bluuebunny/crossref_metadata_2025 huggingface dataset:
Models for multi‐item continuous review inventory policies subject to constraints
Authors: Schrady D. A. , Choe U. C.
Published: May 2007

Models are formulated for determining continuous review (Q, r) policies for a multiitem inventory subject to constraints. The objective function is the minimization of total time‐weighted shortages. The constraints apply to inventory investment and reorder workload. The formulations are thus independent of the normal ordering, holding, and shortage costs. Two models are presented, each representing a convex programming problem. Lagrangian techniques are employed with the first, simplified model in which only the reorder points are optimized. In the second model both the reorder points and the reorder quantities are optimized utilizing penalty function methods. An example problem is solved for each model. The final section deals with the implementation of these models in very large inventory systems.
Optimal location of a single service center of certain types
Authors: Nair K. P. K. , Chandrasekaran R.
Published: May 2007

Hakimi has considered the problem of finding an optimal location for a single service center, such as a hospital or a police station. He used a graph theoretic model to represent the region being serviced. The communities are represented by the nodes while the road network is represented by the ares of the graph. In his work, the objective is one of minimizing the maximum of the shortest distances between the vertices and the service center. In the present work, the region being serviced is represented by a convex polygon and communities are spread over the entire region. The objective is to minimize the maximum of Euclidian distances between the service center and any point in the polygon. Two methods of solution presented are (i) a geometric method, and (ii) a quadratic programming formulation. Of these, the geometric method is simpler and more efficient. It is seen that for a class of problems, the geometric method is well suited and very efficient while the graph theoretic method, in general, will give only approximate solutions in spite of the increased efforts involved. But, for a different class of problems, the graph theoretic approach will be more appropriate while the geometric method will provide only approximate solutions though with ease. Finally, some feasible applications of importance are outlined and a few meaningful extensions are indicated.
Large deviation probabilities for order statistics
Authors: Book Stephen A.
Published: May 2007

Asymptotic representations are found for the large deviation probabilities that the nα‐th order statistic exceeds δ, where δ>α. The probabilities are first expressed in terms of the empirical distribution function, and then the 1960 theorem of Bahadur and Ranga Rao is applied. The result is then shown to be more precise than a logarithmic statement in a 1969 paper of Sievers dealing with the asymptotic relative efficiency of the sample median test.
On the use of standard tables to obtain Dodge‐Romig LTPD sampling inspection plans
Authors: Guenther William C.
Published: May 2007

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.
A model for manpower productivity during organization growth
Authors: Rau John G.
Published: May 2007

A mathematical model is developed that enables organization and manpower planners to quantify the inefficiencies involved in rapid buildups of organizations, such as is frequently found in the aerospace industry shortly after the award of a major contract. Consideration is given to the time required to train, indoctrinate, and familiarize new workers with their jobs and the general program aspects. Once trained, workers are assumed to be productive. If the ratio of untrained to trained workers exceeds a critical value, called the buildup threshold, then the performance of the trained workers is degraded to the extent that they are no longer 100 percent efficient until this ratio returns to a value less than the threshold. The model is sufficiently general to consider an arbitrary manpower plan with more than one peak or valley. The model outputs are functions of real time and consist of the fraction of the total labor force which is productive, the fraction of the total labor units expended for nonproductive effort, the cumulative labor costs for productive effort, and the cumulative labor cost for all effort.
The reliability of multicomponent systems subject to cannibalization
Authors: Simon Richard M.
Published: May 2007

A reliability model for multicomponent multistate systems is presented. This is a generalization of a model previously studied by Hirsch, Meisner, and Boll. In the earlier model, when a failure occurs for which no replacement spare is available, the locations using the same type of part as that having failed are “cannibalized” so as to allocate the shortages to locations where they are least detrimental to system performance. Here, we permit certain restrictions to be imposed upon the cannibalization procedure, and develop effective techniques for relating the probability laws governing the level of system performance to the system structure, cannibalization policy, kit of spare parts, and part reliabilities.
An extension of the (szwarc) truck assignment problem
Authors: Bellmore Mandell , Liebman Jon C. , Marks David H.
Published: May 2007

In this journal in 1967. Szware presented an algorithm for the optimal routing of a common vehicle fleet between m sources and n sinks with p different types of commodities. The main premise of the formulation is that a truck may carry only one commodity at a time and must deliver the entire load to one demand area. This eliminates the problem of routing vehicles between sources or between sinks and limits the problem to the routing of loaded trucks between sources and sinks and empty trucks making the return trip. Szwarc considered only the transportation aspect of the problem (i. e., no intermediate points) and presented a very efficient algorithm for solution of the case he described. If the total supply is greater than the total demand, Szwarc shows that the problem is equivalent to a (mp + n) by (np + m) Hitchcock transportation problem. Digital computer codes for this algorithm require rapid access storage for a matrix of size (mp + n) by (np + m); therefore, computer storage required grows proportionally to p2. This paper offers an extension of his work to a more general form: a transshipment network with capacity constraints on all arcs and facilities. The problem is shown to be solvable directly by Fulkerson's out‐of‐kilter algorithm. Digital computer codes for this formulation require rapid access storage proportional to p instead of p2. Computational results indicate that, in addition to handling the extensions, the out‐of‐kilter algorithm is more efficient in the solution of the original problem when there is a mad, rate number of commodities and a computer of limited storage capacity.
Incremental approximation of optimal allocations
Authors: Stone Lawrence D.
Published: May 2007

This paper concerns the approximation of optimal allocations by δ allocations. δ allocations are obtained by fixing an increment δ of effort and deciding at each step upon a single cell in which to allocate the entire increment. It is shown that δ allocations may be used as a simple method of approximating optimal allocations of effort resulting from constrained separable optimization problems involving a finite number of cells. The results are applied to find δ allocations (called δ plans) which approximate optimal search plans. δ plans have the property that as δ → 0, the mean time to find the target using a δ plan approaches the mean time when using the optimal plan. δ plans have the advantage that. they are easily computed and more easily realized in practice than optimal plans which tend to be difficult to calculate and to call for spreading impractically small amounts of effort over large areas.
Prediction with zero‐one loss structure
Authors: Berger Paul D.
Published: May 2007

This paper poses a prediction problem in which a linear model is assumed. With a “zero‐one” loss structure as the loss from incorrect prediction, it is suggested that least squares may not be appropriate for estimating the parameters of the model. An alternate criterion is proposed and integer programming is used in order to find the estimates, given the proposed criterion.
Generalized implicit enumeration using bounds on variables for solving linear programs with zero‐one variables
Authors: Zionts Stanley
Published: May 2007

In an earlier paper [1] we put forth a framework that helps to tie together a number of approaches for solving integer programming problems. We outlined there how Balas' Additive Algorithm can be explained and generalized in terms of the framework. In the present paper we review Balas' algorithm, and our earlier framework, and present an algorithm generalizing Balas' scheme. In addition, some examples are presented and future research to be done is discussed.
Quadratic programming with quadratic constraints
Authors: Baron David P.
Published: May 2007

A 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

An 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

In 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

In 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.
Effect of switch‐over devices on reliability of a standby complex system
Authors: Das Pritam
Published: May 2007

The behaviour of a standby redundant complex system under imperfect switch‐over devices with general waiting and repair time distributions for both types of components has been studied. The Laplace transform of various state probabilities have been derived. A particular case has also been discussed.
On optimal assembly of systems
Authors: Derman Cyrus , Lieberman Gerald J. , Ross Sheldon M.
Published: May 2007

We 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

Contained 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

The 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

A 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

This 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

Using 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

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

This 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

Military 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 basis

The 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 states

This 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

This 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

Multi‐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

This 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 time

The 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 manner

A 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.
A queue with waiting time dependent service times
Authors: Callahan J. R.
Published: May 2007

Sufficient conditions are developed for the ergodicity of a single server, first‐come‐first‐serve queue with waiting time dependent service times.
An algorithm for separable piecewise convex programming problems
Authors: Soland Richard M.
Published: May 2007

We 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.
Geometry and resolution of duality gaps
Authors: Bazaraa M. S.
Published: May 2007

In this study we interpret the exterior penalty function method as a generalized lagrangian metliod which fills duality gaps in nonconvex problems. Geometry and resolution of these gaps from a duality point of view are highlighted.
Sequential determination of inspection epochs for reliability systems with general lifetime distributions
Authors: Zacks S. , Fenske W. J.
Published: May 2007

The 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

This 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 network

As 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

This 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 departures

The 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

This 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 > Σat

The 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

We 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

The 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.
The single server queue in discrete time‐numerical analysis IV
Authors: Heimann David , Neuts Marcel F.
Published: May 2007

The nonlinear difference equation for the distribution of the busy period for an unbounded discrete time queue of M|G| 1 type is solved numerically by a monotone iterative procedure. A starting solution is found by computing a first passage time distribution in a truncated version of the queue.
Assembly of systems having maximum reliability
Authors: Derman Cyrus , Lieberman Gerald J. , Ross Sheldon M.
Published: May 2007

The 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

This 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.
Lanchester‐type models of warfare and optimal control
Authors: Taylor James G.
Published: May 2007

The optimization of the dynamics of combat (optimal distribution of fire over enemy target types) is studied through a sequence of idealized models by use of the mathematical theory of optimal control. The models are for combat over a period of time described by Lanchester‐type equations with a choice of tactics available to one side and subject to change with time. The structure of optimal fire distribution policies is discussed with reference to the influence of combatant objectives, termination conditions of the conflict, type of attrition process, and variable attrition‐rate coefficients. Implications for intelligence, command and control systems, and human decision making are pointed out. The use of such optimal control models for guiding extensions to differential games is discussed.
An experimental comparison of solution algorithms for the single‐machine tardiness problem
Authors: Baker Kenneth R. , Martin James B.
Published: May 2007

A basic problem in scheduling involves the sequencing of a set of independent tasks at a single facility with the objective of minimizing mean tardiness. Although the problem is relatively simple, the determination of an optimal sequence remains a challenging combinatorial problem. A number of algorithms have been developed for finding solutions, and this paper reports a comparative evaluation of these procedures. Computer programs for five separate algorithms were written and all were run on a data base designed to highlight computational differences. Optimizing algorithms developed by Emmons and by Srinivasan appeared to be particularly efficient in the comparative study.
A note on some series representations of the integral of a bivariate normal distribution over an offset circle
Authors: Gilliland Dennis C. , Hansen Eldon R.
Published: May 2007

Consider the problem of computing an offset circle probability under a normal distribution. One approach is to utilize an infinite series representation in which case it is important to have rapid convergence and a good upper bound on the error introduced by consideration of only a finite number of terms of the series. We relate three seemingly different series representations. In particular we show how two series representations for the bivariate case can be obtained by specializing more general results of Harold Ruben.
On mixed integer quadratic programs
Authors: Agrawal S. C.
Published: May 2007

This paper provides a method for solving mixed integer quadratic programs with the help of cutting‐plane technique.
A note on the costly surveillance of a stochastic system
Authors: Chitgopekar S. S.
Published: May 2007

We consider the costly surveillance of a stochastic system with a finite state space and a finite number of actions in each state. There is a positive cost of observing the system and the system earns at a rate depending on the state of the system and the action taken. A policy for controlling such a system specifies the action to be taken and the time to the next observation, both possibly random and depending on the past history of the system. A form of the long range average income is the criterion for comparing different policies. If RΔ denotes the class of policies for which the times between successive observations of the system are random variables with cumulative distribution functions on [0, Δ], Δ < ∞, we show that there exists a nonrandomized stationary policy that is optimal in RΔ. Furthermore, for sufficiently large Δ, this optimal policy is independent of Δ.
The mixed ordering policy in periodic review stochastic multi‐commodity inventory systems
Authors: Goswick T. E. , Sivazlian B. D.
Published: May 2007

In multi‐commodity inventory systems with variable setup costs, the mixed ordering policy assumes that commodities may be ordered either individually, or may be arbitrarily grouped for joint ordering. Thus, for a two‐commodity system, commodity one or commodity two or commodities one and two may be ordered incurring respectively fixed order costs of K, K1, or K2, where max (K1, K2) ≤ K ≤ K1 + K2, This paper considers a two‐commodity periodic review system. The stationary characteristics of the system are analyzed, and, for a special case, explicit solutions are obtained for the distribution of the stock levels at the beginning of the periods. In a numerical example, optimal policy variables are computed, and the mixed ordering policy is compared with individual and joint ordering policies.
Maintenance policies when failure distribution of equipment is only partially known
Authors: Kander Z. , Raviv A.
Published: May 2007

An optimal schedule for checking an equipment subject to failure which can be detected by inspection only, is derived. Increasing failure rate and one percentile specify the otherwise unknown life distribution. Dynamic programming methodology yields the solution which minimizes the maximum expected cost. Numerical examples are presented and compared with models employing differing amounts of knowledge.
A general treatment of upper unbounded and bounded hitchcock problems
Authors: Dwyer P. S.
Published: May 2007

This paper is designed to treat (a) the problem of the determination of the absolute minimum cost, with the associated assignments, when there is no limit, N, on the number of parcels available for shipment in a modified Hitchcock problem. This is accomplished with the use of a transformed cost matrix. C*, to which the so‐called transportation paradox does not apply. The general Hitchcock solution using C* gives the cost T*, which is the absolute minimum cost of the original problem, as well as sets of assignments which are readily transformed to give the general assignments of the original problem. The sum of these latter assignments gives the value of Nu, the unbounded N for minimum cost. In addition, this paper is designed to show (b) how the method of reduced matrices may be used, (c) how a particular Hitchcock solution can be used to determine a general solution so that one solution using C* can provide the general answer, (d) how the results may be modified to apply to problems with fixed N, and hence (e) to determine the function of the decreasing T as N approaches Nu, and finally (f) to provide a treatment when the supplies at origin i and/or the demands at destination j, are bounded.
Pollution abatement and economic growth: An application of the von neumann model of an expanding economy
Authors: Cremeans John E.
Published: May 2007

The generalized von Neumann model of an expanding economy permits both joint products and alternative processes. Pollutants may be explicitly treated as the normal by‐products of certain economic processes and “clean” and “dirty” production alternatives may be simultaneously available. The paper describes some methods for incorporating pollutants in the model and several techniques that may be used to study the relationship between pollution abatement and economic growth. Numerical examples are used to illustrate cases of direct control of processes, consumer demand for “eliminated pollutant” and the limitation of total produced pollutants by exogenous constraint. In the last case an effluent charge is calculated.
Covariance of weibull order statistics
Authors: Lochner Robert H. , Basu A. P. , Diponzio Margaret
Published: May 2007

Let X1 < X2 <… < Xn denote an ordered sample of size n from a Weibull population with cdf F(x) = 1 ‐ exp (−xp), x > 0. Formulae for computing Cov (Xi, Xj) are well known, but they are difficult to use in practice. A simple approximation to Cov(Xi, Xj) is presented here, and its accuracy is discussed.
A note on a constrained replacement model for ships subject to degradations in utility
Authors: Kaplan Seymour
Published: May 2007

In a recent paper, Peter J. Kalman considers a stochastic constrained optimal replacement model using the case of ship replacement as an example. However, the development of the constrained model proposed is not pursued and the optimal interval between replacements is determined in the absence of constraints. Among other things, it is the purpose of the present paper to extend the previous results to develop explicit types of constraints for the case of ship replacement and to determine how the optimal replacement interval may change as a result of these constraints. The constraints are concerned with the state of readiness of each ship in a group of ships. Readiness is assumed to be measured on an ordinal valued utility scale. It is proposed that ordinal valued data on ship combat readiness ratings collected by the Navy may be a useful source of empirical information for a model of the type discussed.
Postoptimality analysis in integer programming by implicit enumeration: The mixed integer case
Authors: Roodman Gary M.
Published: May 2007

This paper develops a method for doing postoptimality analysis on the mixed integer programming problem. The proposed procedures form a natural adjunct to enumerative I.P. algorithms that are linear programming based, and they are designed, in effect, to capitalize on insights generated as the problem is initially solved to do subsequent analysis upon it. In particular, limited ranging analysis is possible on selected parameters, as is the efficient resolving of the problem following parameter changes.
An efficient heuristic procedure for the capacitated warehouse location problem
Authors: Khumawala Basheer M.
Published: May 2007

This paper introduces an efficient heuristic procedure for solving a special class of mixed integer programming problem called the capacitated warehouse (plant) location problem. This procedure parallels the work reported earlier in [9] on the uncapacitated warehouse location problem. The procedure can be viewed as tracing a judiciously selected path of the branch and bound tree (from the initial node to the terminal node) to arrive at a candidate solution. A simple backtracking scheme is also incorporated in the procedure to investigate possible improvement in the solution. Computational results on problems found in the literature look quite encouraging.
The minimum sphere covering a convex polyhedron
Authors: Elzinga Jack , Hearn Donald
Published: May 2007

A finite algorithm is given for finding the smallest sphere enclosing a convex polyhedron in En described by a given system of linear equalities or inequalities. Extreme points of the polyhedron, and minimum spheres enclosing them, are generated in a systematic manner until the optimum is attained.
On estimating the reliability of a component subject to several different stresses (strengths)
Authors: Chandra Satish , Owen Donald B.
Published: May 2007

This paper is concerned with estimating p = P(X1 < Y …, Xn < Y) or q =P (X < Y1, …, X < Yn) where the X's and Y's are all independent random variables. Applications to estimation of the reliability p from stress‐strength relationships are considered where a component is subject to several stresses X1, X2, …, XN whereas its strength, Y, is a single random variable. Similarly, the reliability q is of interest where a component is made of several parts all with their individual strengths Y1, Y2 …, YN and a single stress X is applied to the component. When the X's and Y's are independent and normal, maximum likelihood estimates of p and q have been obtained. For the case N = 2 and in some special cases, minimum variance unbiased estimates have been given. When the Y's are all exponential and the X is normal with known variance, but unknown mean (or uniform between 0 and θ, θ being unknown) the minimum variance unbiased estimate of q is established in this paper.
Exact first and second order moments of order statistics from the truncated exponential distribution
Authors: Saleh A. K. Md. Ehsanes , Scott Christine , Junkins D. Bruce
Published: May 2007

Exact expressions for the first and second order moments of order statistics from the truncated exponential distribution, when the proportion 1–P of truncation is known in advance, are presented in this paper. Tables of expected values and variances‐covariances are given for P = 0.5 (0.1) 0.9 and n = 1 (1) 10.
Application of the fundamental theorem of games to an example concerning antiballistic missile defense
Authors: Croucher John S.
Published: May 2007

This paper considers a two sided resource allocation game in which both players initially have fixed resources which may be distributed over various targets. Their effectiveness depends on the manner of distribution and also on the strategy of the opponent, a natural payoff function for such a situation being used. The complete solution to the game is derived and a numerical example given.