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A note on the optimality of index priority rules for search and sequencing problems

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  • George J. Kyparisis
  • Christos Koulamas

Abstract

We show that the linear objective function of a search problem can be generalized to a power function and/or a logarithmic function and still be minimized by an index priority rule. We prove our result by solving the differential equation resulting from the required invariance condition, therefore, we also prove that any other generalization of this linear objective function will not lead to an index priority rule. We also demonstrate the full equivalence between two related search problems in the sense that a solution to either one can be used to solve the other one and vice versa. Finally, we show that the linear function is the only function leading to an index priority rule for the single‐machine makespan minimization problem with deteriorating jobs and an additive job deterioration function. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011

Suggested Citation

  • George J. Kyparisis & Christos Koulamas, 2011. "A note on the optimality of index priority rules for search and sequencing problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(2), pages 83-87, March.
    • Handle: RePEc:wly:navres:v:58:y:2011:i:2:p:83-87
    DOI: 10.1002/nav.20442
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    References listed on IDEAS

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    1. Uriel G. Rothblum & Michael H. Rothkopf, 1994. "Dynamic Recomputation Cannot Extend the Optimality-Range of Priority Indices," Operations Research, INFORMS, vol. 42(4), pages 669-676, August.
    2. Joseph B. Kadane, 1978. "A Characterization of the Rau Class of Sequential Problems," Mathematics of Operations Research, INFORMS, vol. 3(1), pages 42-56, February.
    3. Sid Browne & Uri Yechiali, 1990. "Scheduling Deteriorating Jobs on a Single Processor," Operations Research, INFORMS, vol. 38(3), pages 495-498, June.
    4. F. P. Kelly, 1982. "A Remark on Search and Sequencing Problems," Mathematics of Operations Research, INFORMS, vol. 7(1), pages 154-157, February.
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