A Lagrangean heuristic for hub-and-spoke system design with capacity selection and congestion

A Lagrangean heuristic for hub-and-spoke system design with capacity selection and congestion

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Article ID: iaor20104217
Volume: 22
Issue: 2
Start Page Number: 282
End Page Number: 296
Publication Date: Mar 2010
Journal: INFORMS Journal on Computing
Authors: ,
Keywords: programming: integer, queues: applications, heuristics
Abstract:

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.

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