bluuebunny/crossref_metadata_2025 huggingface dataset:
Infinite Dimensional Geometric Properties of Real Interpolation Spaces
Authors: Kutzarova Denka , Nikolova Lyudmila I. , Prus Stanislaw
Published: May 2007

Estimates for the moduli of noncompact convexity of lp‐sums and real interpolation spaces for finite families of spaces are given. It is proved that such an interpolation preserves nearly uniform convexity and property (β).
Boundedness of Sublinear Operators in Herz Spaces on Vilenkin Groups and its Application
Authors: Lu Shanzhen , Yang Dachun
Published: May 2007

The authors establish the boundedness of some sublinear operators in weighted Herz spaces on Vilenkin groups under certain weak local hypotheses on the size of these operators at the identity. This class of operators includes most of the important operators in harmonic analysis on Vilenkin groups. The main theorems are best possible under the conditions of the theorems. As applications, the authors establish the Littlewood‐Paley function characterization of some Herz spaces and the relations between Herz spaces and Herz‐type Hardy spaces.
The Poisson Voronoi Tessellation III. Miles' Formula
Authors: Muche Lutz
Published: May 2007

This paper gives distributional properties of geometrical characteristics of a Voronoi tessellation generated by a stationary Poisson point process. The considerations are based on a well‐known formula given by [10] describing size and shape of a cell of the Delaunay tessellation and on the close connection between Delaunay and Voronoi tessellation. Several results are given for the two‐dimensional case, but the main part is the investigation of the three‐dimensional case. They include the density functions of the angles perpendicular to the ‘typical’ edge, spanned by two neighbouring Poisson points and that spanned by two neighbouring faces, the angle between two edges emanating from the ‘typical’ vertex, the distance of two neighbouring Poisson points, the angle between two edges emanating from the ‘typical’ vertex of the Poisson Voronoi tessellation and some others. These density functions are given partly explicitely and partly in integral form.
The Newton Polygon and Elliptic Problems with Parameter
Authors: Denk Robert , Mennicken Reinhard , Volevich Leonid
Published: May 2007

In the study of the resolvent of a scalar elliptic operator, say, on a manifold without boundary there is a well‐known Agmon‐Agranovich‐Vishik condition of ellipticity with parameter which guarantees the existence of a ray of minimal growth of the resolvent. The paper is devoted to the investigation of the same problem in the case of systems which are elliptic in the sense of Douglis‐Nirenberg. We look for algebraic conditions on the symbol providing the existence of the resolvent set containing a ray on the complex plane. We approach the problem using the Newton polyhedron method. The idea of the method is to study simultaneously all the quasihomogeneous parts of the system obtained by assigning to the spectral parameter various weights, defined by the corresponding Newton polygon. On this way several equivalent necessary and sufficient conditions on the symbol of the system guaranteeing the existence and sharp estimates for the resolvent are found. One of the equivalent conditions can be formulated in the following form: all the upper left minors of the symbol satisfy ellipticity conditions. This subclass of systems elliptic in the sense of Douglis‐Nirenberg was introduced by A. KOZHEVNIKOV [K2].
On Constants of Some Regularity Theorems. De Giorgi's Type Counterexample
Authors: Leonardi Salvatore
Published: May 2007

We shall explicitly evaluate important constants in embedding theorems and Hölder‐regularity theorems for an elliptic equation of the type magnified image.
Tauberian theorem for m‐spherical transforms on the Heisenberg group
Authors: Chang Der‐Chen , Eby Wayne M.
Published: May 2007

In this paper we prove a Tauberian type theorem for the space L $ ^1 _{\bf m} $(Hn ). This theorem gives sufficient conditions for a L $ ^1 _{\bf 0} $(Hn ) submodule J ⊂ L $ ^1 _{\bf m} $(Hn ) to make up all of L $ ^1 _{\bf m} $(Hn ). As a consequence of this theorem, we are able to improve previous results on the Pompeiu problem with moments on the Heisenberg group for the space L∞(Hn ). In connection with the Pompeiu problem, given the vanishing of integrals ∫zmLgf (z, 0) dσ (z) = 0 for all g ∈ Hn and i = 1, 2 for appropriate radii r1 and r2, we now have the (improved) conclusion $ {\bar {\bf Z}}^{\bf m} $ f ≡ 0, where $ {\bar {\bf Z}}^{\bf m} $ = $ \bar Z^{m_1}_1 $ · · · $ \bar Z^{m_n}_n $ and $ \bar Z_j $ form the standard basis for T(0,1)(Hn ). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
An unknotting theorem for delta and sharp edge‐homotopy
Authors: Nikkuni Ryo
Published: May 2007

Two spatial embeddings of a graph are said to be delta (resp. sharp) edge‐homotopic if they are transformed into each other by self delta (resp. sharp) moves and ambient isotopies. We show that any two spatial embeddings of a graph are delta (resp. sharp) edge‐homotopic if and only if the graph does not contain a subgraph which is homeomorphic to the theta graph or the disjoint union of two 1‐spheres, or equivalently G is homeomorphic to a bouquet. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
Positive sharp wave origin: Evidence supporting the electrode initiation hypothesis
Authors: Dumitru Daniel , Maria Daniel L. Santa
Published: May 2007

This investigation analyzes the temporal characteristics of maximal depolarization times for three waveforms: end‐plate spikes, fibrillation potentials, and positive sharp waves (PSWs) to provide support for the electrode initiation hypothesis of PSW induction. The maximal depolarization times for PSWs are documented to comprise two distinct populations conforming to relatively short and comparatively longer maximal depolarization times. Those PSWs with short maximal depolarization times were found to be equivalent to end‐plate spike maximal depolarization times, whereas those with longer times were comparable to fibrillation potentials. The PSW group with shorter maximal depolarization times was encountered more frequently. The combination of two distinct groups of PSWs with respective times comparable to end‐plate spikes and fibrillation potentials supports the hypothesis that the majority of PSWs originate at the recording electrode during insertion, whereas a smaller population of PSWs arises as propagating fibrillation potentials that block at the recording electrode. Subcutaneous compared to intramuscular recordings from denervated muscle document that the recording electrode is necessary to both record and produce PSWs. Hence, this study confirms the proposed hypothesis that the majority of observed PSWs represent a suprathreshold single muscle‐fiber discharge induced by, and originating in close proximity to, a perielectrode crushed membrane that then propagate away from the electrode; a smaller population of PSWs conform to that of a blocked fibrillation potential. Muscle Nerve, 2007
Linear programming in bid evaluation
Authors: Stanley E. D. , Honig D. P. , Gainen Leon
Published: May 2007

This paper presents the difficulties which arise in a particular Government procurement agency in an attempt to determine the allocation of contracts which would result in the lowest over‐all cost to the Government. It is shown how the recently developed mathematical discipline of linear programming can be applied to such problems.
Confidence intervals of preassigned length for quantiles of unimodal populations
Authors: Weiss Lionel
Published: May 2007

For the case he the only information we have about a population is that it has a unimodal density function, a two‐sample method is given for constructing a confidence interval of preassigned length for any quantile of the population.
Programming the supply of a strategic material. Part I. A Nonstochastic Model
Authors: Karreman Herman F.
Published: May 2007

This paper deals with the various ways in which the requirements of a certain strategic material could be met in a period of limited war. Besides a small stock of ores to draw on at the beginning of the period, high‐quality foreign ores have to be imported or low‐quality domestic ores made suitable for the production of alloys. In the latter case, however, the plants for upgrading and processing the ores first have to be constructed. The objective is to meet the requirements, assumed here to be given for the years of limited war, at minimum cost. The cost function contains, besides linear, also quadratic terms, positive as well as negative ones. Two recently developed computational methods have been used to solve the problem.
The marriage of on‐line human decision with computer programs
Authors: Teager Herbert M.
Published: May 2007

As the logistics problems of current interest become more and more complex, it becomes apparent that heuristic methods hold more promise than exhaustive or algorithmic methods of solution. It is also becoming clearer that heuristics, per se, are useless in approaching large combinatorial problems (via pattern recognition, for example), unless some general techniques are developed to draw out the specific “best” heuristics required for each problem. It is a fact that humans are, at present, far more efficient in developing and applying such heuristics than a machine. It is therefore of considerable value to explore how the best features of both human and machine decision can be married. The general problem requires the development of common meaningful languages, specialized input‐output display and entry facilities, and a means of time‐sharing the computer, in order to efficiently match the machine‐vs the human‐decision time.
The use of man‐machine simulation for support planning
Authors: Geisler Murray A.
Published: May 2007

Support planning under present conditions of rapid exploitation of technological advances to maintain the most advanced weapon inventory creates many new stresses for planning the support of these new weapons. In addition, support planning has always been incomplete in that there has not been a systematic way of adjusting plans to reflect operational experience.

The second major experiment of the RAND Logistics Systems Laboratory has produced techniques of support planning for new weapons which may represent major advances in such activities. This paper describes the conditions under which support planning must be performed in the present and future military environment and the experience of LP‐II in performing such planning for an ICBM weapon of the 1963–65 time period, as an example.
On‐line macro‐simulation in systems for logistics decision making
Authors: Dresch Francis
Published: May 2007

Macro‐simulation has three types of application:

1. Computer experimentation with simplified models of complex systems to explore the systems' sensitivity to variation in environmental parameters or changes in controllable decision variables. This use of macro‐simulation facilitates analysis of the realism of the various models as well as determination of optimal strategies.

2. Pilot testing of complex decision systems against a detailed quantitative description of the real operating environment as observed in the past.

3. Continuing on‐line simulation of a system over a future planning period to determine optimal levels or settings for current decision variables or to provide measures of effectiveness for feedback and control.

While the first two applications are most familiar and are most frequent, the third application may have increasing importance in the future. The reasons for this will be discussed with illustrations from work at Stanford Research Institute on stock level policy and on air logistics. All three applications of macro‐simulation techniques have proved important in this work.
A comparative study of prediction techniques
Authors: Brown Bernice
Published: May 2007

This study deals with the techniques for predicting the future demands of spare parts. The results of studies about the Air Force Inventory problem have led us to believe that any improvement in the demand forecast could result in important savings. Demand prediction is actually based upon two separate estimating procedures. First, an estimate is made about the underlying pattern of demands per program element, Second, an estimate is made about the pattern of future program elements. It is the marriage of these two estimates that allows us to make predictions of the number of demands in future time periods. This study is restricted to finding ways of improving the estimates of the demands per program element, We used past demand data with the pattern of program elements known. We also used the known pattern of future program elements to make the prediction of future demand.

There are seven prediction techniques used in this study. The first four techniques are based on the assumption that demand rate (demand per program element) is constant through time. The other three techniques assume that failures (demands) are related to the age of the part. These three techniques are routines for estimating the service Life characteristics of parts.

We used as inputs to the study two batches of data: 33 months of demand, data on a sample of 300 B‐52 parts and 26 months of failures of 27 missile components. We made monthly estimates of demand for a year in the future and measured the prediction errors. In the evaluation of the estimating procedures, we used three measures of the accuracy of the forecasts, namely average monthly error, relative error expressed as percent of the actual demand and root mean square of the errors of the predictions.
Militlry worth and systems development
Authors: Folsom P. L.
Published: May 2007

This is an unclassified treatment of some problems in military worth which arise in the development of large systems. Recent studies in measures of effectiveness and value theory have been used to define this part of the discussion. Although the discussion will have points in common with many “large” systems, the model used in this discussion is a typical real‐time digital data system for executive use. Factors and constraints such as fund limits, pricing, service life, lead time and environment are treated. A typical practical attack on the problem of measuring the military worth of such a system is included. Most systems in this class have not yet accumulated sufficient life in service for measurement and determination of results of plans to “maximize” their military worth. Accordingly, this part of the discussion is restricted to some suggestions concerning defining and measuring military worth of these systems.
The determination and use of military‐worth measurements for inventory systems
Authors: Solomon Henry
Published: May 2007

In this paper an attempt is made to emphasize the significance of military worth measurements for inventory problems and to point to such measurements which are presently available. The general results and implications of these measurements are discussed.
Investment policies for expanding businesses optimal in a long‐run sense
Authors: Breiman Leo
Published: May 2007

An entrepeneur has a given initial fortune and faces the following situation: during any time period he may invest various amounts of his available fortune in various alternatives (differing from interval to interval) and keep the remainder of his money as a reserve fund; The alternatives materialize and pay off according to a probability distribution in which occurrences in different time intervals are independent. We analyze the problem of finding the investment policies (that is, the division of funds during every time interval between the investment alternatives and the reserve) that will make the long‐run growth of the entrepeneur's fortune as rapid as possible.
Principles of dynamic weapon systems programming
Authors: Salveson M. E.
Published: May 2007

Over the last several years, there has been considerable interest in the problems of effective programming, decision‐making, and progress evaluation, in the development and production of weapon systems. The need for solving these problems was great when budget ceilings were less restrictive. At the present time when budgets are more stringent, the need is indeed urgent if defense is to be most adequate. The principles and methods described in this article were developed as guides to the development and installation of a management system for programming, decision‐making, and progress evaluation in weapon systems development, procurement, and production in the U. S. Air Force. The principles, however, have applicability to programming, decision‐making, and control in other governmental and in industrial and business organizations. Some of these principles and methods already have been applied in other situations; some are new. However, the amount that is new is relatively small; we are confident the system is feasible and economic within the existing state of the art, and that it would contribute to efficiency in the development and production of weapon systems.
The organization and operation of a taxi fleet
Authors: Meyer Richard F. , Wolfe Harry B.
Published: May 2007

In dispatching a taxi fleet to meet random customer demand, two types of strategies must be defined: (a) the dispatching strategy, which sets the rules for choosing a taxi to serve a given call, and (b) the idle time strategy, which determines how the idle taxis are to be distributed most advantageously to meet future demand. The effect of dispatching and idle‐time strategies on taxi utilization and on passenger service is demonstrated under several conditions of operation. First, the simples taxi model is examined: random demand between two points serviced by one taxi. Next, we consider the effect of different strategies on the operation of a taxi fleet when demand is uniformly distributed in a two‐dimensional region. In the last section, the main properties of these simplified models are exhibited in an intermediate case by a Monte Carlo simulation of taxi service between a number of discrete points. The purpose of the paper is to provide simple and practical methods to determine the payoff in customer waiting time and/or taxi savings resulting from more sophisticated dispatching and idle‐time strategies. We conclude that good taxi redistribution policies markedly decrease customer waiting times, except when the level of taxi utilization is too high. Our results apply most directly to private transportation fleets, rather than to automobile taxi companies where cruising may be important.
On network flow functions
Authors: Shapley Lloyd S.
Published: May 2007

This article covers an investigation of the capacity of a network as a function of the capacities of its individual arcs. The case of two variables was investigated in detail, and it was found that each pair of arcs either consistently help each other or consistently hinder each other. Interaction types were computed for a number of special cases, such as arcs in parallel or arcs in series.
A direct method for the computation of waiting times
Authors: Lombardi Lionello
Published: May 2007

A recurrence relation for the direct computation of the waiting times of an array of c customers served by s parallel channels on a first come first served basis, where the time of arrival and the holding time of each customer are known, is worked out. The number of operations required by this procedure is proportional to c.s, while the method commonly used, which is due to F. Pollaczek, requires a number of operations proportional to c2. In (c): this improvement is obtained by means of the adoption of sorting by insertion and by saving certain intermediate results.
“Hedging” on statetical assumptions
Authors: Weiss Lionel
Published: May 2007

It is pointed out that in many cases statistical assumptions, such as the assumption of a normal population, really cannot be known to be true with the absolute certainty that the word “assumption” has come to imply. In fact, in some instances data collected for purposes other than testing the assumptions cast serious doubt on the validity of the assumptions. A simple safety or hedging device is proposed, and illustrated for the case where the problem is to estimate the qth quantile (m, say) of a distribution assumed to be normal with given standard deviation σ. Let X, R denote the sample mean and the qth sample quantile, respectively. Under the assumption, the best estimate of m is X + t σ, where t is a properly chosen constant, while R is a reasonable estimate of m even if the assumption is not true. The hedging device is to use X + t σ as the estimate if |X + t σ – R| ≤ d, and to use R as the estimate if || + t σ – R| > d, where d is a preassigned value. In order to choose d to reflect our faith in the validity of the assumption, and to obtain the operating characteristics of our estimation rule, it is necessary to know the joint distribution of X and R. This is shown to approach a bivariate normal distribution as the sample size increases, for any population satisfying mild regularity conditions.
Budget constraints in logistics models
Authors: Hadley G. , Whitin T. M.
Published: May 2007

In application of operations research models in the area of logistics, important constraints are typically encountered in the form of limitations on the funds appropriated. A supply system must be operated within whatever budgeted funds are appropriated by Congress. In the present article, various possible types of budget constraints are discussed as well as their impact on certain types of operations research models. The possible misallocations that can result from the setting of specific budgets designated for particular purposes are discussed. The confusion existing in the literature concerning the type of constraints that are actually encountered versus those that are imposed upon the mathematical models is pointed out as well as the typical inconsistency of budget constraints and steady‐state models. The difference between a steady‐state budget and a transition‐phase budget is clarified.
Lognormal distribution and maintainability in support systems research
Authors: Bovaird R. L. , Zagor H. L.
Published: May 2007

This article presents a method for predicting the downtime distribution for a new complex electronic equipment. A theoretical discussion is given which indicates that the downtime distribution for such an equipment can be represented by a lognormal function. Experimental data are shown which establish that the two‐parameter lognormal distribution function adequately describes the downtimes of a diverse group of electronic equipments. It is concluded that this analytical expression for the downtime distribution of complex electronic equipments provides the basis for a quantitative and scientific approach to the measurement and prediction of maintainability. This approach takes account of equipment maintenance characteristics and maintenance personnel capabilities.
A model for procurement, allocation, and redistribution for low demand items
Authors: Hadley G. , Whitin T. M.
Published: May 2007

Problems of inventory control for items with extremely low demand (say less than one unit per month average demand) have received relatively little attention in the literature. However, for military supply systems it is well known that an extremely large proportion of the total number of items fall into this category. The problem of designing a control system for these low demand items is therefore one of the most critical inventory management problems faced by the National Military Establishment.

In the following, a single echelon, multidepot supply system is studied for low demand items having a stationary Poisson probability distribution for demand. Instantaneous information concerning inventory levels is assumed to be available. Procurement lead time is assumed to be constant as well as the time required for either of two available modes of redistribution. Items are ordered one at a time and decision rules are developed for allocation of new procurement, redistribution of stocks among the depots, and for determining system and depot stockage objectives in order to minimize the expected costs resulting from system and depot stockouts, cost of redistributing stocks among the depots, and costs of transportation from the source. The model is an extension of previous models in that redistribution costs and depot stockout costs are considered in the determination of the stockage objective for the system as a whole. When more than a single unit is on order, the allocation of a unit ready to be delivered is determined by the solution of a dynamic programming problem. When only a single unit is on order (and this is the one ready to be delivered), the optimal allocation procedure is reduced to allocating the unit to the depot which has the greatest probability of using it in a time period T + (1/λ) where T is the procurement lead time and λ the system demand rate for the item.
Multiship, multishop, workload‐smoothing progfum
Authors: Levy F. K. , Thompson G. L. , Wiest J. D.
Published: May 2007

This paper describes a computer program that uses simple rules and applies them probabilistically to minimize manpower requirements in shops of a naval shipyard. Preliminary runs on a small fictitious problem show that this “multiship, multishop, workload‐smoothing” program, called (MS)2, may be able to reduce the maximum number of men required on any one day by 30 to 60 percent.

The program employs the critical path method of analyzing the jobs to be done on a given project (ship) and begins by assigning all jobs at their earliest possible start time. Then suitable jobs on peak workload days are selected at random and shifted to later days beyond the peak days until further shifting no longer reduces peak loads. The first segment of the program smooths the workloads on all shops simultaneously. After the first segment is completed the second segment performs further smoothing on individual shops, beginning with the most expensive shop.

Although a limited amount of experience has been gained with this program, it appears likely that it can be developed further so that it can handle realistic‐sized problems such as those encountered in a Naval Shipyard. Moreover, it can be applied on three levels: (1) smoothing shop workloads in a shipyard; (2) smoothing the workloads of individual shops; and (3) smoothing shipyard workloads.
Analytical study of a problem in air defense
Authors: Mohan C. , Arora K. L.
Published: May 2007

This paper deals with the analytical study of the encounter of fighter interceptors with the incoming formation of an air task force of enemy bombers. An attempt is made to frame a stochastic model of the situation and to determine the probabilities of hit under different conditions. It is indicated that with reasonable estimates of the operational parameters involved the various probabilities are capable of optimization.
A model for the analysis of aew and cap aircraft availability
Authors: Collins F. I. , Guthrie D.
Published: May 2007

As a carrier taskforce proceeds into an operating area it becomes necessary to launch Anti‐Air Warfare (AAW) aircraft, including Airborne Early Warning (AEW) and possibly Combat Air Patrol (CAP) units. The number of aircraft launched depends on the degree of AAW coverage desired, the time period to be covered, and the availability of aircraft. The principal factors determining the availability of aircraft for such employment are the composition of the aircraft complement and the adequacy of the maintenance facilities. This paper presents an analytical model describing the maintenance operation aboard an aircraft carrier. The model is sufficiently general to permit the evaluation of a wide variety of aircraft types and employment schemes. The model was applied to determining: (1) the maximum feasible airborne complement of AEW and CAP aircraft; and (2) the effect of various intra‐carrier and intercarrier cycling operations in task forces containing more than one carrier. For each of these two examples, the output of the model is a probability distribution of the number of a given type of aircraft that are airborne as a function of time in the operating area. A maximum feasible airborne complement is obtained by assuring that the probability that the full complement is maintained remains about a given standard over the period of the operation. The effect of inter‐carrier coordination is measured by the size of the maximum feasible airborne complement under various situations. Other applications for which the model would be useful are the measurement of sensitivity of AAW aircraft availability to variations on the parameters of maintenance process, and the evaluation of the effect of maintenance limitations of the AAW coverage as requirements increase during the later stages of an operation.
Queuing with reneging and multiple heterogeneous servers
Authors: Ancker C. J. , Cafarian A. V.
Published: May 2007

A Poisson stream of items arrive at a multiple parallel serving facility consisting of s heterogeneous servers. The service time density functions are all negative exponential and may all have different means. An arrival balks (refuses to enter) if the queue size is equal to N. If the queue size is less than N, the arrival enters the queue and is served on a first‐come, first‐served basis unless it reneges (leaves the queue). Each entering item has a definite length of time it will wait in queue before reneging. This time is a random variable with negative exponential density function. If on arrival more than one server is free, the server to be used is chosen at random. The results obtained are for steady‐state and include (1) state probabilities; (2) the probability of j or more in system, j=s, s+I,…, s+N; (3) mean number in queue and system and mean number of busy servers; (4) probability that an arrival acquires service; (5) mean rate of loss due to balking and reneging; and (6) density functions and mean values of waiting times in queue for those who are served, those who renege, and all who enter. Certain important special cases are derived from the preceding, namely, (1) unbounded queues, (2) homogeneous servers, (3) no reneging, (4) no reneging and unbounded queues, and (5) single server. Finally, a comparison is made of a heterogeneous system with an equivalent homogeneous system.
A note on a role of intelligence analysis in logistics operations research
Authors: Andrews Robert A.
Published: May 2007

An illustration is provided of an effective use of intelligence analysis in logistics support studies as a contributing discipline in problems susceptible to solution by operations research techniques. Further, it is suggested that application of intelligence analysis might be profitable to other support activities when examining hardware consumption in the environments imposed by area contingency plans.
Equivalence in nonlinear programming
Authors: Mangasarian O. L.
Published: May 2007

The purpose of this work is to show the relation between the Kuhn‐Tucker and the gradient‐projection conditions for constrained maximization (minimization) problems. A similar relationship exists between Kuhn‐Tucker‐type conditions and gradient‐projection‐type conditions for certain constrained saddle‐point problems. This latter relationship may lead to a computational algorithm for these constrained saddle‐point problems.
Minimax surveillance schedules with partial information
Authors: Roeloffs Robert
Published: May 2007

An analysis is made of the problem of finding the optimal schedule for checking an operating system which is subject to failure detectable only by inspection of the system. If a cost is attached to each inspection of the system and also to undetected failure, then there exists the problem of scheduling inspections to minimize total costs. This problem also exists for the surveillance inspection of stored goods subject to deterioration with time.

Previous work by Barlow and Hunter gives the optimal schedules for two special cases — when the failure distribution of the units is known to be exponential, and when it is known to be uniform. Derman has obtained the minimax schedule, that is, the schedule which minimizes the maximum possible expected cost for the case where the failure distribution is entirely unknown.

This paper assumes that the location of one percentile of the failure distribution of the units is known, and is concerned with the optimal use of this partial information. The minimax schedule is obtained for the case where the operation is to continue until either a failure is detected, or a stipulated time has elapsed, and comparisons are made with Derman' s results for an unknown distribution.
Surveillance problems: Wiener processes
Authors: Antelman Gordon R. , Savage I. Richard
Published: May 2007

This paper extends the results presented by I. R. Savage in a previous paper [8]. That paper studied economically optimal policies for inspecting and repairing production processes which behave as Poisson processes. Similar results are presented here for production processes which behave as Wiener processes.

With continuous surveillance, methods are presented which permit the computation of exactly optimal strategies and the optimal income per unit of time. With costly surveillance, a functional equation is presented. The solution of this equation would yield the optimal strategy. Explicit solutions do not seem feasible but many qualitative properties of the solutions are found. The most interesting of these says, roughly (see Proposition 12 for exact statement), that the time between inspections decreases as the observed quality decreases.
A “static” solution to a “dynamic” problem in acquisition probability
Authors: Rasof Bernard , Abrams Leonard S.
Published: May 2007

This paper reports a novel solution to a special case of a classical problem in operations research, “The probability that an acoustic homing torpedo will ‘acquire’ a submarine”. Because of uncertainties in the position of submarine relative to torpedo an exact kinematic solution to the problem is not possible, and only a probabilistic solution may be obtained. The complicated realistic problem is idealized here to a tractable model by a small number of simplifications; later the effect of removing these simplifications one at a time is examined, and it is made plausible that each has only a small influence on the acquisition probability. As an illustration of the application of the concepts developed, an example in which the submarine is assumed to move radially outward from the torpedo –‐ but otherwise incorporating reasonable assumptions about the kinematics of the torpedo and submarine –‐ is completely solved in detail. In this example the uncertain position of the submarine is given by simple frequency distributions; a more complicated case could be solved by numerical methods. The solution of this specialized problem is particularly interesting because of the immediate and unexpected operational research results which may be inferred.
A statistical study of the derailment hazard for U.S. class I railways
Authors: Koopmans L. H.
Published: May 2007

A simple probabilistic model is proposed for the collision and derailment experience for freight trains of U.S. Class I railways. By means of this model, asymptotic confidence intervals are constructed for the probability per mile of a derailment accident as a function of train speed and train length which utilize data available from records for U.S. Class I railways kept by the Interstate Commerce Commission and the Association of American Railroads [l]. Allowance is made in the model for the grouping of data by train length and speed.

The theory is applied to a particular summary of accident data for all U.S. Class I railways for the years 1952 through 1955. On the basis of this data, confidence intervals for the derailment probability are computed for speeds in excess of 10 mph and train lengths of from 11 to 130 cars in groups of 5 cars. In addition, a statistical test of one of the more crucial model hypotheses is performed.

An appendix containing the relevant derivations is included. In particular, a new version of a theorem of Slutsky due to LeCam is stated which greatly facilitates the derivations of the asymptotic distributions for the estimates of the derailment probabilities and the statistic employed in the above mentioned hypothesis test.
A theater materiel model
Authors: Bracken J. , Brossman M. W. , Magruder C. B. , Tholen A. D.
Published: May 2007

This paper summarizes a theater‐level materiel model which has been developed for the Army as a part of a system for gaming or simulating the military aspects of theater, inter‐theater and continental United States (CONUS) logistics.

For purposes of military analysis and computational convenience, the theater under study is divided into geographical subdivisions (i.e., regions) and the military operation is divided into a succession of time periods of specified length. The model operates through one complete cycle for each time period.

A cycle starts with the actual materiel status at the beginning of the period in the theater and in each region. (Depending on the problem presented, the “actual materiel status” at the beginning of the period can be either the actual status now pertaining or one that is assumed for the purpose of the problem.) The model applies changes that take place during the period and computes the actual materiel status at the end of the period for the theater and for each region. Authorized materiel status at the end of the period is computed for the theater and for each region, The authorized materiel status is compared with the actual materiel status and the imbalances are computed.

The model forecasts the materiel expected to be consumed in the next period in the theater and in each region. It determines the materiel movements by source and destination which should take place in the next time period to correct the imbalances from the preceding time period and provide whatever replacement is necessary for meeting forecasted consumption in the next time period so as to leave each region with its authorized stockage at the end of the next period.

Requisitions for materiel to arrive in the order and shipping time are computed using forecasts of consumption and receipts. This completes the cycle.

The model described in this paper has been programmed and utilized in war games for the Department of Army and in a special study for the Department of Defense. It should be useful for a wide range of applications, including developing logistic constraints in combat games, and designing and evaluating logistic systems.
The formulation of some allocation and connection problems as integer programs
Authors: Breuer Melvin A.
Published: May 2007

In this paper a component placement problem and a digital computer backboard wiring problem are formulated as integer linear programs. The component placement problem consists of making a unique assignment of components to column positions such that wireability is maximized. The backboard wiring problem consists of three interrelated subproblems, namely, the placement, the connection, and the routing problems. The placement and connection problems are combined and solved as one, thereby giving the optimal circuit connections as well as minimizing the total lead length. It is shown that under certain assumptions, the number of inequalities and variables in the problem can be greatly reduced. Further simplifying assumptions lead to a near optimal solution.

Examples of other allocation problems to which the models presented here are applicable are given.

The following concepts are formulated as linear inequalities: (1) the absolute magnitude of the difference between two variables; (2) minimize the minimum function of a set of functions; and (3) counting the number of (0, 1) adjacent component pairs in a vector.
Some test functions for the parameters of the weibull distributions
Authors: Dubey Satya D.
Published: May 2007

Test functions, based on various types of censored and noncensored data, for testing several hypotheses about the location, the scale, and the shape parameters of the Weibull distributions are proposed. The exact sampling distributions of these test statistics are derived and their properties in special cases are discussed. A numerical example is considered to illustrate the application of the test functions. The results of this paper possess good possibility of wide application in view of the fact that hosts of real data arising from diverse fields of human endeavor are adequately described by the Weibull distribution.
Values for optimum reject allowances
Authors: Delfausse J. , Saltzman S.
Published: May 2007

Industrial situations exist where it is necessary to estimate the optimum number of parts to start through a manufacturing process in order to obtain a given number of completed good items. The solution to this problem is not straightforward when the expected number of rejects from the process is a random variable and when there are alternative penalties associated with producing too many or too few items. This paper discusses various aspects of this problem as well as some of the proposed solutions to it. In addition, tables of optimum reject allowances based on a comprehensive model are presented.
A bibliography of search theory and reconnaissance theory literature
Authors: Enslow Philip H.
Published: May 2007

This bibliography consists of 75 items on search theory and reconnaissance theory found in periodicals and technical reports. Each entry includes a short summary or a quotation from the pertinent abstract. The items are classified into one or more of the following categories: (1) General Discussion of Problems; (2) Allocation of Effort; (3) Game Theory Formulations; (4) Geometric Search Patterns; (5) Measures of Performance and (6) Miscellaneous.
Statistical decision analysis of stochastic linear programming problems
Authors: Bracken Jerome , Soland Richard M.
Published: May 2007

This paper presents a statistical decision analysis of a one‐stage linear programming problem with deterministic constraints and stochastic criterion function. Procedures for obtaining numerical results are given which are applicable to any problem having this general form. We begin by stating the statistical decision problems to be considered, and then discuss the expected value of perfect information and the expected value of sample information. In obtaining these quantities, use is made of the distribution of the optimal value of the linear programming problem with stochastic criterion function, and so we discuss Monte Carlo and numerical integration procedures for estimating the mean of this distribution. The case in which the random criterion vector has a multivariate Normal distribution is discussed separately, and more detailed methods are offered. We discuss dual problems, including some relationships of this work with other work in probabilistic linear programming. An example is given in Appendix A showing application of the methods to a sample problem. In Appendix B we consider the accuracy of a procedure for approximating the expected value of information.
A tactical warfare simulation program
Authors: Fain W. W. , Fain Janice B. , Karr H. W.
Published: May 2007

The Tactical Warfare Simulation Program is a procedure by which the major interactions among opposing military units and terrain features can be treated in a tactical limited warfare situation. It is a critical‐area, sequence‐of‐event model and is programmed in SIM‐SCRIPT.

In this program a military unit is described by such properties as strength, size, location, velocity, and attrition rates. Some of the events which can occur to a military unit are entering/leaving terrain features, becoming engaged/disengaged with opposing units, retreating, reaching an objective, and breaking. Following a discussion of the general features of the program, a study of a hypothetical war is presented.
Additive utilities with finite sets: Applications in the management sciences
Authors: Fishburn Peter C.
Published: May 2007

A theory of additive utilities is discussed for cases where the set X, on which an individual's preference‐indifference relation is defined, is a subset of the Cartesian product of n finite sets. A number of potential applications of additive utilities in decision making are presented.
Solutions for a class of n‐person games in partition function form
Authors: Lucas W. F.
Published: May 2007

A unique polyhedral solution is given for most n‐person games in partition function form when only partitions into coalitions with 1, n‐1, and n players have large payoffs.
Some rectangular games with a two‐man team
Authors: Jackson James R.
Published: May 2007

Certain zero‐sum games are examined in which an individual player is opposed by a two‐man team. The members of the team have identical interests, but must act separately during play. Most of the paper is devoted to instances in which one teammate has an opportunity to communicate to the other about their mutual opponent's strategy; but he may only be able to transmit a limited amount of information and his choice of a “message” may affect the payoff. The team must thus make economically efficient use of a limited communication opportunity. The present paper treats a variety of models, all of which are formulated as rectangular (matrix) games. Related models, some of which cannot be so formulated either because of restrictions on the team's opportunities to use mixed strategies or because they are non‐zero‐sum games, will be treated in another paper.
A queuing process with bilevel hysteretic service‐rate control
Authors: Gebhard Richard F.
Published: May 2007

The purpose of this paper is to analyze the effect of a particular control doctrine applied to the service mechanism of a queuing process. A bilevel hysteretic control based on queue length control levels is employed in an M/M/1 queuing system. Expressions are obtained for queue length probabilities, the first two factorial moments of queue length and two figures of merit for describing control performance under the assumption of statistical equilibrium. Computational examples illustrate the effects on queuing processes subject to this type of control. Several cost formulae are considered for comparison of costs when the queue control doctrine is varied. Situations in which hysteretic control is useful are discussed.
Normal and weibull distributions
Authors: Dubey Sat Ya D.
Published: May 2007

Numerous applications of the Weibull distribution in diverse fields of human endeavor are well known today. Nevertheless, it is not uncommon to find applications of the normal distribution in such fields of studies as agriculture, biology, chemistry, engineering, physics, sociology and others. At the present time we have at our disposal many more refined statistical techniques for analyzing the normal rather than the Weibull data. Consequently, it is important for applied statisticians to know if some of their data which can be described by the Weibull distribution can also be described by the normal distribution. The present investigation of the author reveals that the normal distri,bution can be considered to be a good approximation to the Weibull distribution as long as its shape parameter is in the open interval (3.25, 3.61). This fact enables them to perform a refined statistical analysis of their data. Conversely, they can now easily compute the desired normal cumulative probabilities from the Weibull distribution function, which would be especially helpful for those standard normal deviates whose cumulative probabilities cannot be read from the available tables of normal cumulative probability. In a similar situation they can also use the Weibull distribution to obtain an approximation to any desired normal deviate for a given normal probability which may be better than those obtained by the linear interpolation method.