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Central European Journal of Operations Research

, Volume 21, Issue 1, pp 225–236 | Cite as

Sequencing interval situations and related games

  • S. Z. Alparslan-Gök
  • R. Branzei
  • V. FragnelliEmail author
  • S. Tijs
Original Paper

Abstract

Uncertainty accompanies almost every situation in real world and it influences our decisions. In sequencing situations it may affect parameters used to determine an optimal order in the queue, and consequently the decision of whether (or not) to rearrange the queue by sharing the realized cost savings. This paper extends the analysis of one-machine sequencing situations and their related cooperative games to a setting with interval data, i.e. when the agents’ costs per unit of time and/or processing time in the system lie in intervals of real numbers obtained by forecasting their values. The question addressed here is: How to determine an optimal order (if the initial order in the queue is not so) and which approach should be used to motivate the agents to adopt the optimal order? This question is an important one that deserves attention both in theory and practice.

Keywords

Cooperative games Interval data Sequencing situations Convex games 

Mathematics Subject Classification (2000)

91A12 

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References

  1. Alparslan Gök SZ, Branzei R, Tijs S (2008) Cores and stable sets for interval-valued games. Preprint, 90, Institute of Applied Mathematics, METU and CentER DP, 17, Tilburg University, Center for Economic Research (revised)Google Scholar
  2. Alparslan Gök SZ, Branzei R, Tijs S (2009a) Convex interval games. J Appl Math Decision Sci 342089: 14–15. doi: 10.1115/2009/342089 Google Scholar
  3. Alparslan Gök SZ, Miquel S, Tijs S (2009b) Cooperation under interval uncertainty. Math Methods Oper Res 69: 99–109CrossRefGoogle Scholar
  4. Borm P, Hamers H, Hendrickx R (2001) Operations research games: a survey. TOP 9: 139–216CrossRefGoogle Scholar
  5. Branzei R, Branzei O, Tijs S, Alparslan Gök SZ (2010a) Cooperative interval games: a survey. Central Eur J Oper Res 18: 397–411CrossRefGoogle Scholar
  6. Branzei R, Tijs S, Alparslan Gök SZ (2010b) How to handle interval solutions for cooperative interval games. Int J Uncertain Fuzziness Knowl Based Syst 18: 123–132CrossRefGoogle Scholar
  7. Curiel I, Hamers H, Klijn F (2002) Sequencing games: a survey. In: Borm P, Peters H (eds) Chapters in game theory—In honor of Stef Tijs. Kluwer, Dordrecht, pp 27–50Google Scholar
  8. Curiel I, Pederzoli G, Tijs S (1989) Sequencing games. Eur J Oper Res 40: 344–351CrossRefGoogle Scholar
  9. Moore R (1979) Methods and applications of interval analysis. SIAM Studies in Applied Mathematics, PhiladelphiaCrossRefGoogle Scholar
  10. Smith W (1956) Various optimizer for single-stage production. Naval Res Logist Q 3: 59–66CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  • S. Z. Alparslan-Gök
    • 1
  • R. Branzei
    • 2
  • V. Fragnelli
    • 3
    Email author
  • S. Tijs
    • 4
    • 5
  1. 1.Faculty of Arts and Sciences, Department of MathematicsSüleyman Demirel UniversityIspartaTurkey
  2. 2.Faculty of Computer Science“Alexandru Ioan Cuza” UniversityIaşiRomania
  3. 3.Department of Science and Advanced TechnologiesUniversity of Eastern PiedmontAlessandriaItaly
  4. 4.CentER and Department of Econometrics and ORTilburg UniversityTilburgThe Netherlands
  5. 5.Department of MathematicsUniversity of GenoaGenoaItaly

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