Solving a time-space network formulation for the convoy movement problem
成果类型：
Article
署名作者：
Chardaire, P; McKeown, GP; Verity-Harrison, SA; Richardson, SB
署名单位：
University of East Anglia; Defence Science & Technology Laboratory; Qinetiq Group Plc
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.1040.0183
发表日期：
2005
页码：
219-230
关键词：
摘要：
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.