The discrete max-min problem

The historic max-min problem is examined as a discrete process rather than in its more usual continuous mode. Since the practical application of the max-min model usually involves discrete objects such as ballistic missiles, the discrete formulation of the problem seems quite appropriate. This paper uses an illegal modification to the dynamic programming process to obtain an upper bound to the max-min value. Then a second but legal application of dynamic programming to the minimization part of the problem for a fixed maximizing vector will give a lower bound to the max-min value. Concepts of optimal stopping rules may be applied to indicate when sufficiently near optimal solutions have been obtained.     

Discrete compound poisson processes and tables of the geometric poisson distribution

This paper discusses the properties of positive, integer valued compound Poisson processes and compares two members of the family: the geometric Poisson (stuttering Poisson) and the logarithmic Poisson. It is shown that the geometric Poisson process is particularly convenient when the analyst is interested in a simple model for the time between events, as in simulation. On the other hand, the logarithmic Poisson process is more convenient in analytic models in which the state probabilities (probabilities for the number of events in a specified time period) are required. These state probabilities have a negative binomial distribution. The state probabilities of the geometric Poisson process, known as the geometric Poisson distribution, are tabled for 160 sets of parameter values. The values of mean demand range from 0.10 to 10; those for variance to mean ratio from 1.5 to 7. It is observed that the geometric Poisson density is bimodal.     

Simulation of multi-echelon macro-inventory policies

Alternative repair part inventory policies are examined for a multi-echelon logistics system. The policies assessed pertain to the design of multi-echelon systems rather than the evaluation of stock level decisions for individual repair parts. Although the context is one of a military inventory system, the policies examined are of importance in nonmilitary systems where item failure rates are low, and only periodic access to resupply is possible.     

A backward recursive technique for optimal sequential sampling plans

This paper presents a procedure akin to dynamic programming for designing optimal acceptance sampling plans for item-by-item inspection. Using a Bayesian procedure, a prior distribution is specified, and a suitable cost model is employed depicting the cost of sampling, accepting or rejecting the lot. An algorithm is supplied which is digital computer oriented.     

An application of linear programming to contingency planning: A tactical airlift system analysis

A linear programming application for the selection of aircraft for a tactical airlift fleet is described.     

On the use of standard tables to obtain Dodge-Romig LTPD sampling inspection plans

Procedures are described which yield single and double sample Dodge-Romig [1] lot tolerance percent defective (LTPD) rectifying inspection plans. For the determination of such plans only a desk calculator and standard tables of the discrete probability distributions are required. Some advantages gained by using these procedures rather than the Dodge-Romig table include: (a) The Consumer's Risk is not limited to 0.10. (b) More choices of LTPD are available. (c) Smaller average total inspection is achieved by using a plan designed for specific “process average” and lot size rather than a compromise plan designed to cover intervals on these two parameters.     

Bayesian estimation: A sensitivity analysis

The robustness of the assigned prior distribution in a Bayesian estimation problem is examined. A Bayesian analysis for a stochastic intensity parameter of a Poisson distribution is summarized in which the natural conjugate is assigned as the prior distribution of the random parameter. The sensitivity analysis is carried out by assuming the existence of a true prior which is different in form from that of the assigned prior distribution. By using mean-squared error as a measure of performance, the ensuing Bayes decision function is compared to the corresponding minimum variance unbiased estimator. Results indicate that the Bayes estimator is largely robust to deviations from the assigned prior and remains squared-error superior to the MVU type within a broad region.     

Stochastic duels with round-dependent hit probabilities

The effect of round dependent hit probabilities in the fundamental stochastic duel are examined. The general solution and several specific examples are derived where one side's hit probabilities are improved from round to round. For these specific cases the advantages of round to round improvement are explicitly displayed.     

Periodic replacement with minimal repair at failure and adjustment costs

We investigate periodic replacement policies with minimal repair at failure, thereby, minimizing the average expected cost per unit time over an infinite time span. The standard cost structure is modified by the introduction of a term which takes adjustment costs into account.