Batch Sequencing and Cooperation

CentER Discussion Paper Series No. 2008-100

21 Pages Posted: 8 Dec 2008

See all articles by Baris Ciftci

Baris Ciftci

Tilburg University - Center for Economic Research (CentER)

Peter Borm

Tilburg University - Center for Economic Research (CentER); Tilburg University - Department of Econometrics & Operations Research

Herbert Hamers

Tilburg University - Center for Economic Research (CentER); Tilburg University - Department of Econometrics & Operations Research

Marco Slikker

Eindhoven University of Technology (TUE) - School of Industrial Engineering

Date Written: December 2, 2008

Abstract

Game theoretic analysis of sequencing situations has been restricted to manufacturing 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 situations 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.

Keywords: Sequencing situations, sequencing games, batch machines

JEL Classification: C71

Suggested Citation

Ciftci, Baris and Borm, Peter E. M. and Hamers, Herbert and Slikker, Marco, Batch Sequencing and Cooperation (December 2, 2008). CentER Discussion Paper Series No. 2008-100. Available at SSRN: https://ssrn.com/abstract=1313039 or http://dx.doi.org/10.2139/ssrn.1313039

Baris Ciftci (Contact Author)

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Peter E. M. Borm

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Tilburg University - Department of Econometrics & Operations Research

Tilburg, 5000 LE
Netherlands

Herbert Hamers

Tilburg University - Center for Economic Research (CentER) ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 4666 2660 (Phone)

Tilburg University - Department of Econometrics & Operations Research

Tilburg, 5000 LE
Netherlands

Marco Slikker

Eindhoven University of Technology (TUE) - School of Industrial Engineering ( email )

P.O. Box 513
5600 MB Eindhoven
Netherlands

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