Optimal search for a moving target with the option to wait

We investigate the problem in which an agent has to find an object that moves between two locations according to a discrete Markov process (Pollock, Operat Res 18 (1970) 883–903). At every period, the agent has three options: searching left, searching right, and waiting. We assume that waiting is costless whereas searching is costly. Moreover, when the agent searches the location that contains the object, he finds it with probability 1 (i.e. there is no overlooking). Waiting can be useful because it could induce a more favorable probability distribution over the two locations next period. We find an essentially unique (nearly) optimal strategy, and prove that it is characterized by two thresholds (as conjectured by Weber, J Appl Probab 23 (1986) 708–717). We show, moreover, that it can never be optimal to search the location with the lower probability of containing the object. The latter result is far from obvious and is in clear contrast with the example in Ross (1983) for the model without waiting. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Dynamic multiattribute models for mixed manpower systems

This paper reviews a wide variety of manpower and personnel models of the goal programming variety. This is done from a strategy-oriented point of view addressing the problems of interest for immediate implementation as well as basic problems of manpower model research development. Particular emphasis in this paper is concerned with how analytical models can be brought to bear on the problems of combining military and civilian manpower into one management system. This includes a discussion of the computer support arrangements necessary to implement the models. First, we discuss an extension of multilevel models to provide an integrated approach to program planning which includes the dynamics of the manpower requirements-inventory relationships of mixed military-civilian manpower systems. Then, focus is given to some of the potential Navy applications particularly in terms of ways the outputs from the global multilevel model might be interfaced with assignment models for operational planning. The paper concludes with a discussion of static and dynamic multiattribute assignment models which operate on the individual man-job matching level. It is at this level of detail that dynamic mixed manpower systems might be constructed for use in equal employment opportunity planning and for local organization design studies.     

Further light on nonparametric selection efficiency

A nonparametric selection procedure ??bs was proposed by Bechhofer and Sobel (1958) and studied by Dudewicz (1971) in comparison with other procedures under normal and uniform alternatives. He found ??BS always required larger sample sizes, sometimes substantially so. For 2-point populations we find more extreme results. We also find that ??BS may be substantially better than reasonable competitors designed specifically for 2-point populations. Finally, a new nonparametric selection procedure (conjectured to be better than ??BS) is proposed.     

Optimal betting strategies for favorable games

We examine the problem of a gambler interested in maximizing the expected value of a convex utility function of his fortune after n plays of a game. We allow any probability distribution to rule the outcome of each play, and this distribution may change from play to play according to a Markov process. We present results regarding the existence of an optimal policy and its structural dependence on the gambler's fortune. The well-known results of Bellman and Kalaba for exponential and logarithmic utility functions and coin-tossing games are generalized. We also examine the situation of general stale spaces and show that the same structural results hold.     

Two-characteristic markov-type manpower flow models

A two-dimensional state space Markov Model of a Manpower System with special structure is analyzed. Examples are given from the military services. The probabilistic properties are discussed in detail with emphasis on computation. The basic equations of manpower stocks and flows are analyzed.     

Estimation of ordered parameters from k stochastically increasing distributions

There are given k (? 2) univariate cumulative distribution functions (c.d.f.'s) G(x; θ_i) indexed by a real-valued parameter θ_i, i=1,…, k. Assume that G(x; θ_i) is stochastically increasing in θ_i. In this paper interval estimation on the i^th smallest of the θ's and related topics are studied. Applications are considered for location parameter, normal variance, binomial parameter, and Poisson parameter.     

More ado about economic order quantities (EOQ)

This paper is concerned with the determination of explicit expressions for economic order quantities and reorder levels, such that the cost of ordering and holding inventory is minimized for specific backorder constraints. Holding costs are applied either to inventory position or on-hand inventory, and the backorder constraint is considered in terms of the total number of backorders per year or the average number of backorders at any point in time. Through the substitution of a new probability density function in place of the normal p.d.f., explicit expressions are determined for the economic order quantities and the reorder points. The resulting economic order quantities are independent of all backorder constraints. It is also concluded that under certain conditions, the minimization of ordering costs and inventory holding costs (applied to inventory position), subject to a backorder constraint, is equivalent in terms of reorder levels to minimization of the safety level dollar investment subject to the same backorder constraint.