A Bi-objective Model for Collaborative Uncapacitated arc Routing Problem Including Coalition Satisfaction

Authors

  • Mostafa Khorramizadeh Shiraz University of Technology
  • Mohammad Sadegh Shiri Department of Mathematics, Islamic Azad University
  • Vahid Ahmadi Shiraz University of Technology
  • Masoud Zarepisheh

Abstract

This paper deals with a carrier collaboration problem in which carriers form a coalition to share and exchange their transportation requests located on the arcs of the network. This problem has recently gained a significant attention to enhance the operational efficiency. However, the existing problem formulations are single objective optimization problems solely focusing on maximizing the profit and overlooking satisfaction criterion which is crucial to the coalition’s long-term survival. This paper proposes a bi-objective integer linear programming model aiming at maximizing profit as well as coalition satisfaction. In order to ensure satisfaction among all members of the coalition, an efficient metric is proposed using proper mathematical norms (L 1 -Norm and L ∞ -Norm) , encouraging a well-distribution of satisfaction among members. Moreover, this paper shows how the carriers’ overtime can be introduced in the problem formulation which could potentially improve the total profitability of the system and coalition satisfaction. The proposed models are tested on a publicly available data set of 1416 instances and the performance of the models are analyzed.

Published

2026-06-16

Issue

Vol. 20

Section

Vol. 20, No. 3, (2026)

License

Upon acceptance of an article, authors will be asked to complete a 'Journal Publishing Agreement'. An e-mail will be sent to the corresponding author confirming receipt of the manuscript together with a "Journal Publishing Agreement" form or a link to the online version of this agreement.

Journal author rights

Authors have copyright but license exclusive rights in their article to the publisher. In this case authors have the right to:

  • Share their article in the same ways permitted to third parties under the relevant user license (together with Personal use rights) so long as it contains a link to the version of record on this website.
  • Retain patent, trademark and other intellectual property rights (including raw research data).
  • Proper attribution and credit for the published work.

Rights granted to this journal

The Journal of Mathematical Extension is granted the following rights:

  • This journal will apply the relevant third party user license where this journal publishes the article on its online platforms.
  • The right to provide the article in all forms and media so the article can be used on the latest technology even after publication.
  • The authority to enforce the rights in the article, on behalf of an author, against third parties, for example in the case of plagiarism or copyright infringement.

Protecting author right

Copyright aims to protect the specific way the article has been written to describe an experiment and the results. This journal is committed to its authors to protect and defend their work and their reputation and takes allegations of infringement, plagiarism, ethic disputes and fraud very seriously.

If an author becomes aware of a possible plagiarism, fraud or infringement we recommend contacting the editorial office immediately.

Personal use

Authors can use their articles, in full or in part, for a wide range of scholarly, non-commercial purposes as outlined below:

  • Use by an author in the author’s classroom teaching (including distribution of copies, paper or electronic)
  • Distribution of copies (including through e-mail) to known research colleagues for their personal use (but not for Commercial Use)
  • Inclusion in a thesis or dissertation (provided that this is not to be published commercially)
  • Use in a subsequent compilation of the author’s works
  • Extending the Article to book-length form
  • Preparation of other derivative works (but not for Commercial Use)
  • Otherwise using or re-using portions or excerpts in other works

These rights apply for all authors who publish their article in this journal. In all cases we require that all authors always include a full acknowledgement and, if appropriate, a link to the final published version hosted on this website.