A note on a model for evasive vehicle movement along a fixed path

A model for a vehicle moving evasively along a fixed path is defined in terms of a two- state semi-Markov process. An important feature of this model is the continuous movement of the vehicle as a function of time. One potential application of this model is the development of a strategy for the deployment of long-range missiles on long underground tracks.     

Evaluation of costs of ordering policies in large machine repair problems

This article examines a version of the machine repair problem where failures may be irreparable. Since the number of machines in the system keeps decreasing, we impose a fixed state-dependent ordering policy of the type often encountered in inventory models. Although the system is Markovian, the number of states becomes very large. The emphasis of the article, therefore, is on deriving computationally tractable formulas for the steady-state probabilities, the long-run average cost per unit time, and the vector of expected discounted costs. When the state space is so large that exact computations may be infeasible, we propose approximations which are relatively quick and simple to compute and which yield very accurate results for the test problems examined.     

Hu's precedence tree scheduling algorithm: A simple proof

This article presents a simple proof of Hu's algorithm for scheduling in minimum time a set of tasks constrained by precedence tree constraints, each task requiring a unit time to complete, and where m processors are available.     

An application of servomechanisms to inventory

In recent years, some attention has been devoted to the application of techniques of control theory to inventory management. In particular, H. Vassian (1955) developed a model for a periodic review inventory system utilizing techniques of discrete variable servomechanisms to analyze the system in a cost-free structure. The resulting model is inherently deterministic, however, and emphasizes the control of inventory fluctuation about a safety level by selecting an appropriate order policy. Such an order policy is defined only up to an arbitrary method of forecasting customer demands. The present paper is a continuation of the model developed by Vassian in which exponential smoothing is used as a specific forecasting technique. Full recognition of the probabilistic nature of demand is taken into account and the requirement of minimizing expected inventory level is imposed. In addition, explicit formulas for the variance in inventory are derived as functions of the smoothing constant and the tradeoff between small variance and rapid system response is noted. Finally, in an attempt to remove the bias inherent in exponential smoothing, a modification of that technique is defined and discussed as an alternate forecasting method.     

Impact of an all volunteer force upon the navy in the 1972-1973 timeframe

This paper develops estimates of true volunteer levels for 1972 and 1973, based on experience gained through 1970 draft lottery data. The paper also formulates estimates of the qualitative characteristics of a 1972-1973 Navy volunteer force, and establishes a relationship between rate of volunteerism and military pay. Utilizing estimates generated in the paper, Navy military personnel budget requirements for FY '72 and '73 are presented.     

A technique which combines modified pattern search methods with composite designs and polynomial constraints to solve constrained optimization problems

This paper presents a method of selecting design parameters which optimizes a specific measure (aircraft design example: minimum weight, maximum mission effectiveness) and guarantees designated levels of response in specified areas (such as combal ceiling, acceleration time). The method employs direct search optimization applied to a nonlinear functional constrained by nonlinear surfaces. The composite design technique is combined with regression methods to determine adequate surface representations with a minimum of required data points. A sensitivity analysis is conducted at the optimum set of design parameters to test for uniqueness.     

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.     

The initial provisioning decision for insurance type items

Initial provisioning decisions (inventory stocking requirements) for low demand items often have to be made without much knowledge of what future demand rates will be. When the nature of an item is such that little demand for it is expected, the problem of whether to stock initially or risk not stocking the item is most critical. This report discusses this problem and presents decision procedures which can be used to handle this aspect of initial provisioning. The procedures relate an item's provisioning desirability to its provisioning characteristics, such as expected cost, expected resupply time, current information on its likely demand rate, and to an overall operating policy or criterion. The criterion function measures the total system degredation as a function of the events of having items out of stock when demand occurs. Several different policy functions are discussed and the provisioning decision rules which apply to each are presented. Demand rate information is handled through a Bayesian type approach. The decision rules presented in this report can be utilized to either determine stocking requirements within a budgetary constraint, or determine the relative stocking desirability on an item-by-item basis.