This Article Full Text (PDF) Alert me when this article is cited Alert me if a correction is posted Services Email this article to a friend Similar articles in this journal Alert me to new issues of the journal Download to citation manager Google Scholar Articles by Elhedhli, S. Articles by Wu, H.

A Lagrangean Heuristic for Hub-and-Spoke System Design with Capacity Selection and Congestion

Department of Management Sciences, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
Department of Management Sciences, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
elhedhli{at}uwaterloo.ca
h2wu{at}uwaterloo.ca

Hub-and-spoke networks are widely applied in a variety of industries such as transportation, postal delivery, and telecommunications. Although they are designed to exploit economies of scale, hub-and-spoke networks are known to favour congestion, jeopardizing the performance of the entire system. This paper looks at incorporating congestion and capacity decisions in the design stage of such networks. The problem is formulated as a nonlinear mixed-integer program (NMIP) that explicitly minimizes congestion, capacity acquisition, and transportation costs. Congestion at hubs is modeled as the ratio of total flow to surplus capacity by viewing the hub-and-spoke system as a network of M/M/1 queues. To solve the NMIP, we propose a Lagrangean heuristic where the problem is decomposed into an easy subproblem and a more difficult nonlinear subproblem. The nonlinear subproblem is first linearized using piecewise functions and then solved to optimality using a cutting plane method. The Lagrangean lower bound is found using subgradient optimization. The solution from the subproblems is used to find a heuristic solution. Computational results indicate the efficiency of the methodology in providing a sharp bound and in generating high-quality feasible solutions in most cases.

Key words: hub and spoke; capacity selection; congestion; nonlinear mixed-integer programming; piecewise linearization; Lagrangean relaxation
History: received June 2006; revised June 2008; accepted April 2009.