Open Access
July, 1975 Discrete Sequential Search for One of Many Objects
Furman H. Smith, George Kimeldorf
Ann. Statist. 3(4): 906-915 (July, 1975). DOI: 10.1214/aos/1176343191


Suppose N objects are hidden multinomially in m boxes, where m is known and N is random. The boxes are to be searched sequentially. Asssociated with a search of box k is a cost $c_k>0$ and a conditional probability ${alpha k}$ of finding a specific object in box k, given that it is hidden there. An optimal strategy is one which minimizes the total expected cost required to find at least one object. If N has a positive-Poisson distribution, then an optimal strategy is shown to take a simple form. Conversely, if for all possible ${c_k}$ and ${\alpha_k}$ an optimal strategy takes this simple form, then N has a positive-Poisson distribution.


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Furman H. Smith. George Kimeldorf. "Discrete Sequential Search for One of Many Objects." Ann. Statist. 3 (4) 906 - 915, July, 1975.


Published: July, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0312.90033
MathSciNet: MR378772
Digital Object Identifier: 10.1214/aos/1176343191

Primary: 90B40

Keywords: Discrete sequential search , dynamic programming , positive-Poisson distribution

Rights: Copyright © 1975 Institute of Mathematical Statistics

Vol.3 • No. 4 • July, 1975
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