Trade-Offs Between the Stepwise Cost Function and Its Linear Approximation for the Modular Hub Location Problem

32 Pages Posted: 13 Jul 2018

See all articles by Milad Keshvari Fard

Milad Keshvari Fard

University of Bath, School of management

Laurent Alfandari

ESSEC Business School - Information & Decision Sciences Department

Date Written: May 1, 2018

Abstract

There exist situations where the transportation cost is better estimated as a function of the number of vehicles required for transporting a load, rather than a linear function of the load. This provides a stepwise cost function, which defines the so-called Modular Hub Location Problem (MHLP, or HLP with modular capacities) that has received increasing attention in the last decade. In this paper, we consider formulations to be solved by exact methods. We show that by choosing a specific generalized linear cost function with slope and intercept depending on problem data, one minimizes the measurement deviation between the two cost functions and obtains solutions close to those found with the stepwise cost function, while avoiding the higher computational complexity of the latter. As a side contribution, we look at the savings induced by using direct shipments in a hub and spoke network, given the better ability of a stepwise cost function to incorporate direct transportation. Numerical experiments are conducted over benchmark HLP instances of the OR-library.

Suggested Citation

Keshvari Fard, Milad and Alfandari, Laurent, Trade-Offs Between the Stepwise Cost Function and Its Linear Approximation for the Modular Hub Location Problem (May 1, 2018). Available at SSRN: https://ssrn.com/abstract=3201012 or http://dx.doi.org/10.2139/ssrn.3201012

Milad Keshvari Fard (Contact Author)

University of Bath, School of management ( email )

Claverton Down
Bath, BA2 7AY
United Kingdom

Laurent Alfandari

ESSEC Business School - Information & Decision Sciences Department ( email )

Avenue Bernard Hirsch B.P. 50105
Cergy-Pontoise (Paris), 95021
France

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