Technical note: Worst‐case performance of power‐of‐two policies for serial inventory systems with incremental quantity discounts

This study presents power‐of‐two policies for a serial inventory system with constant demand rate and incremental quantity discounts at the most upstream stage. It is shown that an optimal solution is nested and follows a zero‐inventory ordering policy. To prove the effectiveness of power‐of‐two policies, a lower bound on the optimal cost is obtained. A policy that has a cost within 6% of the lower bound is developed for a fixed base planning period. For a variable base planning period, a 98% effective policy is provided. An extension is included for a system with price dependent holding costs. © 2007 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Simulation of nonhomogeneous poisson processes by thinning

A simple and relatively efficient method for simulating one-dimensional and two-dimensional nonhomogeneous Poisson processes is presented The method is applicable for any rate function and is based on controlled deletion of points in a Poisson process whose rate function dominates the given rate function In its simplest implementation, the method obviates the need for numerical integration of the rate function, for ordering of points, and for generation of Poisson variates.     

A single server queue with arrival rate dependent on server breakdowns

This paper considers a single server queueing system that alternates stochastically between two states: operational and failed. When operational, the system functions as an M/E_k/1 queue. When the system is failed, no service takes place but customers continue to arrive according to a Poisson process; however, the arrival rate is different from that when the system is operational. The durations of the operating and failed periods are exponential with mean 1/cβ and Erlang with mean 1/cβ, respectively. Generating functions are used to derive the steady-state quantities L and W, both of which, when viewed as functions of c, decrease at a rate inversely proportional to c². The paper includes an analysis of several special and extreme cases and an application to a production-storage system.     

Damage calculations for unreliable warheads

For large numbers of perfectly reliable, optimally targeted warheads the square-root law approximates the expected fraction damage achieved on an area target. In this paper a more exact expression is derived for this damage fraction which Holds for all numbers of warheads. This expression is shown to converge to the square-root law when a large number of warheads are fired. The more exact expression is used in a procedure to calculate expected damage when warheads are unreliable, and this procedure is shown to be superior to a modified square-root approximation which has been used previously.     

Duality for quasi-concave programs with application to economics

A duality theory is developed for mathematical programs with strictly quasi-concave objective functions to be maximized over a convex set. This work broadens the duality theory of Rockafellar and Peterson from concave (convex) functions to quasi-concave (quasi-convex) functions. The theory is closely related to the utility theory in economics. An example from economic planning is examined and the solution to the dual program is shown to have the properties normally associated with market prices.     

The optimum design of multivariate acceptance sampling plans

A model is developed which may be used to determine the expected total cost of quality control per inspection lot under acceptance sampling by variables where several characteristics are to be simultaneously controlled. Optimization of the model is accomplished through the application of a conventional search procedure. The sensitivity of the model and the optimum solution to the shape of the underlying probability distributions is discussed and associated analyses are presented through an example.     

Optimal selection from a random sequence with observation errors

A form of sequential decision problem is introduced in which options are presented in sequence. with no recall of rejected options (as in the secretary problem), but in which the value of each option may only he inferred from experiments. Decisions have thus to be made concerning both the acceptance and rejection of each option and the degree of experimentation. General properties of the optimal policy are derived, and an algorithm is obtained for the solution in a special case. This special case suggests a heuristic rule for more general situations. the performance of which rule has been investigated by a Monte Carlo study.     

A note on a confidence interval for an interclass mean

An exact confidence interval for an interclass mean, that is, the mean of a composite sample made up several subsamples of unequal sizes n_i, is presented.     

A bayesian approach to evaluating military investments in product improvement and testing

Two issues of frequent importance in new product development are product improvement and reliability testing. A question often faced by the developer is: Should the product be distributed in its present state, or should it be improved further and/or tested before distribution? A more useful statement of the question might be: What levels of investment in further improvement and testing are economically permissible? Products for which this question is relevant may vary widely in type and intended use. This paper presents a model for determining these levels for one such product—an equipment modification procedure. The model presented makes use of present value analysis to compare cost streams and of Bayesian statistics to relate the costs to various outcomes under conditions of uncertainty. The model is applied to an actual military problem and a method is described for examining the sensitivity of the results to changes in the prior probabilities and discount rate.