bluuebunny/crossref_metadata_2025 huggingface dataset:
Queuing with Alternating Priorities
Authors: Avi-Itzhak B. , Maxwell W. L. , Miller L. W.
Published: November 2008

For a service facility serving more than one class of customers a problem arises as to the order in which customers should be served (i.e., the priority rule). A typical example is a manufacturing facility that produces two products to meet a random stream of incoming orders. In this paper the alternating priority rule (also known as the “zero switch rule”) is introduced and investigated. Two classes of customers are served by a single service facility. Customers of class i(i = 1, 2) have priority over customers of class j(j = 1, 2; j ≠ 1) whenever a class i customer is in service. When the service facility is idle, the first arriving customer enters service and acquires the priority right for customers of his class. Within classes the “first-come, first-served” rule is observed. Customers' arrivals are assumed to be Poisson and service times are assumed to be arbitrarily distributed independent random variables. The steady-state densities of queuing times are formulated by the use of a special mathematical procedure. The expectations of queuing times and sizes of queues as well as the first two moments of the busy periods are obtained in terms of the basic parameters of the arrival process and service time distributions. All the results are related to the case where switching from one type of customers to another is not penalized by setup time. The alternating priority rule is compared to the “head-of-the-line” and the “first-come, first-served” rules with respect to expected queuing times and queue sizes. The last part of the paper discusses the possibilities of extending the suggested rule to cases involving more than two classes of customers and nonzero setup times and setup costs.
Single Facility Sequencing with Random Execution Times
Authors: Banerjee B. P.
Published: November 2008

A single facility sequencing problem where the execution time for each job at the facility is random with known probability distribution, is formulated and solved. The solution is shown to be easily extended to situations where further jobs arrive while the program is in operation. Further extensions are discussed, where (a) the facility is taken to consist of multiple (identical or otherwise) units of equipment and, (b) special priorities are attached to some of the jobs.
A Queue with Simultaneous Arrivals and Erlang Service Distribution
Authors: Restrepo Rodrigo A.
Published: November 2008

In this paper the method of generating functions is applied to a queue where the moments of arrival follow a Poisson distribution, but where at each of these moments several persons may arrive simultaneously. Assuming an Erlang distribution for the service times and first-come first-served discipline for the arriving groups, explicit formulas are obtained for the limiting values of the mean number of persons in the queue and in the system, and the mean time that a group of persons who arrive together must wait before one of them is served.
The Estimation of the Mean and Variance of a “PERT” Activity Time
Authors: Donaldson William A.
Published: November 2008

An alternative method of estimating the variance of a PERT activity time is proposed given that one of the initial estimates is the mean. The beta-distribution of the activity time is assumed to be tangential to the x-axis at each end. Restrictions in the current method are relaxed, and the inconsistency of the implicit assumption of a fixed coefficient of skew removed. The skew of the distribution is determined by the three estimates of the activity time. No difficult computations are involved.
A Relation Between Decision Making Penalty and Simulation Sample Size for Inventory Systems
Authors: Brenner Michael E.
Published: November 2008

The paper contains results from experiments in which two inventory models, with known analytical solutions have been simulated to learn about simulation. The author suggests a relation between the simulation sample size and the economic penalty for an incorrect decision from inaccuracy in the simulated information. The relation is W̄ = A/nk, where W̄ is the average penalty in dollars, n is the sample size, and A and k are parameters obtained from a regression analysis. A series of results are reported with values given for A and K. The values of A vary monotonically with some of the inventory parameters. The values of k have moderate variability. It is hoped that the ideas suggested and the result presented may be helpful to others conducting experiments to learn more about simulation.
Linear and Nonlinear Separation of Patterns by Linear Programming
Authors: Mangasarian O. L.
Published: November 2008

A pattern separation problem is basically a problem of obtaining a criterion for distinguishing between the elements of two disjoint sets of patterns. The patterns are usually represented by points in a Euclidean space. One way to achieve separation is to construct a plane or a nonlinear surface such that one set of patterns lies on one side of the plane or the surface, and the other set of patterns on the other side. Recently, it has been shown that linear and ellipsoidal separation may be achieved by nonlinear programming. In this work it is shown that both linear and nonlinear separation may be achieved by linear programming.
On the Parts Requirements Problem
Authors: Thompson Gerald L.
Published: November 2008

The parts requirements (or “explosion”) problem is that of finding the total numbers of components, subassemblies, and assemblies needed to fulfill an order, given the individual requirements needed in each assembly. In this paper two methods are presented for solving the problem, together with the so-called “spare parts” and “netting” problems. The first method involves the use of the inverse of the matrix I − Q where Q is the quantity matrix. The second method is a generalization of the successive multiplication algorithm, first discussed in a special case by Elmaghraby. Mathematical proofs of the methods are presented, as is computational experience with small problems.
Letter to the Editor—Note on Computing Optimum Discrete Allocations
Authors: Young Henry A.
Published: November 2008

The object of this Note is to extend the discussion of the recursive (dynamic programming) solution of discrete allocation problems found in the first two chapters of Bellman and Dreyfus, Applied Dynamic Programming, Princeton University Press, 1962. These problems frequently involve a continuous state space, characterizing a total amount of resource, and optimum return and policy functions that can change over small segments of this space. In order to compute these functions recursively, it is necessary to replace the continuous space by a discrete grid and compute values of the functions on this grid. The possibility of rapid changes in these functions makes impossible the accurate interpolation of values of an optimum partial return function from those of its predecessor if the grid is chosen arbitrarily. Instead, when problem constants are positive rational numbers, there is a unique grid size that essentially scales the problem to a minimum equivalent solvable all-integer problem.
Time-Dependent Solution of a Priority Queue with Bulk Arrival
Authors: Hawkes A. G.
Published: November 2008

The time-dependent distribution of the number of customers in the queue and the lapsed service time is obtained, in terms of Laplace transforms, for a head-of-the-line priority queue in which both classes of customer arrive in bunches. From this we obtain the equilibrium distribution and the distribution of the number of customers left behind a departing customer. The latter is then used to find the equilibrium distribution of queuing times for both classes of customer. It is not easy to obtain a complete explicit solution, even for exponential service times, but the mean queuing times are readily obtained.
On Serial Files with Relocatable Records
Authors: McCabe John
Published: November 2008

A serial file is considered in which, after a query is processed, the order in the file is changed by moving the record to which the query referred into the first place in the file. The theory of regular Markov chains is used to demonstrate the existence of E(X) and to show that the law of large numbers holds, where E(X) is the limiting average position of a queried record. A closed-form expression for E(X) is determined. A second method of relocation is proposed, in which the queried record exchanges positions with the record immediately before it in the file. It is conjectured that this method of relocation is at least as good as the first method. It is pointed out that, whichever method of relocation is used, if one only relocated after every Mth query, the limiting average position of a queried record is the same as it is if we relocate after every query.
Towards a Coordinated Approach to the Structuring of Cost and Design Models: A Case Example
Authors: Hill L. S.
Published: November 2008

During the early phases of design, engineering decisions are made affecting costs for the entire life cycle of a man-machine system, that is, from development through manufacture and operations. These critical decisions are commonly made without reference to total cost effects. Cost studies are conducted, of course, at various times and places in the organization. The difficulty is, however, that such efforts are too belated and/or fragmentary to be useful in attempts to evolve an economically efficient design.
Minimax Detection Station Placement
Authors: Smallwood Richard D.
Published: November 2008

A model for the placement of n detection stations for optimum coverage of an arbitrary plane area is described. The stations are assumed to be identical and to have a probability of detection that is a function only of the distance between the station and the event to be detected. Furthermore, the stations are assumed to operate independently of each other. It is also assumed that the enemy has complete knowledge of the station locations and effectiveness and is interested only in eluding detection by the detection stations. Thus, the situation is reduced to the minimax problem of placing the stations so that the maximum probability of not detecting an enemy event is minimized. A hill climbing iterative technique for finding the optimum locations is described in some detail. This technique is illustrated for the problem of locating detection stations within the United States and Soviet Union. The results of these applications are presented and discussed. The paper concludes with some remarks on how this model can be made more descriptive of the real world situations being modeled.
Optimal Design of Optimization Experiments
Authors: Dean Burton V. , Marks Eli S.
Published: November 2008

Experimental optimization methods are used to determine optimal decision policies in the cases where the functional form or parameter values are unknown. The optimal design of such experiments is developed in this paper for a variety of methods of experimentation. Parameter values are estimated, an optimal decision policy is obtained, and estimates of the expected gain from experimentation are derived. Expected gains are compared for alternative experimental designs. In particular, methods are derived for obtaining the optimal size, organization structure, and duration time of the experiment. The general methods are applied to the problem of design of a maintenance experiment to obtain the scheduled maintenance frequency that achieves maximum cost savings.
Letter to the Editor—Comments on Preceding Note
Authors: Everett Hugh
Published: November 2008

Comments on Charnes, A., W. W. Cooper. 1965. A note on the “fail-safe” properties of the “generalized Lagrange multiplier method”. Oper. Sci. 13 674–677.
Letter to the Editor—Comments on Preceding Note
Authors: Leeman Wayne A.
Published: November 2008

Comments on Saaty, T. L. The burdens of queuing charges—comments on a letter by Leeman. Oper. Sci. 13 679.
Dynamic Inference
Authors: Howard Ronald A.
Published: November 2008

We consider a model for dynamic uncertain processes that affords considerably more generality of formulation than do Markovian models or their derivatives. The underlying statistical parameters of a stochastic process that produces observable outputs are themselves allowed to change at times generated by another stochastic process. We would like to make probability assignments to future outputs of the process, given only the past outputs. We develop the inferential relations for the case where the changes of parameters are governed by a renewal process, and where the process that generates observables depends only on its present parameters. We illustrate these results using an example with a Bernoulli observable distribution, a beta parameter distribution, and a geometric distribution for for the time between parameter changes. The numerical results indicate a complexity of behavior that challenges intuition. Possible applications of the general class of dynamic inference models range from marketing to anti-submarine warfare.
Multistage Replacement Strategies with Finite Duration of Transfer
Authors: Naik M. D. , Nair K. P. K.
Published: November 2008

For failing type of equipment, two-stage and multistage replacement strategies are available in literature. The strategies bring economy by transfering failure rates from groups where the replacement cost is higher to those where it is smaller. Certain important aspects, which prevail in practice, were neglected in those works. The finite time taken for the transfer of units manifests into the down-time loss and, together with the transportation medium, gives possible failures during transfer. In this paper the effects of finite transfer time, as well as the possibilities of failures during insertion and removal of units, are considered, and the condition for multistage strategies to be more economical is derived. The role of transportation medium, the possibility of reducing the down time by inter-stage inventories and the method to arrive at optimum sizes of such inventories are also presented. The impact of these factors on the economy and the optimum number of stages are brought out. The strategies are, thus, more powerful as they cover the realities of actual situation.
Jacobians in Constrained Nonlinear Optimization
Authors: Wilde Douglass J.
Published: November 2008

In constrained optimization problems the rates of change of the objective function with respect to the independent (nonbasic) variables have been interpreted as shadow prices, dual variables, and Lagrange multipliers. These derivatives are shown here to be ratios of Jacobians of the transformations between certain sets of variables. This result extends the Kuhn-Tucker conditions of nonlinear programming to optimum seeking problems in which information about the objective and constraint functions can be obtained only by direct measurement, the functions not being given in closed analytic form. Other derivatives helpful for maintaining feasibility during a search are also shown to be ratios of Jacobians. An example shows how these results might be incorporated into algorithms for seeking a constrained optimum.
Letter to the Editor—An Experiment in Teaching Operations Research
Authors: Grenander Ulf
Published: November 2008

An experiment is described for training operations-research students in actual problem solving. The students are given real life problems in their raw form and are asked to work out practical solutions with some help and advice from a supervising teacher. This training complements the usual one given in the form of lectures, seminars, thesis writing, and case studies. It is intended to produce a problem-oriented attitude among the students.
Optimization of Maintenance Resources
Authors: Lifsey Jeremy A.
Published: November 2008

Dynamic; programming techniques appropriate to optimizing a maintenance function are evaluated to demonstrate the feasibility of applying them to large-scale systems involving many equipments. The objective is to determine the proper number, mix, and level of military and/or contractor maintenance personnel, and to apportion expenditures on other maintenance resources, such as test equipment, computer programs, and manuals. The tasks to which the model was applied (drawn from comprehensive data on a developmental AF environment) considered maintenance of 15 digital display consoles, and used personnel, computer programs, computer manuals, procedural manuals (including circuit diagrams), and test equipment as the variable resources. The results yield the mix of resources that achieves a given mean-time-to-repair at minimum cost. Alternatively, the results can yield the trade-off of cost and mean-time-to-repair. Constraints on particular variables can be injected into the procedure—and, in fact, have the effect of reducing required computer runs—but must be carefully restricted to those that realistically reflect the actual situation. The model not only realistically represents the maintenance function, but also can be readily expanded to other equipments by adding stages and data to the tables.
Letter to the Editor—Linear Fractional Functionals Programming
Authors: Swarup Kanti
Published: November 2008

The present paper deals with the problem of maximizing the ratio of two linear functions subject to a set of linear equalities and nonnegativity constraints on the variables. The problem is attacked directly, beginning with a basic feasible solution and showing the conditions under which the solution can be improved. Conditions for optimality criteria are established. The method followed is similar to “simplex technique” in linear programming.
Letter to the Editor—Timing of Check Out Before a Critical Event
Authors: Truelove A. J.
Published: November 2008

A system with constant failure rate must be operable at time T. Prior to this we permit only one check-out, and one repair if necessary. How far should we “back off” from T in scheduling check out? Approximate solutions are derived for exponential and log normal repair time distributions, with graphical results in the latter case.
A Computer Code for Integer Solutions to Linear Programs
Authors: Haldi John , Isaacson Leonard M.
Published: November 2008

This paper reports on a new computer code (called “LIP1”) for solving integer programming problems, which will be distributed for general use through SHARE. LIP1 was written as an experimental program for the purpose of reexamining and further testing the efficiency of Gomory's original cutting-plane technique. Many trial problems have now been solved with this code. Of particular interest, however, are 25 test problems that have been solved with other integer programming codes (all these other codes incorporate the method of Gomory's more recent all-integer algorithm). The basis for comparing the performance of the various codes is the number of iterations required to solve each problem. For these 25 test problems LIP1 appears generally as efficient as the other codes tested. Moreover, on the more difficult problems LIP1 generally performed better than the other codes. We conclude that Gomory's original cutting-plane method merits further investigation and development as an efficient computational technique.
A Resource Allocation Problem
Authors: Litsios Socrates
Published: November 2008

In this paper two sequencing problems are investigated that arise in the course of allocating one or more constrained resources to two or more tasks. The general problem considered is one of determining the optimal sequence of tasks and the optimal scheduling of resource usage where the objective is to minimize the time by which all tasks are completed. The fundamental solution technique utilized involves a combination of dynamic programming and combinatorial analysis techniques. In the single resource case the two problems are shown to be graphical “duals” of each other thereby allowing an iterative solution to the second problem.
Bayesian Determination of the Reorder Point of a Slow Moving Item
Authors: Silver Edward A.
Published: November 2008

Consider an inventory item for which the procurement (or production setup) lead time is nonzero. One of the commonly used methods of determining the reorder point of such an item is to specify the probability of a stockout or a desired service level (fraction of demand that is to be instantaneously satisfied) and then select the reorder level that will provide such service. However, such an approach has assumed that the probability distribution of demand during the lead time is exactly known. In many inventory situations this assumption is not justified, particularly in the case of a slow moving item with limited available sales history. For such a situation this paper explores the use of a Bayesian approach to selecting a reorder point.
A Queuing Model for Unitized Cargo Generation
Authors: Novaes A. , Frankel E.
Published: November 2008

The generation of cargo in a port is a stochastic process subject to a large number of factors. In the model presented, each unit of cargo is assumed equivalent from the handling point of view. Reneging and balking and the consequent availability of alternate service is considered. In the main model presented here, constant service time and uniform vessel capacity on each arrival is assumed, and a two-port trade route with “homogeneous equipment” is simulated. Some of these restrictions are later relaxed. The model may be of use for the design of short to medium distance container, roll-on roll-off, or all palletized cargo operations and the related terminal requirements.
Letter to the Editor—Super-Critical Arcs of a PERT Network
Authors: Welsh D. J. A.
Published: November 2008

This note proposes a method of determining supercritical arcs of a PERT network.
A Class of Variational Problems in Search Theory and the Maximum Principle
Authors: Beltrami E. J. , McGill R.
Published: November 2008

In this paper we consider certain nonlinear and constrained variational problems that occur in the theory of search. The problems are definitely of a nonclassical variety, but, by using a device of R. Courant, a sequence of unconstrained variational problems is generated, the solutions of which converge to the solution of the constrained problem. The maximum principle of L. Pontryagin et al., is then utilized to construct a corresponding sequence of nonlinear, two-point boundary value problems such that a solution to the variational problem will then necessarily satisfy the boundary value problem. An effective computational method, based on the notion of a generalized Newton-Raphson operator, is then applied to solve iteratively, in a rapid and accurate manner, the nonlinear boundary value problem; under suitable assumptions, this method yields solutions to the variational problem. The technique is illustrated in several examples.
Choosing a Good Appointment System—A Study of Queues of the Type (D, M, 1)
Authors: Jansson Birger
Published: November 2008

A queuing system with exponentially distributed service times and constant interarrival times is studied for the case with one service station. The characteristics of the queue are determined both in its transient part and in its steady part. The cost of the system is defined as a linear sum of the cost of keeping customers waiting for service and the cost of having the service station idle. The statistical distribution of this cost is derived and it is also shown how its mean may be minimized by proper choices of the constant interarrival time and the initial numbers of customers in the queue.
Letter to the Editor—Queuing with Balking—A Simple Method to Study the Transient Behavior
Authors: Satyamurty P. R.
Published: November 2008

We study the queuing system where every customer on arrival makes one of two possible decisions—to join the queue or to go away without taking service never to return. Assuming such a decision to be entirely governed by the queue size at the instant of customer arrival, we obtain the transient solutions for the queuing system M/M/1 using an approximate method. As an illustration of the method, some results of the computations are given.
Cost/Effectiveness Analysis: Its Tasks and Their Interrelation
Authors: Fields David S.
Published: November 2008

Studies of the cost/effectiveness of specific systems and mathematical techniques used in such investigations have frequently been presented at ORSA meetings and published in Operations Research. A few other papers have described the general theory of cost/effectiveness or a special approach to one or more of the major tasks involved in its application. This paper discusses the nature of these tasks and how they are interrelated, using as an example the design of a communication system in a nuclear environment.
Letter to the Editor—A Cost Effectiveness Comparison Involving a Tradeoff of Performance, Cost, and Obtainability
Authors: Seiler Karl
Published: November 2008

The purpose of this paper is to develop an algorithm to examine the tradeoffs of performance versus cost versus time of obtainability. Consider three hypothetical aircraft with three obtainabilities: At (current), At+1 (one year later), and At+2 (two years later). Assume that an array of the variables reveals that no single aircraft has the ideal combination of lowest cost, best performance, and current obtainability. Decisions confronted with such dilemmas may be clarified by various tradeoff techniques. A description of such a technique is presented, although one fully realizes that the final choice will, perforce, require the introduction of judgment.
Road Networks in an Expanding Circular City
Authors: Tan T.
Published: November 2008

The effect of growth in the number of persons living in the suburbs of an idealized circular city and working in a central business district of constant size is investigated in the case of five alternative basic road systems. It is shown that the total city size, relative to the size of its central business district, can increase only up to a critical value beyond which a major change in the basic road network is necessary to ensure efficient travel. Critical values for the ratio of the density of work places to homes are then obtained. The criteria used to evaluate the road networks are distance traveled, road space required, and travel time.
Random Service, Finite-Source Delay Distribution for One Server with Constant Holding Time
Authors: Burke Paul J.
Published: November 2008

Formulas are derived suitable for calculating the stationary waiting-time distribution for the model described in the title of this paper.
Letter to the Editor—Some Confidence Intervals for Queues
Authors: Lilliefors Hubert W.
Published: November 2008

It is possible to calculate for many queuing situations, in the steady state, the state probabilities, the expected number of units in the system or in the queue, the proportion of idle time per channel, and other quantities of interest. These quantities are calculated as a function of the number of channels, the queuing discipline, and the parameters of the distributions of arrival and service times. If the parameters of the distributions are known exactly, then the results are exact. In many cases of interest, however, the parameters are not known exactly and estimates must be used. In such situations one obtains estimates rather than exact values for the state probabilities, expected number of units in the queue, and the other quantities. In order to make use of these estimates it is important to know the precision of the estimates as measured by their respective confidence intervals. In this paper confidence intervals are calculated for several cases of interest.
Letter to the Editor—A Queuing System with Bulk Service
Authors: Stuart I. M. , McMahon G. B.
Published: November 2008

A simple queuing system is envisaged that is similar to a car ferry departing at regular intervals, or to a plant of fixed capacity processing work that can arrive only at regular intervals. The integral equation is found that relates the queue properties to the pattern of arrival of work. By analysis of this integral equation it is found that when the mean rate of arrival of work x̄p approaches the plant capacity (unity), the product of the mean queue length x̄q and 1 − x̄p approaches one half the variance of the arrival distribution.
Transfer of Detection Contacts to Tracking Contacts in Surveillance
Authors: Dobbie James M.
Published: November 2008

Surveillance of a region is conducted by using a search system to detect targets and a tracking system or force to follow them. After the search system detects a target, the tracking force will attempt to gain contact, usually by a local search. Before the tracking force detects the target, and thereby completes transfer, contact may be lost by the search system. If recontact is made by the search system, the new contact will be used by the tracking force to localize its search for the target. As the local search by the tracking force proceeds, contact by the search system may be lost and regained a number of times. The probability of transfer is obtained under the assumption that the transfer rate decreases as the time since last contact by the search system increases. The particular problem considered is that of sea surveillance for submarines, in which the search system is a fixed field of sensors and the tracking force consists of mobile units, such as ships, aircraft, and helicopters. However, the model can be adapted to other transfer problems, such as the transfer of a contact by a search radar to contact by a tracking radar.
The Probability of an “Excessive Nonfunctioning Interval”
Authors: von Ellenrieder A. , Levine A.
Published: November 2008

A “component” is defined as a zero-one function of time. The probability that this function is not continuously equal to “one” for longer than a stated value (the “excessive nonfunctioning interval”) anywhere in a given time period is derived assuming a common type of Markov process. This probability is found as the probability of “first passage” of a derived stochastic process.
One-Pass Algorithms for Some Generalized Network Problems
Authors: Charnes A. , Raike W. M.
Published: November 2008

The generalized network problem and the closely related restricted dyadic problem are two special model types that occur frequently in applications of linear programming. Although they are next in order after pure network or distribution problems with respect to ease of computation, the jump in degree of difficulty is such that, in the most general problem, there exist no algorithms for them comparable in speed or efficiency to those for pure network or distribution problems. There are, however, numerous examples in which some additional special structure leads one to anticipate the existence of algorithms that compare favorably with the efficiency of those for the corresponding pure cases. Also, these more special structures may be encountered as part of larger or more complicated models. In this paper we designate by topological properties two special structures that permit evolution of efficient algorithms. These follow by extensions of methods of Charnes and Cooper and of Dijkstra for the corresponding pure network problems. We obtain easily implemented algorithms that provide an optimum in one “pass” through the network. The proofs provided for these extended theorems differ in character from those provided (or not provided) in the more special “pure” problem algorithms published.
Letter to the Editor—An Extention of Lanchester's Linear Law
Authors: Hellman Olavi
Published: November 2008

A stochastic model of military engagement, which is made up of individual duels, is considered. The process is neither Markovian nor stationary. The starting instants of duels are a Poisson process of density λ. The length of a duel is a random variable with a fairly general distribution. The case where the lengths of duels are subject to the exponential law, is considered as an example.
Letter to the Editor—Computational Experience with a “Balasian” Integer Programming Algorithm
Authors: Freeman Raoul J.
Published: November 2008

A recent and significant addition to the literature of partial enumeration methods for solving integer linear programming problems has been the work of Balas. This paper describes some computational experience with a version of the algorithm and discusses future avenues of research that may be undertaken.
Letter to the Editor—A Poisson Generalization Based on Counts that are Delayed but Not Lost
Authors: Haight Frank A.
Published: November 2008

This paper deals with a model in which Poisson events in fixed time periods are recorded with probability α and left to accumulate into the succeeding period with probability 1 − α. The distribution of number of events recorded is obtained, together with its mean, variance, and generating function.
Letter to the Editor—Reliability Estimates in the Exponential Case
Authors: Enns E. G.
Published: November 2008

The best reliability estimate obtained from a finite sample of time intervals taken from an exponential distribution has previously been derived. Instead of solving an integral equation, this result can readily be obtained by dividing an interval of fixed length in a random fashion and considering the resulting subinterval statistics.
Letter to the Editor—Fractional Functionals Programming with a Quadratic Constraint
Authors: Aggarwal S. P. , Swarup Kanti
Published: November 2008

In the present paper a procedure, in two phases is developed for maximizing a linear fractional functionals subject to one quadratic and a number of linear constraints. The method depends upon the technique of solving both the linear fractional functionals programming and the quadratic programming subject to linear constraints with nonnegativity restrictions on the variables.
A Many Server Bulk Queue
Authors: Roes P. B. M.
Published: November 2008

In this study the theory of derived Markov chains is applied to a queuing system with n servers and group service. Application to a queuing system with only one server and group service or arrival in batches has been dealt with already. Although the quasi-derived Poisson servicing is not without its restrictions on the batch size distribution, it seems to be the only approach to date that makes the queuing system GI/M(x)/n accessible for investigation.
A Model of Adaptive Control of Promotional Spending
Authors: Little John D. C.
Published: November 2008

Companies try to conduct their marketing operations so as to respond to changing market conditions. A model of such a process is studied for the case of setting promotion rate. Company sales are functions of promotional spending, but the relation changes with time. An adaptive system is devised that works as follows: Information about sales response is collected by performing an experiment. The experimental results are used to update a sales response model. Promotion rate is chosen to maximize expected profit in the next time period. The cycle is repeated. In designing the experiment, sample size is chosen to minimize the cost of imperfect information plus the cost of experimentation. The model employs a quadratic sales response function with a parameter that, changes according to a first order, autoregressive process. The optimal adaptive system turns out to involve exponential smoothing of the experimental results. A numerical example is studied analytically and by simulation. The adaptive system is found to work better than various other policies. In a sensitivity analysis, an adaptive system derived for one underlying model of the market is found to perform well even when certain other models actually apply.
Chance-Constrained Generalized Networks
Authors: Charnes A. , Kirby M. , Raike W.
Published: November 2008

An extension to the theory of linear programming over generalized networks is presented which replaces the generalized Kirchoff node conditions by chance constraints. The extension is motivated by a class of problems in sanitary and chemical engineering in which the nonzero entries in the generalized incidence matrix may be random variables. Duality relations are established for appropriate pairs of such chance-constrained programming problems by showing that their deterministic equivalents consist of a deterministic generalized network problem and its dual. It is also shown how these duality relations may be exploited in order to obtain actual solutions to chance-constrained generalized network problems.
Letter to the Editor—Expected Coverage of a Circular Target by Bombs all Aimed at the Center
Authors: Jarnagin M. P.
Published: November 2008

The exact mathematical formulation is given for the expected proportional coverage of a circular target from n weapons all aimed at the center of the target, for arbitrary n. It is assumed that the weapons fall in a circular normal distribution and that the lethal area of each weapon is a circle of specified radius (cookie-cutter lethality function). Typical pages are given from a set of tables. The tables were computed on an IBM 7030 (STRETCH) computer.
Letter to the Editor—A Note on Recent Developments in Additive Utility Theories for Multiple-Factor Situations
Authors: Fishburn Peter C.
Published: November 2008

Many significant developments in theories of additive values or utilities have come forth in the past few years. This note summarizes these developments for research workers interested in the subjective evaluation of multiple-factor alternatives. In particular, assumptions (axioms) that permit the use of an additive-value formula are presented. These may enable one to test the warrantability of an additive procedure in specific situations where the theory might be applied.
Cost-of-Research Index, 1920–1965
Authors: Milton Helen S.
Published: November 2008

The cost-of-research index provides a measure of the cost of technical man-years supported by research and development (R&D) funds expended yearly in the US relative to effort—in contrast to dollars—that has been put forth in US R&D.
Stream of Overflows from a Finite Queue
Authors: Çinlar Erhan , Disney Ralph L.
Published: November 2008

A finite queuing system with a recurrent arrival process and a single negative exponential server is considered. A customer who, upon his arrival, finds the system full departs never to return, i.e., he “overflows.” The process of overflows is shown to be a recurrent process and the distribution of the time between overflows is derived as a recurrence time distribution in a semi-Markov process. In the special case where the maximum number of customers allowed in the system is one, the problem is known as Palm's overflow problem.
A Discrete Version of Pontryagin's Maximum Principle
Authors: Hwang C. L. , Fan L. T.
Published: November 2008

A basic algorithm of a discrete version of the maximum principle and its simplified derivation are presented. An example is solved to illustrate the use of the algorithm.
Letter to the Editor—Stronger Cuts in Gomory's All-Integer Integer Programming Algorithm
Authors: Wilson Robert B.
Published: November 2008

Stronger cuts are available, and easily calculated, than those obtained by Gomory in the construction of his all-integer integer programming algorithm.
Letter to the Editor—Comments on “Reliability Considerations for a Two Element Redundant System with Generalized Repair Times”
Authors: Jewell W. S.
Published: November 2008

It is shown that the reliability improvement factor has an asymptotic behaviour that can be inferred directly, rather than by computational example; a shorter derivation is also presented. Dominant asymptotic terms for an N-element redundant system are derived.
Letter to the Editor—Editor's Note
Authors: Harrison Joseph O.
Published: November 2008

Editor's Note about some resources for researchers.
Two-Stage Programming under Uncertainty with Discrete Distribution Function
Authors: El Agizy M.
Published: November 2008

This paper establishes the relation between two approaches for solving two-stage programming under uncertainty with discrete distribution function. To accomplish this we use optimality conditions and a simple change in variables. We also review, as special cases, a transportation problem and a production-inventory model. For the transportation model we show that any of the corresponding deterministic equivalent linear programs represents a directed network. For the inventory problem we show that the demand constraints can be eliminated in the equivalent linear program. Finally, a stochastic Leontief production model is introduced. Under reasonable assumptions, we establish that its solution can be obtained by solving a certainty Leontief program. Also, we show that the optimal selection of alternative substitute activities is independent of the demand distribution.
A Nonlinear Programming Model for Launch Vehicle Design and Costing
Authors: Rush Benjamin C. , Bracken Jerome , McCormick Garth P.
Published: November 2008

A nonlinear programming model is developed that has as the objective function (to be minimized) total cost of the development, manufacture, and launching of a launch vehicle. Constraints on physical interrelations, basic performance relations, and desired achievements are given as functions of the variables. The variables are physical properties of the launch vehicle such as airframe weight, total inert weight, mass fraction, thrust, propellant weight, length, and other similar properties. The model is for the purpose of assisting in launch vehicle design by generating designs that have minimum cost for selected performance characteristics. Previous work has mostly been in estimating or predicting costs of given designs. This model goes one step further in that it uses cost-estimating relations (CERs) to influence the design. The nonlinear programming models are not convex. The basic model has 25 variables, 34 inequality constraints, and 9 equality constraints. Nonnegativity restrictions hold on all the variables. The nonlinear programming problems have been solved using the sequential unconstrained minimization technique (SUMT).
A Priority Queuing System with Server-Walking Time
Authors: Skinner Charles E.
Published: November 2008

This paper is concerned with the queuing process which arises when one imposes nonzero crossover times on a nonpreemptive priority system with two classes of customers. The objective is to derive the Laplace-Stieltjes transform of the waiting-time distribution function and the queue-size generating function for each class of customers. The results are obtained by first analyzing a simple single queue model with walking time and then extending this model to fit the two queue problem by an appropriate choice of variables.
Letter to the Editor—Optimal Replacement Policies for Hyperexponentially and Uniformly Distributed Lifetimes
Authors: Schweitzer Paul J.
Published: November 2008

Policies of block replacement and replacement only of individual failures are compared. Block replacement is never desirable for hyperexponentially distributed lifetimes. For uniformly distributed lifetimes, block replacement is preferred only if the ratio of per item block replacement cost to per item individual replacement cost is less than 0.3863. The optimal time between block replacements is graphed as a function of this ratio.
Decision CPM: A Method for Simultaneous Planning, Scheduling, and Control of Projects
Authors: Crowston W. , Thompson G. L.
Published: November 2008

DCPM is a method for formally considering the interaction between the scheduling and the planning phases of a project. Thus, if there are a number of competing methods of performing some of the jobs, each method having a different cost, a different time duration, and different technological dependencies, these possibilities are included in the project graph. Then in the scheduling phase, consideration is made of the effects of the alternate methods of performing tasks on the total cost of completing the project. The alternatives that minimize this cost are then selected. The same method can also be applied to the control of the project during its completion, to revise previous decisions in light of actual performance observed.
A Model for Measuring Stock Depletion Costs
Authors: Chang Yu Sang , Niland Powell
Published: November 2008

This paper develops a model for calculating the cost of stock depletion (i.e., being out of stock) for a steel warehouse. A method is presented for computing expected stock depletion costs as a function of prior inability to meet a customer’s demands, both for one stock-out and for a series of future stock-outs. The model considers a set of possible outcomes following each stock depletion, the probabilities for these, and their conditional costs. Costs considered include those of emergency procurement, the opportunity cost of the typical order, and the opportunity cost of the future business to be obtained from the customer. In the problem treated here, one buyer was the sole, or at least the principal, customer for each stock item.
Flow-Shop Scheduling with the Branch-and-Bound Method
Authors: McMahon G. B. , Burton P. G.
Published: November 2008

The branch-and-bound technique has been applied to the three machine flow shop problem where the objective is to minimize makespan. A new method of obtaining the bound has been developed. Rules for ordering the machines and listing the jobs prior to application of the algorithm have been proposed. Computational results are given for a large number of job sets up to 10 jobs, and for a few cases up to 45 jobs.
Deterministic Solutions for a Class of Chance-Constrained Programming Problems
Authors: Symonds Gifford H.
Published: November 2008

It is desired to select a deterministic decision vector x to maximize a function Z(x) subject to one or more independent probability constraints of the form Pr[y(x) ≦ 0] ≧ α, where y(x) is a random vector for each given vector x, and α is a given probability. For this purpose we develop a certainty equivalent model without random variables for our chance-constrained model such that feasible and optimal solutions of a chance-constrained problem and of its associated certainty equivalent problem coincide. Problems with any number of single chance-constraints of the form Pr[y(x) ≦ 0] ≧ α, i ϵ I, where the yı(x) are independent single random variables for given vector x, can be solved directly after converting them to the certainty equivalent form. Problems with joint chance-constraints of the form Pr[y(x) ≦ 0] ≧ α, where y(x) is a random vector for given vector x, require selection from a set of certainty equivalent values in order to optimize the objective function. For the case of linear chance-constrained problems with joint constraints, and where only the b bector contains random variables, we develop a method for transforming any linear programming problem of the form max cx, Ax = b, x ≧ 0 into a cost unitized linear programming problem of the form max 1y, AT−1y = b, y ≧ 0. We then determine how to solve the chance-constrained problem max cx, Pr[A(x) ≦ b] ≧ α, where b is a random vector.
Capacity of Queuing Networks
Authors: Evans Richard V.
Published: November 2008

The equivalence of two concepts of the capacity is developed. Capacity is the limiting load ratio (arrival rate measured in service rate units) for stable behavior. It is also defined as the expected output rate of the system operated under a saturation load. Additional information is obtained about the behavior of a specific example previously considered by the author.
Letter to the Editor—Remarks on Network Simplification
Authors: Hobbs Arthur M.
Published: November 2008

In “The Use of Wye-Delta Transformations in Network Simplification,” Sheldon B. Akers, Jr. stated two conditions that together were supposedly sufficient for the validity of delta-wye transformations on networks with finite vertex capacities. This letter gives a counterexample to the sufficiency of the two conditions and demonstrates the necessity of the first condition to delta-wye transformations.