Trade-offs between the Stepwise Cost Function and its Linear Approximation for the Modular Hub Location Problem

Keshvari Fard Milad and Alfandari Laurent ()
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Keshvari Fard Milad: ESSEC Research Center, ESSEC Business School, Postal: ESSEC Research Center, BP 105, 95021 Cergy, France
Alfandari Laurent: ESSEC Research Center, ESSEC Business School, Postal: ESSEC Research Center, BP 105, 95021 Cergy, France

No WP1805, ESSEC Working Papers from ESSEC Research Center, ESSEC Business School

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.

Keywords: Cost Function (search for similar items in EconPapers)
JEL-codes: A00 (search for similar items in EconPapers)
Pages: 30 pages
Date: 2018-05
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