On the Balancedness of Relaxed Sequencing Games

This paper shows that some classes of relaxed sequencing games, which arise from the class of sequencing games as introduced in Curiel, Pederzoli, Tijs (1989), are balanced.sequencing situations;sequencing games;balancedness;game theory

Operations Research Games: A Survey

This paper surveys the research area of cooperative games associated with several types of operations research problems in which various decision makers (players) are involved.Cooperating players not only face a joint optimisation problem in trying, e.g., to minimise total joint costs, but also face an additional allocation problem in how to distribute these joint costs back to the individual players.This interplay between optimisation and allocation is the main subject of the area of operations research games.It is surveyed on the basis of a distinction between the nature of the underlying optimisation problem: connection, routing, scheduling, production and inventory.cooperative games;operational research

Partitioning Sequencing Situations and Games

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.Sequencing situations;sequencing games

On Games corresponding to Sequencing Situations with Precedence Relations

In this paper we study a class of cooperative sequencing games that arise from one-machine sequencing situations in which chain precedence relations are imposed on the jobs. It is shown that these sequencing games are convex.cooperative games, sequencing situations, convexity

Batch Sequencing and Cooperation

Game theoretic analysis of sequencing situations has been restricted to manufactur- ing systems which consist of machines that can process only one job at a time. However, in many manufacturing systems, operations are carried out by batch machines which can simultaneously process multiple jobs. This paper aims to extend the game theoretical approach to the cost allocation problems arising from sequencing situations on systems that consist of batch machines. We first consider sequencing situations with a single batch machine and analyze cooperative games arising from these situations. It is shown that these games are convex and an expression for the Shapley value of these games is provided. We also introduce an equal gain splitting rule for these sequencing situa- tions and provide an axiomatic characterization. Second, we analyze various aspects of flow-shop sequencing situations which consist of batch machines only. In particular, we provide two cases in which the cooperative game arising from the flow-shop sequencing situation is equal to the game arising from a sequencing situation that corresponds to one specific machine in the flow-shop.Sequencing situations;sequencing games;batch machines

Balancedness of sequencing games with multiple parallel machines

We provide simple constructive proofs of balancedness of classes of m-PS games, which arise from sequencing situations with m parallel machines. This includes the setting that is studied by Calleja et al. (2001) and Calleja et al. (2002), who provided a complex constructive proof and a simple non-constructive proof of balancedness of a restricted class of 2-PS games, respectively. Furthermore, we provide two counterexamples to illustrate that our balancedness results cannot be extended to a general setting

On the Convexity of Precedence Sequencing Games

In this paper we study a class of cooperative sequencing games that arise from one-machine sequencing situations in which chain precedence relations are imposed on the jobs.It is shown that these sequencing games are convex.cooperative games;sequencing games

Sequencing Games with Controllable Processing Time

In this paper we study a class of cooperative sequencing games that arise from sequencing situations in which the processing times are not fixed.We show that these games are balanced by obtaining two core elements that depend only on the optimal schedule for the grand coalition.Furthermore we show that, although these games are not convex in general, many marginal vectors are core elements. We also consider convexity for special instances of the sequencing situation.cooperative games

The Socially Stable Core in Structured Transferable Utility Games

We consider cooperative games with transferable utility (TU-games), in which we allow for a social structure on the set of players, for instance a hierarchical ordering or a dominance relation.The social structure is utilized to refine the core of the game, being the set of payoffs to the players that cannot be improved upon by any coalition of players.For every coalition the relative strength of a player within that coalition is induced by the social structure and is measured by a power function.We call a payoff vector socially stable if at the collection of coalitions that can attain it, all players have the same power.The socially stable core of the game consists of the core elements that are socially stable.In case the social structure is such that every player in a coalition has the same power, social stability reduces to balancedness and the socially stable core coincides with the core.We show that the socially stable core is non-empty if the game itself is socially stable.In general the socially stable core consists of a finite number of faces of the core and generically consists of a finite number of payoff vectors.Convex TU-games have a non-empty socially stable core, irrespective of the power function.When there is a clear hierarchy of players in terms of power, the socially stable core of a convex TU-game consists of exactly one element, an appropriately defined marginal vector.We demonstrate the usefulness of the concept of the socially stable core by two applications.One application concerns sequencing games and the other one the distribution of water.game theory;utility theory