Locating Direction Finders Optimally under Risk of Detection

  • Suhwan Kim Korea National Defense University
Keywords: direction finder, military application, risk management, conditional value at risk, label-setting algorithm


The military uses direction finders (DFs) to determine the locale of enemy forces by estimating the positions of their transmitters, which emit radio frequencies. This paper considers the problem of locating DFs with the goal of maximizing the accuracy with which transmitter positions can be estimated in a target area while managing the expected number of DFs that will not be detected by the enemy. Once detected, a DF is subject to jamming or attack by the enemy. This paper presents six models, each appropriate for a different battlefield situation. It casts three models as network flow problems and presents an efficient label-setting algorithm to solve them. The remaining formulations represent novel applications of the Conditional Value at Risk (CVaR) to deal with the probability of DF detection. Computational tests compare model solutions.

Author Biography

Suhwan Kim, Korea National Defense University
Associate ProfessorDepartment of Military Operations ResearchKorea National Defense Unversity


U.S. Army,Field Manual 34-4-9, Direction finding operations, Headquarters, Department of the Army: Washington, 1991.

U.S. Army,Field Manual 101-5-1, Operational terms and graphics, Headquarters, Department of the Army: Washington, 1997.

P. Artzner, F. Delbaen, J.M. Eber and D. Heath, Coherent measures of risk, Mathematical Finance 9.3: 203-228, 1999.

M. Desrochers and F.A. Soumis, A generalized permanent labeling algorithm for the shortest path problem with time windows, INFOR 26: 193-214, 1988.

I. Dumitrescu and N. Boland, Algorithms for the weight constrained shortest path problem, International Transactions in Operational Research 8.1: 15-29, 2001.

H.D. Kennedy and R.B. Woolsey, Direction-Finding Antennas and Systems, in Antenna Engineering Handbook, 3rd Edition, edited by R.C. Johnson, Ed, New York: McGraw-Hill, Chapter 39, 1993.

H.H. Jenkins, Small-aperture radio direction-finding, Artech house, Norwood, 1991

S.H. Kim and W.E. Wilhelm, On the optimal deployment of direction finders, IEEE Transactions on Automation Science and Engineering 11(2), 2014.

P. Krokhmal, R. Murphey, P. Pardolas, and S. Uryasev, Robust decision making: Addressing uncertainties in distributions, Cooperative Control:Models, Applications, and Algorithms:165-185, 2003.

H.J. Lee, Y.D. Kim, and S.B. Lee, A simulation-based heuristic algorithm for disposition of direction finders, Computers and Industrial Engineering 55(1): 134-149. 2008.

L. Jingwen and S.A. Quek, Locating a target from directional data, Naval Research Logistics 45(4): 353-364, 1998.

R.T. Rockafellar and S. Uryasev, Optimization of conditional value-at-risk, Journal of risk 2: 21-42, 2000.

R.G. Stansfield, Statistical theory of DF fixing. Electrical Engineers-Part IIIA: Radiocommunication, Journal of the Institution of 94(15): 762-770, 1947.

I. Toumazis, C. Kwon, and R. Batta, Value-at-Risk and Conditional Value-at-Risk Minimization for Hazardous Materials Routing, Handbook of OR/MS Models in Hazardous Materials Transportation. Springer. New York, 2013.

S. Uryasev, Conditional value-at-risk: Optimization algorithms and applications, Computational Intelligence for Financial Engineering, Proceedings of the IEEE/IAFE/INFORMS 2000 Conference on. IEEE, 2000.

X. Zhu and W.E. Wilhelm, A three-stage approach for the resource-constrained shortest path as a sub-problem in column generation, Computers and Operations Research 39(2): 164-178, 2012.

How to Cite
Kim, S. (2018). Locating Direction Finders Optimally under Risk of Detection. Statistics, Optimization & Information Computing, 6(2), 219-232. https://doi.org/10.19139/soic.v6i2.399
Research Articles