Discrete Sequential Search for One of Many Objects

Abstract

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.