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Queueing Systems

, Volume 70, Issue 2, pp 165–186 | Cite as

Flexible servers in tandem lines with setup costs

  • Sigrún Andradóttir
  • Hayriye Ayhan
  • Eser Kırkızlar
Article

Abstract

We study the dynamic assignment of flexible servers to stations in the presence of setup costs that are incurred when servers move between stations. The goal is to maximize the long-run average profit. We provide a general problem formulation and some structural results, and then concentrate on tandem lines with two stations, two servers, and a finite buffer between the stations. We investigate how the optimal server assignment policy for such systems depends on the magnitude of the setup costs, as well as on the homogeneity of servers and tasks. More specifically, for systems with either homogeneous servers or homogeneous tasks, small buffer sizes, and constant setup cost, we prove the optimality of “multiple threshold” policies (where servers’ movement between stations depends on both the number of jobs in the system and the locations of the servers) and determine the values of the thresholds. For systems with heterogeneous servers and tasks, small buffers, and constant setup cost, we provide results that partially characterize the optimal server assignment policy. Finally, for systems with larger buffer sizes and various service rate and setup cost configurations, we present structural results for the optimal policy and provide numerical results that strongly support the optimality of multiple threshold policies.

Keywords

Flexible servers Finite buffers Markov decision processes Setup costs Tandem production systems Threshold policies 

Mathematics Subject Classification (2000)

90B22 90C40 60J28 

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Supplementary material

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Sigrún Andradóttir
    • 1
  • Hayriye Ayhan
    • 1
  • Eser Kırkızlar
    • 2
  1. 1.H. Milton Stewart School of Industrial and Systems EngineeringGeorgia Institute of TechnologyAtlantaUSA
  2. 2.School of ManagementState University of New York–BinghamtonBinghamtonUSA

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