Explicit flow-risk allocation for cooperative maximum flow problems under interval uncertainty

Adil Baykasoğlu () and Burcu Kubur Özbel
Additional contact information
Adil Baykasoğlu: Dokuz Eylül University
Burcu Kubur Özbel: Dokuz Eylül University

Operational Research, 2021, vol. 21, issue 3, No 27, 2149-2179

Abstract: Abstract Many decision-making problems in transportation networks can be defined as maximum flow problems. During the last five decades, several efficient solution approaches have been proposed for the deterministic maximum flow problems. On the other hand, arc capacities of networks cannot be precisely defined in many real life settings. These networks are called uncertain. In this case, it becomes challenging to maintain a stable flow on the network. This paper presents a new approach based on the framework of interval analysis for the solution of maximum flow problems. We address a multiple-owners network problem by presenting a risk explicit interval linear programming model for the desired value of the system aspiration level. Afterwards, we employ a well-known collaborative game theoretic approach (the Shapley value) in a multiple-owners network under interval uncertainty in order to solve the maximum flow problem. A detailed numerical example is provided to present the suitability of the proposed approach in devising a stable network flow. The obtained numerical results and the trade-offs between decision risk and network flow information would be very valuable for supporting decision makers in resolving maximum flow problems when facing uncertainty.

Keywords: Maximum flow problem; Multiple-owners graph; Cooperative games; Risk explicit interval linear programming; Risk allocation; The Shapley value (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s12351-019-00500-5 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:operea:v:21:y:2021:i:3:d:10.1007_s12351-019-00500-5

Ordering information: This journal article can be ordered from
https://www.springer ... search/journal/12351

DOI: 10.1007/s12351-019-00500-5

Access Statistics for this article

Operational Research is currently edited by Nikolaos F. Matsatsinis, John Psarras and Constantin Zopounidis

More articles in Operational Research from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().