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On Optimal Ammunition Usage When Hunting Fleeing Targets

Published online by Cambridge University Press:  27 July 2009

Masahiro Sato
Affiliation:
Doctoral Program in Policy and Planning Sciences, University of Tsukuba, Tsukuba, Ibaraki 305, Japan

Abstract

A hunter hunts over a planning horizon t with i bullets. The distribution of the value of targets appearing and the probability of a bullet hitting are known. Encountering a target of value w, he has a choice of retiring from hunting completely, shooting a single bullet, or moving on to the next period to find another target. If he retires, he immediately obtains a terminal reward dependent on the remaining periods and bullets. If he fires and succeeds, he obtains the reward w and decides whether to retire or move on to the next epoch. If he misses and the target remains stationary, he must immediately decide whether to fire an additional bullet, retire, or move on to the next period. The objective in this paper is to examine the optimal decision rules that would maximize the total expected reward. We reveal that the optimal decision rule for firing is not always monotone in the number of remaining bullets and the optimal decision rule for retirement may become possibly the following form. It is better to continue hunting than retire, only if the hunter has neither too few bullets nor too many.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1997

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References

1.Derman, C., Lieberman, G.J., & Ross, S.M. (1972). A sequential stochastic assignment problem. Management Science 18: 349355.CrossRefGoogle Scholar
2.Derman, C., Lieberman, G.J. & Ross, S.M. (1975). A stochastic sequential allocation model. Operations Research 23: 11201130.CrossRefGoogle Scholar
3.Kisi, T. (1976). Suboptimal decision rule for attacking targets of opportunity. Naval Research Logistics Quarterly 23: 525533.CrossRefGoogle Scholar
4.Klinger, A. & Brown, T.A. (1968). Allocating unreliable units to random demands. In Karreman, H. (ed.), Stochastic Optimization and Control. Publication 20, Mathematical Research Center, U.S. Army and University of Wisconsin. New York: Wiley.Google Scholar
5.Mastran, D.V. & Thomas, C.J. (1973). Decision rule for attacking targets of opportunity. Naval Research Logistics Quarterly 20: 661672.CrossRefGoogle Scholar
6.Namekata, T., Tabata, Y. & Nishida, T. (1979). A sequential allocation problem with two kinds of targets. Journal of the Operations Research Society of Japan 22: 1628.CrossRefGoogle Scholar
7.Namekata, T., Tabata, Y. & Nishida, T. (1981). A sequential allocation problem with perishable goods. Journal of the Operations Research Society of Japan 24: 202212.CrossRefGoogle Scholar
8.Namekata, T., Tabata, Y. & Nishida, T. (1981). Some remarks on sequential allocation problem over unknown number of periods. Journal of the Operations Research Society of Japan 24: 339349.CrossRefGoogle Scholar
9.Prastacos, G.P. (1983). Optimal sequential investment decisions under conditions of uncertainty. Management Science 29: 118134.CrossRefGoogle Scholar
10.Sakaguchi, M. (1976). A sequential allocation problem for randomly appearing targets. Mathematica Japonica 21: 89103.Google Scholar
11.Samuel, E. (1970). On some problems in operations research. Journal of Applied Probability 7: 157164.CrossRefGoogle Scholar
12.Sato, M. (1995). A stochastic sequential allocation problem where the resources can be replenished. Discussion Paper 637, Institute of Socio-Economic Planning, University of Tsukuba.Google Scholar
13.Sato, M. (1996). A sequential allocation problem with search cost where the shoot-look-shoot policy is employed. Journal of the Operations Research Society of Japan 39(3): 435454.CrossRefGoogle Scholar
14.Weber, R.R. (1985). A problem of ammunition rationing. In Radermacher, F.J., Ritter, G. & Ross, S.M. (eds.), Stochastic Dynamic Optimization and Applications in Scheduling and Related Areas. Passau, West Germany: University of Passau.Google Scholar