A note on an optimal choice problem

Abstract

An item has probabilityp ₀ of not being workable. Before, going into use it has to be controlled by some deliberately chosen checksC _i which costsc _i ≥0,1≤i≤n. Total checking costs must be not larger thanc ₀>0. It may happen that a check breaks a workable item, and failures may be overlooked. The problem is to determine an optimal sequence of checks subject to the cost constraints, such that the probability is maximized that an item leaving the checks is workable. In [1] this problem is solved by W. Stadje, but numerically the solution method only is applicable to problems of modest size.

In this paper a simple reformulation of the original problem is presented. This first allows a simpler derivation of some of the results in [1]. Further, a dynamic programming algorithm is presented, which is pseudopolynomial, if costsc _i are integers. It then requiresO(n·c ₀) time.