID: iaor20073817
Country: United States
Volume: 53
Issue: 2
Start Page Number: 219
End Page Number: 230
Publication Date: Mar 2005
Journal: Operations Research
Authors: , , ,
Keywords: transportation: general, vehicle routing & scheduling, programming: integer
Abstract:

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.

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