Relaxed sequencing games have a nonempty core

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Abstract

We study sequencing situations with a fixed initial order and linear cost functions. Cost savings can be obtained by rearranging jobs. Next to finding an optimal order, an additional issue is formed by the division of these savings. Cooperative game theory studies this issue. A common assumption states that cooperation between players is restricted to groups that are connected according to the initial order. The value of disconnected groups is defined additively over their connected components. In this paper we allow players in disconnected coalitions to switch places as long as they do not hurt the players not in the coalition under consideration. The resulting games are called relaxed sequencing games. Although they have been studied before, no general results on stable profit divisions have been derived so far. In this paper we prove that relaxed sequencing games have a nonempty core, i.e., they all have stable profit divisions. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2006
Original languageEnglish
Pages (from-to)235-242
Number of pages8
JournalNaval Research Logistics
Volume53
Issue number4
DOIs
Publication statusPublished - 2006

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Sequencing
Division
Profitability
Game
Coalitions
Profit
Game theory
Cost functions
Cooperative Game Theory
Logistics
Switches
Connected Components
Linear Function
Cost Function
Switch
Costs
Cost savings
Savings
Cooperative game theory
Cost function

Cite this

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Relaxed sequencing games have a nonempty core. / Slikker, M.

In: Naval Research Logistics, Vol. 53, No. 4, 2006, p. 235-242.

Research output: Contribution to journalArticleAcademicpeer-review

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