2,643 research outputs found

    Sequencing Games with Controllable Processing Time

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    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

    Partitioning Sequencing Situations and Games

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    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

    Batch Sequencing and Cooperation

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    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

    Sequencing Games with Controllable Processing Time

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    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.

    Cooperation in Networks and Scheduling

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    This thesis deals with various models of cooperation in networks and scheduling. The main focus is how the benefits of this cooperation should be divided among the participating individuals. A major part of this analysis is concerned with stability of the cooperation. In addition, allocation rules are investigated, as well as properties of the underlying situations and games.

    An O(nlogn) algorithm for the two-machine flow shop problem with controllable machine speeds

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    Production Planning;Scheduling;produktieleer/ produktieplanning

    Cooperation in Networks and Scheduling.

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    This thesis deals with various models of cooperation in networks and scheduling. The main focus is how the benefits of this cooperation should be divided among the participating individuals. A major part of this analysis is concerned with stability of the cooperation. In addition, allocation rules are investigated, as well as properties of the underlying situations and games.

    Proportionate Flow Shop Games

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    In a proportionate flow shop problem several jobs have to be processed through a fixed sequence of machines and the processing time of each job is equal on all machines.By identifying jobs with agents, whose costs linearly depend on the completion time of their jobs, and assuming an initial processing order on the jobs, we face an additional problem: how to allocate the cost savings obtained by ordering the jobs optimally?In this paper, PFS games are defined as cooperative games associated to proportionate flow shop problems.It is seen that PFS games have a nonempty core.Moreover, it is shown that PFS games are convex if the jobs are initially ordered in decreasing urgency.For this case an explicit expression for the Shapley value and a specific type of equal gain splitting rule which leads to core elements of the PFS game are proposed.Proportionate flow shop problems;core;convexity

    Family Sequencing and Cooperation

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    Proportionate flow shop games

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    htmlabstractIn a proportionate flow shop problem several jobs have to be processed through a fixed sequence of machines and the processing time of each job is equal on all machines. By identifying jobs with agents, whose costs linearly depend on the completion time of their jobs, and assuming an initial processing order on the jobs, we face two problems: the first one is how to obtain an optimal order that minimizes the total processing cost, the second one is how to allocate the cost savings obtained by ordering the jobs optimally. In this paper we focus on the allocation problem. PFS games are defined as cooperative games associated to proportionate flow shop problems. It is seen that PFS games have a nonempty core. Moreover, it is shown that PFS games are convex if the jobs are initially ordered in decreasing urgency. For this case an explicit game independent expression for the Shapley value is provid
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