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Scheduling target illuminators in naval battle‐group anti‐air warfare

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  • Hanif D. Sherali
  • Youngho Lee
  • Donald D. Boyer

Abstract

We schedule a set of illuminators (homing devices) to strike a set of targets using surface‐to‐air missiles in a naval battle. The task is viewed as a production floor shop scheduling problem of minimizing the total weighted flow time, subject to time‐window job availability and machine downtime side constraints. A simple algorithm based on solving assignment problems is developed for the case when all the job processing times are equal and the data are all integer. For the general case of scheduling jobs with unequal processing times, we develop two alternate formulations and analyze their relative strengths by comparing their respective linear programming relaxations. We select the better formulation in this comparison and exploit its special structures to develop several effective heuristic algorithms that provide good‐quality solutions in real time; this is an essential element for use by the Navy. © 1995 John Wiley & Sons, Inc.

Suggested Citation

  • Hanif D. Sherali & Youngho Lee & Donald D. Boyer, 1995. "Scheduling target illuminators in naval battle‐group anti‐air warfare," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(5), pages 737-755, August.
    • Handle: RePEc:wly:navres:v:42:y:1995:i:5:p:737-755
    DOI: 10.1002/1520-6750(199508)42:53.0.CO;2-T
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    References listed on IDEAS

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    1. Sherali, Hanif D., 1988. "Bounds on penalties for dummy arcs in transportation networks," European Journal of Operational Research, Elsevier, vol. 36(3), pages 353-359, September.
    2. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    3. C. N. Potts, 1980. "Technical Note—Analysis of a Heuristic for One Machine Sequencing with Release Dates and Delivery Times," Operations Research, INFORMS, vol. 28(6), pages 1436-1441, December.
    4. Blazewicz, Jacek & Dror, Moshe & Weglarz, Jan, 1991. "Mathematical programming formulations for machine scheduling: A survey," European Journal of Operational Research, Elsevier, vol. 51(3), pages 283-300, April.
    5. Roy E. Marsten, 1974. "An Algorithm for Large Set Partitioning Problems," Management Science, INFORMS, vol. 20(5), pages 774-787, January.
    6. Grabowski, J. & Nowicki, E. & Zdrzalka, S., 1986. "A block approach for single-machine scheduling with release dates and due dates," European Journal of Operational Research, Elsevier, vol. 26(2), pages 278-285, August.
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    Cited by:

    1. Orhan Karasakal & Nur Evin Özdemirel & Levent Kandiller, 2011. "Anti‐ship missile defense for a naval task group," Naval Research Logistics (NRL), John Wiley & Sons, vol. 58(3), pages 304-321, April.
    2. Moustafa Elshafei & Hanif D. Sherali & J. Cole Smith, 2004. "Radar pulse interleaving for multi‐target tracking," Naval Research Logistics (NRL), John Wiley & Sons, vol. 51(1), pages 72-94, February.

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