The discrete search problem and the construction of optimal allocations

✍ Scribed by Ingo Wegener

• Publisher: John Wiley and Sons
• Year: 1982
• Tongue: English
• Weight: 646 KB
• Volume: 29
• Category: Article
• ISSN: 0894-069X
• DOI: 10.1002/nav.3800290203

✦ Synopsis

Abstract

Suppose one object is hidden in the k‐th of n boxes with probability p(k). The boxes are to be searched sequentially. Associated with the j‐th search of box k is a cost c(j,k) and a conditional probability q(j,k) that the first j ‐ 1 searches of box k are unsuccessful while the j‐th search is successful given that the object is hidden in box k.

The problem is to maximize the probability that we find the object if we are not allowed to offer more than L for the search. We prove the existence of an optimal allocation of the search effort L and state an algorithm for the construction of an optimal allocation. Finally, we discuss some problems concerning the complexity of our problem.