Stopping-allocation problem

Monotone stopping-allocation problems are first investigated. This aim of the decision maker here is to maximize the expected payoff. The stopping rule is first fixed and optimization is done with respect to the allocation rule; under some monotonicity and boundedness conditions, the local and global (with additional restrictions) optimality of the myopic allocation rule are derived. Some applications are considered, namely the insepection problem, the search problem, and the selection problem with imperfect information. Next, optimization is done with respect to both the allocation rule and the stopping rule. For any given stopping-allocation rule, it is shown that the decision maker can improve on it by using a "partial" myopic allocation rule depending on the given rule and a generalized one-stage-look-ahead stopping rule provided the problem has a certain monotonicity structure and some boundedness conditions are satisfied; this result is then extended, under the same conditions and other monotonicity requirements, to derive the joint optimality of the myopic allocation rule and the one-stage-look-ahead stopping rule. This latter result is then applied to the inspection problem.;The second topic deals with asymptotic stopping-allocation problems. The aim of the decision maker here is to minimize the payoff function in the sense of asymptotic pointwise optimality. The payoff includes a cost per observation which is different from population to population; the total cost of observation at any stage depends only on the cost per observation from each population and the number of observations collected from each population by that stage. For each population, a sequence of functions of the observations collected from that population, called posterior losses, is defined; they are the usual minimum conditional Bayes expected losses for either estimation or testing hypothesis problems. The payoff function is defined as a function of the posterior losses plus the total cost of observation. The goal is to choose stopping-allocation rules that are asymptotically pointwise optimal (A.P.O.), that is, they minimize the payoff function as the cost per observation from each population is going to zero. (Abstract shortened with permission of author.).