NDLI: On games arising from multi-depot Chinese postman problems

Content Provider	Springer Nature Link
Author	Platz, Trine Tornøe Hamers, Herbert
Copyright Year	2015
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.
Starting Page	675
Ending Page	692
Page Count	18
File Format	PDF
ISSN	02545330
Journal	Annals of Operations Research
Volume Number	235
Issue Number	1
e-ISSN	15729338
Language	English
Publisher	Springer US
Publisher Date	2015-09-03
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Chinese postman problem Cooperative game Balancedness Submodularity Operation Research/Decision Theory Combinatorics Theory of Computation
Content Type	Text
Resource Type	Article
Subject	Management Science and Operations Research

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