Partitioning sequencing situations and games

Abstract

Abstract:The research that studies the interaction between sequencing situations and cooperative games, that started with the paper of Curiel et al. (1989), has become an established line of research.This paper introduces a new model in this field: partitioning sequencing situations and games. The characteristic of partitioning sequencing situations is that the jobs arrive in batches, and those jobs that arrive in earlier batches have some privileges over jobs in later arrived batches. For partitioning sequencing situations we introduce and characterise the partitioning equal gain splitting rule. Next, we define cooperative games that arise from these partitioning sequencing situations. It is shown that these games are convex. Moreover, we present a game independent expression for the Shapley value. Finally, it is shown that the partitioning equal gain splitting rule can be used to generate a core allocation and can be viewed as the average of two specific marginal vectors.

Research on game scheduling of galvanizing pipe production

“…From the results of the allocation, we can see from the results of the allocation that the tasks numbered 2,3,4,5 have no contribution to the promotion of profit, which implies the change of processing order of this four tasks has no effect on the profit pro-motion. And this statement is confirmed in the reality of that there is no change of the order of this 4 tasks in optimal game scheduling order [13,2,3,4,5,7,12,11,10,8,6,14,9,1].…”

On interactive sequencing situations with exponential cost functions

“…We mention Hamers, Borm, and Tijs (1995) by imposing ready times, Borm, Fiestras-Janeiro, Hamers, Sánchez, and Voorneveld (2002) by imposing due dates, Rustogi and Strusevich (2012) by studying positional effects, Lohmann, Borm, and Slikker (2014) by analyzing just-in-time arrivals and Musegaas, Borm, and Quant (2015) by considering step out-step in sequencing games. Moreover, Grundel, Çiftçi, Borm, and Hamers (2013), Gerichhausen and Hamers (2009) and Çiftçi, Borm, Hamers, and Slikker (2013) studied the grouping of players in families or batches. Finally, we mention Klijn and Sánchez (2006), who studied uncertainty sequencing games.…”

Batch sequencing and cooperation

“…This observation also leads to an expression for the Shapley value of these games. We also consider an equal gain splitting rule and provide an axiomatic characterization of this rule by using efficiency, symmetry and consistency axioms along the lines of Suijs et al (1997) and Gerichhausen and Hamers (2008).…”