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The Split Core for Sequencing Games

  • Mathematics


~ ~ DiscussionR for a ers414 ~mic Research 1994 NR.48 ii iii i iii i i i iii u i iuni i i NN i uii ii iii iui iii i `i H Center for Economic Research No. 9448 THE SPLIT CORE FOR SEQUENCING GAMES by Herbert Hamers, Jeroen Suijs, Stef Tijs and Peter Borm June 1994 ISSN 0924-7815 D K.U.B. BIBLtOTHEEK TILBURG THE SPLIT CORE FOR SEQUENCING GAMES HEItBERT 1~AMERS~~1 .JEROEN SUIJS ~ STEF rIJS 3 PETER ~ORM 1 May 31, 1994 Abstract The split core is a refinement of the core for sequencing games. The split core arises from a generalization of the Equal Gain Splitting (EGS) rule that is intro- duced by Curiel, Pederzoli and Tijs (1989). It is pointed out that the split core is the convex hull of permutation based gain spitting allocations and the EGS allo- cation is in the barycenter of the split core. Finally, an axiomatic characterization of the split core is provided. KEVwoRDS: Sequencing games, EGS-rule, Scheduling, Split core. ~CentER and Department oE F,conometrics, Tilburg University, P.O. Dox 9015:3, 5000 LE Tilburg, "I'bc Nctherlands. ~Herbert Ilamers is financially supported by the Dutch Organization for Scientific Desearch(NWO). z 1 Introduction [n one-rnachine si~ctucncing situations each agent (player) has one job Lhat has to be processed on a single machine. hach job is specified by its processing time, the tirne the machine takes to handle the job. We assume that the cost of a player depends linearly on the completion time of his job. Furthermore, there is an initial order on the jobs of the agPnts heforP t.he processing of the machine starts. Each group of agents (coalition) is allowed to obtain cost savings by rearranging their jobs in a way that is admissible with respect to the initial order. An optimal order of a coalition is an admissible rearrangement that maximizes the cost savings of this coalition. By defining the worth of a coalition as the (maximum) cost savings a coalition can make by an optimal rearrangement, we

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