The multi-commodity network flow problem with soft transit time constraints: Application to liner shipping

45 Pages Posted: 9 Mar 2020 Last revised: 8 Mar 2021

See all articles by Alessio Trivella

Alessio Trivella

University of Twente; ETH Zurich

Francesco Corman

ETH Zurich

David Franz Koza

Vattenfall Vindkraft A/S

David Pisinger

Technical University of Denmark - Management Engineering

Date Written: September 22, 2020

Abstract

The multi-commodity network flow problem (MCNF) consists in routing a set of commodities through a capacitated network at minimum cost and is relevant for routing containers in liner shipping networks. As commodity transit times are often a critical factor, the literature has introduced hard limits on commodity transit times. In practical contexts, however, these hard limits may fail to provide sufficient flexibility since routes with even tiny delays would be discarded. Motivated by a major liner shipping operator, we study an MCNF generalization where transit time restrictions are modeled as soft constraints, in which delays are discouraged using penalty functions of transit time. Similarly, early commodity arrivals can receive a discount in cost. We derive properties that distinguish this model from other MCNF variants and adapt a column generation procedure to efficiently solve it. Extensive numerical experiments conducted on realistic liner shipping instances reveal that the explicit consideration of penalty functions can lead to significant cost reductions compared to hard transit time deadlines. Moreover, the penalties can be used to steer the flow towards slower or faster configurations, resulting in a potential increase in operational costs, which generates a trade-off that we quantify under varying penalty functions.

Keywords: Networks; multi-commodity flow; column generation; commodity transit time; liner shipping application

JEL Classification: C44, C02, C61

Suggested Citation

Trivella, Alessio and Corman, Francesco and Koza, David Franz and Pisinger, David, The multi-commodity network flow problem with soft transit time constraints: Application to liner shipping (September 22, 2020). Available at SSRN: https://ssrn.com/abstract=3537743 or http://dx.doi.org/10.2139/ssrn.3537743

Alessio Trivella (Contact Author)

University of Twente ( email )

Postbus 217
Twente
Netherlands

ETH Zurich ( email )

Stefano-Franscini-Platz 5
Postfach 193
Zürich, 8093
Switzerland

Francesco Corman

ETH Zurich ( email )

Stefano-Franscini-Platz 5
Postfach 193
Zürich, 8093
Switzerland

David Franz Koza

Vattenfall Vindkraft A/S ( email )

Jupitervej 6
Kolding, 6000
Denmark

David Pisinger

Technical University of Denmark - Management Engineering ( email )

Produktionstorvet 424
room 043
Kgs. Lyngby, 2800
Denmark

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