An Analysis of the Stability of Hinterland Container Transport Cooperation

Alberto Giudici, Tao Lu, Clemens Thielen, Rob Zuidwijk

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We study cooperation among hinterland container transport operators that may share transport capacity and demand in corridors between inland and sea ports. We model this transportation problem as a minimum cost flow problem and assume that operators share the total cost based on a bargaining outcome, which has been proven equivalent to the Shapley value. To examine the stability of such cooperation, we perform a sensitivity analysis of the membership of the Shapley value (the bargaining outcome) to the core (the set of stable outcomes) by leveraging a novel concept of parametric cooperative games. We obtain closed-form solutions for identical players that explicitly characterize the impact of overcapacity on the stability of cooperation. For more general cases, we develop a computational approach based on parametric optimization techniques. The numerical results indicate that our primary analytical result, that is, that overcapacity undermines stability, is generally valid, and that overcapacitated networks may permit stable cooperation in only a limited range of settings.

Original languageEnglish
Pages (from-to)1170-1186
Number of pages17
JournalTransportation Science
Issue number5
Publication statusPublished - 25 Aug 2021

Bibliographical note

Funding Information:
The research of A. Giudici, T. Lu, and R. Zuidwijk was partially supported by the European Union’s Horizon 2020 research and innovation programme [Grant Agreement 690588]. The research of C. Thielen was partially supported by the Bavarian State Ministry of Education, Science and the Arts within the Bavarian Funding Programme for the Initiation of International Cooperations (BayIntAn).

Publisher Copyright:
© 2021 INFORMS


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