On games arising from multi-depot Chinese postman problems

Trine Platz and Herbert Hamers

Annals of Operations Research, 2015, vol. 235, issue 1, 675-692

Abstract: A multi-depot Chinese postman problem (MDCP) arises from a network (e.g. cityplan) in which several depots are located wherefrom edges (e.g. streets) have to be served. Since costs are involved with each visit to an edge, the objective is to find a minimum cost tour in the network that visits all edges of the network. Such a minimum cost tour consists of a collection of subtours such that the subtours originate from different depots, and each subtour starts and ends at the same depot. This typical OR problem turns into a multi decision maker problem if agents are assigned to the streets. In this new setting the cost of a minimum cost tour that visits all edges have to be paid by the agents. However, now each group of agents (coalition) has the opportunity to find its own minimum cost tour, i.e. a minimum cost tour that only visits the edges owned by the group of agents. Therefore, the main objective is to find allocations of the cost of a minimum tour that visits all agents in such a way that no coalition has higher costs than the costs incurred by its own minimum tour. We will use cooperative game theory to investigate whether these so-called core allocations exist. Therefore, we consider a cooperative Chinese postman (CP) game that is induced by an MDCP by associating every edge of the network with a different agent. In this paper, we characterize classes of networks that ensure the existence of core allocations, the so-called CP balanced graphs, and the existence of specific core allocations, the so-called CP submodular graphs. Copyright Springer Science+Business Media New York 2015

Keywords: Chinese postman problem; Cooperative game; Balancedness; Submodularity (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://hdl.handle.net/10.1007/s10479-015-1977-3 (text/html)
Access to full text is restricted to subscribers.

Related works:
Working Paper: On Games Arising From Multi-Depot Chinese Postman Problems (2013)
Working Paper: On Games Arising From Multi-Depot Chinese Postman Problems (2013)
Working Paper: On games arising from multi-depot Chinese postman problems (2012)
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:annopr:v:235:y:2015:i:1:p:675-692:10.1007/s10479-015-1977-3

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/10479

DOI: 10.1007/s10479-015-1977-3

Access Statistics for this article

Annals of Operations Research is currently edited by Endre Boros

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