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Lagrangian relaxation approach to the targeting problem

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  • Ojeong Kwon
  • Donghan Kang
  • Kyungsik Lee
  • Sungsoo Park

Abstract

In this paper, we consider a new weapon–target allocation problem with the objective of minimizing the overall firing cost. The problem is formulated as a nonlinear integer programming model. We applied Lagrangian relaxation and a branch‐and‐bound method to the problem after transforming the nonlinear constraints into linear ones. An efficient primal heuristic is developed to find a feasible solution to the problem to facilitate the procedure. In the branch‐and‐bound method, three different branching rules are considered and the performances are evaluated. Computational results using randomly generated data are presented. © 1999 John Wiley & Sons, Inc. Naval Research Logistics 46: 640–653, 1999

Suggested Citation

  • Ojeong Kwon & Donghan Kang & Kyungsik Lee & Sungsoo Park, 1999. "Lagrangian relaxation approach to the targeting problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 46(6), pages 640-653, September.
    • Handle: RePEc:wly:navres:v:46:y:1999:i:6:p:640-653
    DOI: 10.1002/(SICI)1520-6750(199909)46:63.0.CO;2-Q
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    References listed on IDEAS

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    1. Richard H. Day, 1966. "Allocating Weapons to Target Complexes by Means of Nonlinear Programming," Operations Research, INFORMS, vol. 14(6), pages 992-1013, December.
    2. Hanif D. Sherali & Seong‐In Kim & Edna L. Parrish, 1991. "Probabilistic partial set covering problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(1), pages 41-51, February.
    3. F. Lemus & K. H. David, 1963. "An Optimum Allocation of Different Weapons to a Target Complex," Operations Research, INFORMS, vol. 11(5), pages 787-794, October.
    4. Marshall L. Fisher, 1981. "The Lagrangian Relaxation Method for Solving Integer Programming Problems," Management Science, INFORMS, vol. 27(1), pages 1-18, January.
    5. Norman T. O'Meara & Richard M. Soland, 1992. "Optimal strategies for problems of simultaneous attack against an area defense with impact‐point prediction," Naval Research Logistics (NRL), John Wiley & Sons, vol. 39(1), pages 1-28, February.
    6. Alan S. Manne, 1958. "A Target-Assignment Problem," Operations Research, INFORMS, vol. 6(3), pages 346-351, June.
    7. Marshall L. Fisher, 1985. "An Applications Oriented Guide to Lagrangian Relaxation," Interfaces, INFORMS, vol. 15(2), pages 10-21, April.
    8. Eitan Wacholder, 1989. "A Neural Network-Based Optimization Algorithm for the Static Weapon-Target Assignment Problem," INFORMS Journal on Computing, INFORMS, vol. 1(4), pages 232-246, November.
    9. Gershon G. Furman & Harvey J. Greenberg, 1973. "Optimal Weapon Allocation with Overlapping Area Defenses," Operations Research, INFORMS, vol. 21(6), pages 1291-1308, December.
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    Cited by:

    1. Ahmet Silav & Esra Karasakal & Orhan Karasakal, 2022. "Bi-objective dynamic weapon-target assignment problem with stability measure," Annals of Operations Research, Springer, vol. 311(2), pages 1229-1247, April.
    2. 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.
    3. Ojeong Kwon & Kyungsik Lee & Donghan Kang & Sungsoo Park, 2007. "A branch‐and‐price algorithm for a targeting problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 54(7), pages 732-741, October.
    4. Alexander G. Kline & Darryl K. Ahner & Brian J. Lunday, 2020. "A heuristic and metaheuristic approach to the static weapon target assignment problem," Journal of Global Optimization, Springer, vol. 78(4), pages 791-812, December.

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