Abstract
In this paper we consider three discrete-time discounted Bayesian search problems with an unknown number of objects and uncertainty about the distribution of the objects among the boxes. Moreover, we admit uncertainty about the detection probabilities. The goal is to determine a policy which finds (dependent on the search problem) at least one object or all objects with minimal expected total cost. We give sufficient conditions for the optimality of the greedy policy which has been introduced in Liebig/Rieder (1996). For some examples in which the greedy policy is not optimal we derive a bound for the error.
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References
Assaf D, Zamir S (1985) Optimal sequential search: A Bayesian approach. Ann Stat 13:1213–1221
Assaf D, Zamir S (1987) Continuous and discrete search for one of many objects. Oper Res Letters 6:205–209
Kimeldorf G, Smith FH (1975) Discrete sequential search for one of many objects. Ann Stat 3:906–915
Kimeldorf G, Smith FH (1979) Binomial searching for a random number of multinomially hidden objects. Manage Sci 25:1115–1126
Lehnerdt M (1982) On the structure of discrete sequential search problems and of their solutions. Optimization 13:523–557
Liebig T, Rieder U (1996) Optimal greedy policies for stochastic control models. Mathem Meth Oper Res 44:115–133
Liebig T (1995) Strukturuntersuchungen in Bayesschen Suchproblemen. Dissertation, Universität Ulm
Rieder U (1991) Structural results for partially observed control models. ZOR-Mathem Meth Oper Res 35:473–490
Sharlin A (1987) Optimal search for one of many objects hidden in two boxes. Eur J Oper Res 32:251–259
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Liebig, T. Discounted Bayesian search problems with unknown detection probabilities. Mathematical Methods of Operations Research 44, 233–254 (1996). https://doi.org/10.1007/BF01194333
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DOI: https://doi.org/10.1007/BF01194333