bluuebunny/crossref_metadata_2025_split huggingface dataset:
Quadratic programming with quadratic constraints
Authors: Baron David P. 
Published: May 2007

AbstractA program with a quadratic objective function and quadratic constraints is considered. Two duals to such programs are provided, and an algorithm is presented based upon approximations to the duals. The algorithm consists of a sequence of linear programs and programs involving the optimization of a quadratic function either unconstrained or constrained to the nonnegative orthant. An example involving production planning is presented.
A duel complicated by false targets and uncertainty as to opponent type
Authors: Sweat Calvin W. 
Published: May 2007

AbstractAn attacker, being one of two types, initiates an attack at some time in the interval [‐T, 0]. The a priori probabilities of each type are known. As time elapses the defender encounters false targets which occur according to a known Poisson process and which can be properly classified with known probability. The detection and classification probabilities for each type attacker are given. If the defender responds with a weapon at the time of attack, he survives with a probability which depends on the number of weapons in his possession and on attacker type. If he does not respond, his survival probability is smaller. These probabilities are known, as well as the current number of weapons in the defender's possession. They decrease as the number of weapons decreases. The payoff is the defender's survival probability.An iterative system of first‐order differential equations is derived whose unique solution V1(t),V2(t),…,Vk(t) is shown to be the value of the game at time t, when the defender has 1, 2,…, k,… weapons, respectively. The optimal strategies are determined. Limiting results are obtained as t→‐∞, while the ratio of the number of weapons to the expected number of false targets remaining is held constant.
Mathematical control theory solution of an interactive accounting flows model
Authors: Ijiri Yuji , Thompson Gerald L. 
Published: May 2007

AbstractIn this paper we have applied the mathematical control theory to the accounting network flows, where the flow rates are constrained by linear inequalities. The optimal control policy is of the “generalized bang‐bang” variety which is obtained by solving at each instant in time a linear programming problem whose objective function parameters are determined by the “switching function” which is derived from the Hamiltonian function. The interpretation of the adjoint variables of the control problem and the dual evaluators of the linear programming problem demonstrates an interesting interaction of the cross section phase of the problem, which is characterized by linear programming, and the dynamic phase of the problem, which is characterized by control theory.
Statistical auditing of large‐scale management information systems
Authors: Haber Sheldon E. , Segel Frank W. , Solomon Henry 
Published: May 2007

AbstractIn recent years many large government and commercial organizations have developed large‐scale management information systems. During the early phases of any system development, questions are likely to be raised concerning the criteria of completeness and accuracy of the data. How to respond to these questions is difficult, and represents the general subject of this paper. In particular, this paper describes the application of statistical techniques, namely, various kinds of multivariate data analysis, to the problem of assessing the quality of a large‐scale data collection system in the U. S. Navy. Results of using these techniques are described and indicate their usefulness as auditing procedures. While the discussion is placed in a particular context, the procedures should be of value for other large‐scale information systems.
On optimal assembly of systems
Authors: Derman Cyrus , Lieberman Gerald J. , Ross Sheldon M. 
Published: May 2007

AbstractWe are concerned with the following reliability problem: A system has k different types of components. Associated with each component is a numerical value. Let {aj}, (j= 1,…,k), denote the set of numerical values of the k components. Let R(a1,…, ak) denote the probability that the system will perform satisfactorily (i. e., R(a1,…. ak) is the reliability of the system) and assume R(a1,…,ak) has the properties of a joint cumulative distribution function.Now suppose aj1 ≤… ≤ ajn are n components of type j (j= 1,…, k). Then n systems can be assembled from these components. Let N denote the number of systems that perform satisfactorily. N is a random variable whose distribution will depend on the way the n systems are assembled. Of all different ways in which the n systems can be assembled, the paper shows that EN is maximized if these n systems have reliability R(a1j,…, akj) (i = 1,…,n). The method used here is an extension of a well known result of Hardy, Littlewood, and Polya on sums of products. Furthermore, under certain conditions, the same assembly that maximizes EN minimizes the variance of N.Finally, for a similar problem in reliability, it is shown that for a series system a construction can be found that not only maximizes the expected number of functioning modules, but also possesses the stronger property of maximizing the probability that the number of functioning modules is at least r, for each 0 ≤ r ≤ n.
An informal survey of multi‐echelon inventory theory
Authors: Clark Andrew J. 
Published: May 2007

AbstractContained herein is an informal nonmathematical survey of research in multi‐echelon inventory theory covering published results through 1971. An introductory section defines the term, “multi‐echelon,” and establishes the kinds of problems involving multi‐echelon considerations. Subsequent sections provide surveys of research on deterministic and stochastic multi‐echelon inventory control problems, allocation models, and multi‐echelon planning and evaluation models. A final section discusses the present state of the art and suggests directions for future research. A bibliography of papers concerning multi‐echelon inventory theory and applications is included.
Minimal disconnecting sets in directed multi‐commodity networks
Authors: Jarvis John J. , Tindall John B. 
Published: May 2007

AbstractThe problem of finding minimal disconnecting sets for multi‐commodity directed networks may be solved using an arc‐path formulation and Gomory's all‐integer integer programming algorithm. However, the number of network constraints may be astronomical for even moderately sized networks. This paper develops a finite algorithm similar to Gomory's, but requiring no more than m rows in the tableau, where m is the number of arcs in the network.
An optimum t‐test for the scale parameter of an extreme‐value distribution
Authors: Chan Lai K. , Cheng S. W. H. , Mead E. R. 
Published: May 2007

AbstractA Student's t‐test proposed by Ogawa is considered for the hypothesis Ho: σ=σo against the alternative hypothesis H1: σ ≠ σo, where σ is the scale parameter of the Extremevalue distribution of smallest values with known location parameter μ. The test is based on a few sample quantiles chosen from a large sample so as to give asymptotically maximum power to the test when the number of sample quantiles is fixed. A table which facilitates the computation of the test statistic is given. Several schemes for determining the ranks of the sample quantiles by the optimal spacings are compared and the effect of the bias of the estimate of σ on the test is investigated through a Monte Carlo study.
Scheduling jobs, with exponentially distributed processing times, on two machines of a flow shop
Authors: Cunningham Andrew A. , Dutta Sujit K. 
Published: May 2007

AbstractThis paper treats the problem of sequencing n jobs on two machines in a “flow shop.” (That is, each job in the shop is required to flow through the same sequence of the machines.) The processing time of a given job on a given machine is assumed to be distributed exponentially, with a known mean. The objective is to minimize the expected job completion time. This paper proves an optimal ordering rule, previously conjectured by Talwar [10]. A formula is also derived through Markov Chain analysis, which evaluates the expected job completion time for any given sequence of the jobs. In addition, the performance of a heuristic rule is discussed in the light of the optimal solution.
Applications of Mills' Differential
Authors: Moeschlin O. , Bol G. 
Published: May 2007

AbstractUsing Mills Differential a game value function ϕ, used in the Kemeny‐Morgenstern‐Thompson growth model to show the existence of solutions, is discussed. In doing so, several proofs become shorter, in addition known results are seen in a new context. Finally connections between the existence of a so‐called economic solution and the differentiability or non‐differentiability of function ϕ are analyzed.
The initial provisioning decision for insurance type items
Authors: Burton Robert W. , Jaquette Stratton C. 
Published: May 2007

AbstractInitial 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.
Determination of the optimal investment in end products and repair resources
Authors: Rose Marshall 
Published: May 2007

AbstractThis paper demonstrates how to determine the minimal cost combination of end products and repair service capability in order to maintain a given level of operating end products. It is shown that the general rule for optimal resource allocation requires simply that the absolute value of the marginal factor cost of repair services divided by the marginal factor cost of end products be equal to the arrival rate of end products to repair. The model is applied to the problem of determining the resources required to support an operating level of Navy F‐4 aircraft.
A cost analysis of sampling inspection under Military Standard 105D
Authors: Brown Gerald G. , Rutemiller Herbert C. 
Published: May 2007

AbstractMilitary Standard 105D has been almost universally adopted by government and private consumers for the lot‐by‐lot sampling inspection of product which may be inspected on a dichotomoun basisThe plan specifies, for each lot size, a random sample size and set of acceptance numbers (maximum allowable number of defectives in each sample). The acceptance numbers are based upon the binomial distribution and depend upon the quality required by the purchaser. Where several consecutive lots are submitted, a shift to less severe (“reduced”) inspection or more severe (“tightened”) inspection is specified when the ongoing quality is very high or low. Further experience permits a return to normal sampling from either of these statesThis paper examines the long range costs of such a sampling scheme. The three inspection types are considered as three distinct Markov chains, with periodic transitions from chain to chain. The expected sample size and the expected proportion of rejected product are determined as a function of the two parameters under control of the manufacturer, lot size and product quality. Some numerical examples are given which illustrate how to compute the overall cost of sampling inspection. Suggestions are made concerning the choice of parameters to minimize this cost.
Optimal ordering policies for a product that perishes in two periods subject to stochastic demand
Authors: Nahmias Steven , Pierskalla William P. 
Published: May 2007

AbstractThis paper considers the problem of computing optimal ordering policies for a product that has a life of exactly two periods when demand is random. Initially costs are charged against runouts (stockouts) and outdating (perishing). By charging outdating costs according to the expected amount of outdating one period into the future, a feasible one period model is constructed. The central theorem deals with the n‐stage dynamic problem and demonstrates the appropriate cost functions are convex in the decision variable and also provides bounds on certain derivatives. The model is then generalized to include ordering and holding costs. The paper is concluded with a discussion of the infinite horizon problem.
A stock redistribution model
Authors: Kaplan Alan J. 
Published: May 2007

AbstractMulti‐depot supply systems are subject to stock distribution imbalances; i. e., the fraction of total system stock located at a depot may be too small to support the fraction of system demand expected to be placed on it. In the supply system of concern, a cutomer is always satisfied if there is stock anywhere in the system. Stock redistributions to correct imbalances may reduce both transportation costs and customer waiting times. A model for determining optimum redistribution quantities is formulated, and a practical method of solution for the two depot case is described. Selected numerical illustrations are given.
The single server queue in discrete time‐numerical analysis II
Authors: Klimko Eugene M. , Neuts Marcel F. 
Published: May 2007

AbstractThis paper deals with the numerical problems arising in the computation of higher order moments of the busy period for certain classical queues of the M|G|I type, both in discrete and in continuous timeThe classical functional equation for the moment generating function of the busy period is used. The higher order derivatives at zero of the moment generating function are computed by repeated use of the classical differentiation formula of Fá di Bruno. Moments of order up to fifty may be computed in this mannerA variety of computational aspects of Fá di Bruno's formula, which may be of use in other areas of application, are also discussed in detail.
An algorithm for separable piecewise convex programming problems
Authors: Soland Richard M. 
Published: May 2007

AbstractWe present a branch and bound algorithm to solve mathematical programming problems of the form: Find x =|(x1,…xn) to minimize Σϕi0(x1) subject to xϵG, l≦x≦L and Σϕi0(x1)≦0, j=1,…,m. With l=(l1,…,ln) and L=(L1,…,Ln), each ϕij is assumed to be lower aemicontinuous and piecewise convex on the finite interval [li.Li]. G is assumed to be a closed convex set. The algorithm solves a finite sequence of convex programming problems; these correspond to successive partitions of the set C={x|l ≦ x ≦L} on the bahis of the piecewise convexity of the problem functions ϕij. Computational considerations are discussed, and an illustrative example is presented.
Sequential determination of inspection epochs for reliability systems with general lifetime distributions
Authors: Zacks S. , Fenske W. J. 
Published: May 2007

AbstractThe problem of determining the optimal inspection epoch is studied for reliability systems in which N components operate in parallel. Lifetime distribution is arbitrary, but known. The optimization is carried with respect to two cost factors: the cost of inspecting a component and the cost of failure. The inspection epochs are determined so that the expected cost of the whole system per time unit per cycle will be minimized. The optimization process depends in the general case on the whole failure history of the system. This dependence is characterized. The cases of Weibull lifetime distributions are elaborated and illustrated numerically. The characteristics of the optimal inspection intervals are studied theoretically.
Production‐allocation scheduling and capacity expansion using network flows under uncertainty
Authors: Prawda Juan 
Published: May 2007

AbstractThis paper extends Connors and Zangwill's work in network flows under uncertainty to the convex costs case. In this paper the extended network flow under uncertainty algorithm is applied to compute N‐period production and delivery schedules of a single commodity in a two‐echelon production‐inventory system with convex costs and low demand items. Given an initial production capacity for N periods, the optimal production and delivery schedules for the entire N periods are characterized by the flows through paths of minimal expected discounted cost in the networkAs a by‐product of this algorithm the multi‐period stochastic version of the parametric budget problem for the two‐echelon production‐inventory system is solved.
The single server queue in discrete time‐numerical analysis III
Authors: Neuts Marcel F. , Klimko Eugene 
Published: May 2007

AbstractThis paper deals with the stationary analysis of the finite, single server queue in discrete time. The following stntionary distributions and other quantities of practical interest are investigated: (1) the joint density of the queue length and the residual service time, (2) the queue length distribution and its mean, (3) the distribution of the residual service time and its mean, (4) the distribution and the expected value of the number of customers lost per unit of time due to saturation of the waiting capacity, (5) the distribution and the mean of the waiting time, (6) the asymptotic distribution of the queue length following departuresThe latter distribution is particularly noteworthy, in view of the substantial difference which exists, in general, between the distributions of the queue lengths at arbitrary points of time and those immediately following departures.
Readiness and the optimal redeployment of resources
Authors: Kaplan Seymour 
Published: May 2007

AbstractThis paper considers the problem of the optimal redeployment of a resource among different geographical locations. Initially, it is assumed that at each location i, i = 1,…, n, the level of availability of the resource is given by a1 ≧ 0. At time t > 0, requirements Rf(t) ≧ 0 are imposed on each location which, in general, will differ from the a1. The resource can be transported from any one location to any other in magnitudes which will depend on t and the distance between these locations. It is assumed that ΣRj > ΣatThe objective function consideis, in addition to transportation costs incurred by reallocation, the degree to which the resource availabilities after redeployment differ from the requirements. We shall associate the unavailabilities at the locations with the unreadiness of the system and discuss the optimal redeployment in terms of the minimization of the following functional forms: \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_{j = 1}^n {kj(Rj - yj) + } $\end{document} transportation costs, Max \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {Max}\limits_j \,[kj(Rj - yj)] + $\end{document} transportation costs, and \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_{j = 1}^n {kj(Rj - yj)^2 + } $\end{document} transportation costs. The variables yj represent the final amount of the resource available at location j. No benefits are assumed to accrue at any location if yj > Rj. A numerical three location example is given and solved for the linear objective.
Target selection in Lanchester combat: Linear‐law attrition process
Authors: Taylor James G. 
Published: May 2007

AbstractWe develop the solution to a simple problem of target selection in Lanchester combat against two enemy force types each of which undergoes a “linear‐law” attrition process. In addition to the Pontryagin maximum principle, the theory of singular extremals is required to solve this problem. Our major contribution is to show how to synthesize the optimal target selection policies from the basic optimality conditions. This solution synthesis methodology is applicable to more general dynamic (tactical) allocation problems. For constant attrition‐rate coefficients we show that whether or not changes can occur in target priorities depends solely on how survivors are valued and is independent of the type of attrition process.
An n‐step, 2‐variable search algorithm for the component placement problem
Authors: Heider Charles H. 
Published: May 2007

AbstractThe component placement problem is a specialization of the quadratic assignment problem that has been extensively studied for a decade and which is of considerable practical value. Recently, interest in component placement algorithms has risen primarily as a result of increased activity in the field of computer‐aided design automation. This paper deals with the methodology of component placement and is based on the results of considerable operational experience. A tutorial presentation of tree search placement algorithms is provided, and an improved placement procedure is described which is demonstrated to be effective in generating near optimal solutions to the component placement problem. These solutions are completely reproducible and are obtained at an acceptable expenditure of computational resources. An additional objective is an assessment of performance of the class of near optimal algorithms. In particular, the question‐ how close to optimal are the near optimal solutions‐ is examined.
Assembly of systems having maximum reliability
Authors: Derman Cyrus , Lieberman Gerald J. , Ross Sheldon M. 
Published: May 2007

AbstractThe first problem considered in this paper is concerned with the assembly of independent components into parallel systems so as to maximize the expected number of systems that perform satisfactorily. Associated with each component is a probability of it performing successfully. It is shown that an optimal assembly is obtained if the reliability of each assembled system can be made equal. If such equality is not attainable, then bounds are given so that the maximum expected number of systems that perform satisfactorily will lie within these stated bounds; the bounds being a function of an arbitrarily chosen assembly. An improvement algorithm is also presented.A second problem treated is concerned with the optimal design of a system. Instead of assembling given units, there is an opportunity to “control” their quality, i.e., the manufacturer is able to fix the probability, p, of a unit performing successfully. However, his resources, are limited so that a constraint is imposed on these probabilities. For (1) series systems, (2) parallel systems, and (3) k out of n systems, results are obtained for finding the optimal p's which maximize the reliability of a single system, and which maximize the expected number of systems that perform satisfactorily out of a total assembly of J systems.
A proportional defense model
Authors: Shumate K. C. , Howard G. T. 
Published: May 2007

AbstractThis paper considers the problem of defending a set of point targets of differing values. The defense is proportional in that it forces the offense to pay a price, in terms of reentry vehicles expended, that is proportional to the value of the target. The objective of the defense is to balance its resources so that no matter what attack is launched, the offense will have to pay a price greater than or equal to some fixed value for every unit of damage inflicted. The analysis determines which targets should be defended and determines the optimal firing doctrine for interceptors at defended targets. A numerical example is included showing the relationship between the total target damage and the size of the interceptor force for different values of p, the interceptor single shot kill probability. Some generalizations are discussed.