bluuebunny/crossref_metadata_2025 huggingface dataset:
Markov-Renewal Programming. II: Infinite Return Models, Example
Authors: Jewell William S.
Published: November 2008

This paper is a continuation of a previous one which investigates programming over a Markov-renewal process—in which the intervals between transitions of a system from state i to state j are independent samples from a distribution that may depend upon both i and j. Given a reward structure, and a decision mechanism that influences both the rewards and the Markov-renewal process, the problem is to select alternatives at each transition so as to maximize total expected reward. The first portion of the paper investigated various finite-return models. In this part of the paper, we investigate the infinite-return models, where it becomes necessary to consider only stationary policies that maximize the dominant term in the reward. It is then important to specify whether the limiting experiment is (I) undiscounted, with the number of transitions n → ∞, (II) undiscounted, with a time horizon t → ∞, or (III) discounted, infinite n or t, with discount factor a → 0. In each case, a limiting form for the total expected reward is shown, and an algorithm developed to maximize the rate of return. The problem of finding the optimal or near-optimal policies in the case of ties is still computationally unresolved. Extensions to nonergodic processes are indicated, and special results for the two-state process are presented. Finally, an example of machine maintenance and repair is used to illustrate the generality of the models and the special problems that may arise.
Commentary on “An Outline for Research in Penology” by Robert H. Roy
Authors: Pollard John C.
Published: November 2008

Commentary on Roy, Robert H. 1964. An outline for research in Penology. Oper. Res. 12 1–12.
Optimality Properties of a Special Assignment Problem
Authors: Parikh S. C. , Wets Roger
Published: November 2008

In this paper, it is shown that if the cost matrix of an assignment problem has the following property cij = |j − i| then any basic feasible solution is optimal if and only if its unit components belong to two well-defined symmetric regions. The matrix with above mentioned property is called the “reordering matrix,” because it arose for the first time in the reordering of nodes of a critical path and other acyclic network problems. One deals with similar matrices in some problems related to order statistics.
Response to Commentary by John C. Pollard
Authors: Roy Robert H.
Published: November 2008

Response to Commentary by John C. Pollard (Pollard, John C. 1964. Commentary on “An outline for research in Penology” by Robert H. Roy. Oper. Res. 12 12–14.).
Approximate Circular and Noncircular Offset Probabilities of Hitting
Authors: Grubbs Frank E.
Published: November 2008

For equal or unequal delivery errors and an offset point of aim, the chance that the burst point of a warhead occurs within a given distance of a selected point of the target is approximated by reference to weighted noncentral chi-square distributions. Offset circular and noncircular probabilities of hitting for the two and three dimensional cases may thus be approximated with a single, straight-forward and rather simple technique by the use of an approximate central chi-square distribution with fractional number of degrees of freedom or a transformation to approximate normality. Computations of probabilities of hitting are illustrated by examples. The approximations recommended appear to be of sufficient accuracy for many weapon systems evaluation problems. We do not claim originality for the various parts of theory involved, but rather our purpose is to provide the weapon systems analyst with a reasonable and useful analytical procedure.
Queues with Hyper-Poisson Input and Exponential Output with Finite Waiting Space
Authors: Gupta S. K. , Goyal J. K.
Published: November 2008

In this paper we consider the steady-state solution of the queuing system in which (i) units arrive according to the Hyper-Poisson distribution with n branches; (ii) the queue discipline is first-come, first-served; and (iii) the service time distribution is exponential. Assuming a finite waiting space, we derive the system-size distribution and the mean number of units therefrom. Results are also deduced when an infinite queue is allowed. Another interesting case is discussed when the over-all arrival rate for all the n branches is pre-assigned. Towards the end we study the simple case when no queue is allowed.
A Statistical Evaluation of Recurrent Medical Examinations
Authors: Lincoln Thomas L. , Weiss George H.
Published: November 2008

In this paper we consider the efficiency of different policies for scheduling medical examinations in a search for diseases like cancer, which start without overt symptoms. We treat both periodic and random examinations and allow for imperfect diagnosis depending on how long the disease has been present. The results of our theory are then checked against a rough data fit to the incidence curve of cervical cancer.
Airline System Simulation
Authors: Gunn William A.
Published: November 2008

Evaluation of airline operations considering criteria for both the airlines and the aircraft manufacturer by means of a system simulation is discussed. The airlines must make decisions concerning fleet compositions and flight assignments in the consideration of earnings, competition, and growth. Manufacturers must make decisions years in advance concerning the size of the market and the price of its aircraft. Concepts and model are presented in terms of the factors considered and the more important relations between these factors. The list of factors includes demand, frequency of service, persistence, preference, variability, number of seats, and passengers. Additional considerations include route interaction resulting from the alternate means of traveling from origin to destination using both nonstop and one-stop routes. Other factors considered include system direction, wind, aircraft data, fleet size, cargo, airport data, scheduling period, variable cost, revenue, and net earnings. The output includes the flight assignments on each nonstop and one-stop route as well as related results, an analysis of the service by origin-destination, and a system summary.
A Mathematical Model for Strategic Movement
Authors: Stearns S. D.
Published: November 2008

The mathematical model discussed in this report is meant to be applicable to the problem of planning strategic movements that are “optimum” in the sense that expected nuclear attack casualties to a given population are minimized. In the model, an “attack area” is divided into sectors. Within each sector, the vulnerability of personnel in various categories representing varying degrees of protection is specified, along with the maximum number of occupants allowed each category and the allowed movements between sectors. The principal problem discussed is that of determining a movement plan that minimizes the expected number of postattack casualties in a given attack area. A linear method for finding optimum movement plans is derived, and examples of such plans are given.
Two-Server Bulk-Service Queuing Process
Authors: Arora K. L.
Published: November 2008

In the present paper a two-server queuing process fed by Poisson arrivals and exponential service time distributions has been considered under the bulk-service discipline. Time-dependent probabilities for the queue length have been obtained in terms of Laplace transforms, from which different measures associated with the queuing process could be determined. The mean queue-length and the distributions of the length of busy periods for (i) at least one channel is busy and (ii) both channels being busy, are obtained.
Bargaining Behavior: A Comparison Between Mature Industrial Personnel and College Students
Authors: Siegel S. , Harnett D. L.
Published: November 2008

The study reported here was conducted for two purposes. The primary purpose was to provide an experimental test of certain theoretical models of bargaining behavior. A second purpose, emphasized in this paper, was to study the bargaining behavior of experienced personnel in business as contrasted with the bargaining behavior of college students. The design of the study was dictated by the requirements of the theoretical model; the interest in comparing businessmen with students was subordinate, and did not in itself influence the fundamental features of the design. Thus, while the test of the hypothesis is formal and has some rigor, the comparison of the two subject populations is informal, and is suggestive and provocative, perhaps, rather than definitive. In general the groups were notably similar in regard to their bidding patterns and the equilibrium solutions they reached.
Letter to the Editor—Acknowledgment
Authors: Hardgrave William W. , Nemhauser George L.
Published: November 2008

It has been pointed out that our paper in Operations Research, 11, 889–900 (1963), is quite similar (even to the extent of notation in some cases) to a paper by W. Szwarc in Operations Research, 8, 782–788 (1960). To our embarrassment, we neglected to refer to this earlier paper. To say the least, it should have been given as a reference and, in fact, some of our results should be considered as rediscoveries of original contributions by Szwarc.
Surveillance of a Region by Detection and Tracking Operations
Authors: Dobbie James M.
Published: November 2008

A study is made of the capabilities of a surveillance system to detect and track submarines that are in a region that is under surveillance. The operation consists of barrier searches for submarines entering the region, area searches for submarines that have entered the region undetected, tracking procedures to hold contact on detected submarines, and special searches to regain contact when contact has been lost. The capabilities of the surveillance system are found for a general distribution of submarine on-station times, under the assumption that the recontact rate decreases with increasing time after loss of contact.
A “String Algorithm” for Shortest Path in Directed Networks
Authors: Klee Victor
Published: November 2008

Any shortest-path algorithm A for undirected networks can be combined with the simple cutting procedure C described below so as to form a shortest-path algorithm for directed networks. If a directed network has v nodes and e arcs, then a shortest path joining two specified nodes can be found by min[v, 1/2(e + 2)] or fewer applications of A, each followed by an application; of C.
The Optimal Order to Serve in Certain Servicing Problems
Authors: Frank Ove
Published: November 2008

A production and transportation system is considered in which the produced items successively are transported to N different selling places. Transportation to the N places may be ordered in N! different ways and the effects on the system of different orderings among the selling places when servicing them are studied. If the production capacity is K units per unit of time, and if the N places have associated with them times of transport t1, …, tN and functions f1, …, fN expressing the demand as depending on the time of arrival, it is possible to obtain the total sale on the form KgN{gN−1[… g1(0) …]} where the functions gn are defined in terms of K, tn and fn. Thus the problem to determine the order to serve that maximizes the total sale is reduced to the problem of finding the optimal permutation of gN{gN−1[… g1(0) …]}. When deriving criterions of optimality for the total sale and related measures of effectiveness the following principle is used: Let E(1, …, N) be the effectiveness associated with the ordering 1, …, N and let kn, be some characteristic of place n. If k1 ≦ ⋯ ≦ kN is sufficient (necessary) for E(1, …, N) ≧ E(1, …, n − 1, n + 1, n, n + 2, … N) for n = 1, …, N − 1 then this condition is also sufficient (necessary) for E(1, …, N) ≧ E(i1, …, iN) for every permutation i1, …, iN of 1, …, N.
Development of M-Stage Decision Rule for Scheduling N Jobs Through M Machines
Authors: Dudek Richard A. , Teuton Ottis Foy
Published: November 2008

This paper describes an algorithm that will yield an optimum sequence for n jobs requiring processing through M machines when no passing is allowed. Theoretical development utilizing combinatorial analysis precedes the algorithm and an example problem.
Letter to the Editor—An Algorithm for the Sequential Solution of Schedule Networks
Authors: Goldberg Charles R.
Published: November 2008

A method is presented for the construction of schedule networks on a rectangular lattice and for the solution of the resulting matrix in terms of the event times, slack, and critical path of the network. Some implications for the utilization of the technique are reviewed.
Letter to the Editor—The Distribution of Busy Time for a Simple Queue
Authors: Greenberg Irwin
Published: November 2008

In a single channel queue with Poisson arrivals and exponential service, an arbitrary interval of length τ can be decomposed into busy time, t, and idle time, t0 = τ − t. The frequency function for t is derived for the stationary process.
A Probability Problem Arising in Reliability and Traffic Studies
Authors: Gaver D. P.
Published: November 2008

A system is alternately operative and inoperative; operative times and inoperative times are identically and independently distributed according to arbitrary distributions. Demands for system service occur at exponentially distributed time intervals, and persist for exponentially distributed times thereafter. The system “disappointment time” is discussed, where the latter is the time until either the system fails while a demand is being satisfied, or a demand occurs during an inoperative period. Approximations to the expected disappointment time and to the distribution of disappointment time are suggested. Numerical examples are given.
Lagrange Multipliers and the Optimal Allocation of Defense Resources
Authors: Pugh George E.
Published: November 2008

A simple extension of the Lagrange optimization method is valuable in allocating defense resources among a large number of independent defense locations. This kind of allocation problem is complicated by the fact that the attacker can optimize his attack against whatever defense is chosen. This paper describes an extended or double Lagrange method, which provides strictly optimal allocations for the attacker, but not necessarily for the defender. Nevertheless, by careful use of the method, it is possible to obtain defense allocations that are at least approximately optimum. The major part of the paper provides a technique for verifying results and computing bounds for the error—a technique that is necessary because the uncritical application of the method can occasionally give results that are far from optimum.
A Model for the Control of Arms
Authors: Saaty Thomas L.
Published: November 2008

As the problems and ideas of arms control and disarmament have gained substantial momentum in recent years, the need has developed to look into the refinements of disarmament questions within the framework of national security. Here we have sought to initiate the development of a framework within which one could examine various disarmament questions. Our purpose is to stimulate some operations-research thinking in this area. The model emphasizes the importance of finding criteria for evaluating weapons for disarmament purposes and for establishing rules of disarmament compatible with the broad objectives of the future allowing for possibly different power configurations and new conflicts. The problem of resolving conflicts is another essential area of disarmament briefly touched on here.
Sequencing a One State-Variable Machine: A Solvable Case of the Traveling Salesman Problem
Authors: Gilmore P. C. , Gomory R. E.
Published: November 2008

We consider a machine with a single real variable x that describes its state. Jobs J1, …, JN are to be sequenced on the machine. Each job requires a starting state A, and leaves a final state Bi. This means that Ji can be started only when x = Ai and, at the completion of the job, x = Bi. There is a cost, which may represent time or money, etc., for changing the machine state x so that the next job may start. The problem is to find the minimal cost sequence for the N jobs. This problem is a special case of the traveling salesman problem. We give a solution requiring only 0(N2) simple steps. A solution is also provided for the bottleneck form of this traveling salesman problem under special cost assumptions. This solution permits a characterization of those directed graphs of a special class which possess Hamiltonian circuits.
Occupation Time Problems in the Theory of Queues
Authors: Takács Lajos
Published: November 2008

The author considers a single-server queue and deals with the problem of finding the distribution of the total occupation time of the server in the time interval (0, t) and the distribution of the number of services among the first n services that are not preceded by an idle period. The author also points out the use of the results in the theory of dams.
Letter to the Editor—An Ill-Conceived Proposal for Apportionment of the U.S. House of Representatives
Authors: Gilbert E. J. , Schatz J. A.
Published: November 2008

Burt and Harris advocate the use of minimum range for the apportionment of the U.S. House of Representatives. In this note we suggest that (1) their statements on fairness are ill-considered, (2) their statements on uniqueness are misleading, and (3) the computation they suggest is unnecessarily long. Our discussion of (2) and (3) involves the presentation of an alternative computational scheme. In an appendix, we present a formal proof that the alternative computational scheme always works.
Errata
Authors: Hu T. C.
Published: November 2008

Corrections to “On the Feasibility of Simultaneous Flows in a Network,” Operations Research, Vol. 12, 359–364 (1964).
Removing Arcs from a Network
Authors: Wollmer Richard
Published: November 2008

This paper proposes an algorithm for making a sensitivity analysis on a flow network, specifically, the problem of removing n arcs in a network such that the reduction in the maximum flow between an origin and destination node is maximized. Such an algorithm might be helpful in determining how sensitive a transportation system is to having its roads closed for repairs.
Two Stochastic Traffic Systems Whose Service Times Increase with Occupancy
Authors: Helly Walter
Published: November 2008

Some traffic service systems are characterized by service times that increase with the number of patrons undergoing service simultaneously. Two examples, the operation of a road traffic circle and the placement of toll telephone calls, are modelled to explore this property. The traffic circle model may yield information to determine whether a flow control system is justified. The telephone model leads to a doctrine for the rejection of calls during congested operation. Generally, the traffic capacity of such systems can be maximized only if some of the customers are thus rejected or retarded.
Some Probability Distributions Associated with Commuter Travel in a Homogeneous Circular City
Authors: Haight Frank A.
Published: November 2008

A commuter living outside a circular city arrives at a point on the circumference and is equally likely to wish to travel to every point of the interior. In the present paper we give the probability distribution for trip length, and the probability distribution for traffic weight at each point, under the assumption of six different routing systems.
The Stochastic Properties of Large Battle Models
Authors: Brooks Franklin C.
Published: November 2008

This paper considers stochastic models of large battles. Such battle models are said to be stochastically determined if the gross results—for example, the casualties to each side—show low variance in repeated plays in which only the random numbers are changed. Here, low variance means a standard deviation small compared to the initial number of weapons engaged. When stochastic determinism exists in a large battle model, only a few replications of the model are needed to get good estimates of the gross results. Stochastic determinism with respect to casualties is shown to be present when the correlations between losses of individual weapons are relatively small or few in number; that is, when the fate of a given weapon has strong influence on the fates of only a limited number of other weapons. Three stochastic models—the Lanchester Linear and Square Law models and a simple missile battle model—which can be studied analytically are shown to be stochastically determined. Features of battle models that would lead to violation of stochastic determinism are discussed.
Planning Transistor Production by Linear Programming
Authors: Smith Spencer B.
Published: November 2008

A linear programming model of the production process for transistors is presented. The model has been used in production planning to select materials, processing variables, and activity levels. Model formulation, data collection, operation, and results are described.
A Stochastic Personnel-Assignment Model
Authors: King William R.
Published: November 2008

Personnel assignment decisions involve (a) performance prediction of job success using test results etc., and (b) the determination of optimal allocations of individuals to jobs. A model is developed that integrates these two phases and obviates the theoretical difficulties introduced by their independent application. One form of the model requires value measurements that are beyond the scope of current techniques, making it necessary to present “information conditions” that may reduce the level of the required value measurements.
Signals, Ambiguity, and Strategic Force Structure
Authors: Averch Harvey , Wildhorn Sorrel
Published: November 2008

In this paper we consider some problems that arise when a nation attempts to implement a strategy of stable deterrence over time. The problems arise when a nation's planners make strategic inferences based on an adversary's ambiguous signals of intent and action. A necessary condition for inferring an opponent's strategic objectives is good technical intelligence. We explore some alternative intelligence models and their effect on national response. It appears that even small improvements in the content and timing of intelligence information received by a nation pursuing stable deterrence would help constrain a noncooperative adversary and open new channels of communication.
A Nonlinear Decomposition Principle
Authors: Sanders J. L.
Published: November 2008

A decomposition principle is developed for nonlinear optimization problems. This principle also allows certain classes of problems with convex objective functions subject to concave constraints to be transformed into a problem with convex objective function with convex constraints.
Some Remarks on Finite Horizon Markovian Decision Models
Authors: Derman Cyrus , Klein Morton
Published: November 2008

It is shown that finite horizon Markovian decision problems can be handled as linear programming problems. Thus, problems with large numbers of side constraints, which would be difficult to treat by dynamic programming methods, can be handled by linear programming methods. Fixed and random horizon problems are discussed.
On the Concept of FIFOV in Queues
Authors: Krishnamoorthi B.
Published: November 2008

In several queuing situations, the order in which the units depart is not the same as the order in which they arrived at the system. We call this phenomenon, the “Violation of the ‘First In, First Out’ principle” (FIFOV). A quantitative study of FIFOV is of operational importance in tandem queuing and many other situations. In this paper we give a general discussion of the concept, and study a special aspect of FIFOV in a Poisson Queue (Poisson input and exponential service times) with two heterogeneous servers working in parallel. In this connection the time-dependent distribution of the output in a M/M/1 queue has been explicitly obtained. Defining X as the number of customers superseding a customer taking service from the slower channel, we obtain the distribution and the first two moments of X under a queue discipline that is a modification of the usual one. An optimality criterion has also been suggested.
Some Network Flow Problems Solved with Pseudo-Boolean Programming
Authors: Ivănescu Peter L.
Published: November 2008

The aim of this paper is to apply the method of pseudo-Boolean programming to the determination of the minimal cut and of the value of the maximal flow through a network without, or with, given lower bounds on the arc flows, as well as to the solution of some feasibility problems in networks.
The Optimal Inventory Policy for Batch Ordering
Authors: Veinott Arthur F.
Published: November 2008

We consider a single product dynamic inventory problem in which the demands in each period are independent and identically distributed random variables. There is a constant lead time, a discount factor 0 ≦ α ≦ 1, a unit ordering cost c and an expected holding and penalty cost function L(·) for which −[c(l − α)y + L(y)] is unimodal, and total backlogging of unfilled demand. In addition each order for stock must be in some nonnegative integral multiple of Q, a fixed positive constant. It is shown that the (k, Q) policy is optimal for the finite and infinite period models. With the (k, Q) policy if the initial inventory on hand and on order in a period is less than k, an order is placed for the smallest multiple of Q that will bring the inventory on hand and on order to at least k; otherwise, no order is placed. The optimal value of k is easy to compute and is the same for the finite and infinite period models. The results are generalized to the case where the demand distributions and cost functions vary over time. The (k, Q) policy is not optimal in general for the case where there is also a fixed charge for placing an order.
Optimum Distribution of Switching Centers in a Communication Network and Some Related Graph Theoretic Problems
Authors: Hakimi S. L.
Published: November 2008

The concept of a median in a weighted graph is generalized to a multimedian. Then, it is shown that the optimum distribution of p switching centers in a communication network is at a p-median of the corresponding weighted graph. The following related problem in highway networks is also considered: What is a minimum number of policemen that can be distributed in a highway network so that no one is farther away from a policeman than a given distance d? This problem is attacked by generating all vertex-coverings (externally stable sets) of a graph by means of a Boolean function defined over the vertices of a graph. Then this idea is extended to Boolean functions that generate all matchings, all factors, and all possible subgraphs of G with given degrees.
Letter to the Editor—Kill Probability When the Lethal Effect is Variable
Authors: McNolty Frank
Published: November 2008

Traditionally the probability of killing a point target is analyzed by means of employing a lethal circle (in two dimensions) or a lethal sphere (in three dimensions). The concept of a lethal circle or sphere is based on the assumption of a “kill-no kill” situation in which a target anywhere within the circle (sphere) is killed and a target anywhere outside of the lethal region is not killed. Another aspect of the “kill-no kill” approach is that it combines all lethal effects (heat, shock, x-rays, etc.) in one parameter—the radius R of the lethal circle (sphere). In many problems of weapon systems effectiveness this approach is extremely useful, but in other areas the attendant assumptions are unrealistic and the purpose of this paper is to present a useful alternative methodology. All of the formulas derived are amenable to desk-calculator computation.
Letter to the Editor—On Optimal Extracting from a Multiple File Data Storage System: An Application of Integer Programming
Authors: Day Richard H.
Published: November 2008

This study shows how the problem of optimally selecting files for extracting from an overlapping, multiple file data storage system can be treated as an integer programming problem and solved by means of existing integer programming computer routines. It presents several heuristic file selection problems and suggests how existing integer programming routines could be used in an extracting system. The study concludes that the integer programming formulation is a feasible means of expressing the file selection problem and that existing computer programs may afford useful methods of solution. The file selection problem gives an especially simple integer programming problem; available algorithms, modified to account for this simple structure may be expected to eliminate any chance of failure in operation.
Scoring and Profitability Models for Evaluating and Selecting Engineering Projects
Authors: Dean Burton V. , Nishry Meir J.
Published: November 2008

Recent developments in allocation theory may be applied to research management decision problems in the firm. Of major importance to firms employing engineers in new product development activities are problems involving the specification and allocation of resources such as manpower, funds, equipment, and facilities. To solve these problems, quantitative measures of organizational performance must be derived that are consistent with corporate goals and that include the relevant resource variables, noncontrollable variables, parameters, and constraints. Mathematical models are constructed and solved in this paper that yield solutions for allocating manpower resources to projects. A scoring model is constructed and then used to determine the important factors in a profitability model. The significant elements in the decision process are the uncertainty in estimating model parameter values and the optimal utilization of limited engineering manpower resources where this uncertainty exists.
Letter to the Editor—A Note on the “Fail-Safe” Properties of the “Generalized Lagrange Multiplier Method”
Authors: Charnes A. , Cooper W. W.
Published: November 2008

This paper shows that the Lagrange multiplier method suggested by H. Everett does not have “Fail-Safe” properties when applied to simple situations with nonconvexity only in the functional. Although each Lagrange multiplier problem for these situations has immediate solutions no means of combining them to obtain a solution to any reasonable approximation appears to be visible.
The Remaining Busy Period for a Single Server Queue with Poisson Input
Authors: Erlander Sven
Published: November 2008

Consider a single-server queuing process with Poisson input and general service time distribution. Define the remaining busy period χ(t) as the time from a given instant t until the server becomes idle for the first time. Let ξ(t) be the number of customers in the system at time t. Let χ1(t) be the remaining service time for the customer being served at time t. In this paper we shall study the stochastic law of the remaining service time χ1(t) given that ξ(0) = i and ξ(t) = r. The result will then be applied to the problem of finding the joint distribution of the remaining busy period χ(t) and the number of customers served during χ(t) given that ξ(0) = i and ξ(t) = r.
Divisible Activities in Critical Path Analysis
Authors: Jewell William S.
Published: November 2008

A critical path scheduling problem is investigated in which a single activity can have its completion time divided up and allocated to different “locations” in the project precedence network. An algorithm for determining the allocation that minimizes total project duration is given, together with an outline of an optimality proof, and an example. Although the algorithm is very similar to those used in network-flow type problems, and uses only integer-valued variables, the final results for the divisible-activity network are, in general, rational numbers.
A Class of One-Period Inventory Models
Authors: Fromovitz Stan
Published: November 2008

In most inventory models one of the costs considered is shortage cost. However, this cost is often very hard to measure. For the models considered in this paper, instead of introducing a shortage cost, we define a stock-out penalty function and impose a constraint on it. For example, a constraint on the probability of stock-out can be viewed this way. We exhibit the general, randomized, optimal policy and give graphical and numerical methods of calculating it. We also discuss how our stock-out penalty function is related to shortage cost.
Optimum Redundancy Under Multiple Constraints
Authors: Proschan Frank , Bray T. A.
Published: November 2008

In this paper we develop an algorithm for allocating redundancy among subsystems so as to achieve maximum system reliability without exceeding any of several linear constraints on redundancy. The algorithm represents a generalization of the one developed by Kettelle for the case of a single constraint on redundancy, published in this Journal in 1962.
Letter to the Editor—A Modification of Lanchester's Equations
Authors: Helmbold Robert L.
Published: November 2008

The familiar Lanchester square law attrition model assumes that the attrition produced by a force is independent of enemy force size. This assumption may require modification if the larger force suffers inefficiencies of scale when force sizes are grossly unequal. A modification that alters relative force attrition capability by a factor depending on the force ratio is introduced and discussed in terms of a special case.
Queuing with Nonpreemptive and Preemptive-Resume Priorities
Authors: Chang Wei
Published: November 2008

This paper considers a special queue situation, one in which a single facility serves two major priority classes of customers. Within each class, there are several levels of priorities. The first class has the higher priority. On arrival, a customer of the first class immediately replaces any customer of lower priority being served. The second class has the lower priority, as compared to the first class. On its arrival, a customer of the second class cannot interrupt the current service of a lower priority customer in the system; it must wait until the service is completed. The first class is the preemptive priority, and the second class is the nonpreemptive priority. This paper formulates a theoretical solution for this queuing system, which has a wide range of application in the computer industry. The real-time control program under the multiprogramming environment is an analog of this priority queuing model.
Letter to the Editor—Third International Symposium on the Theory of Traffic Flow
Authors: Edie L. C. , Gazis D. C. , Helly W. , Herman R. , Rothery R.
Published: November 2008

The Third International Symposium on the Theory of Traffic Flow held in New York City, June, 1965, is summarized by the Symposium Committee responsible for the organization of the Symposium held under the auspices of the Transportation Science Section of the Operations Research Society of America.
A Multiphase-Dual Algorithm for the Zero-One Integer Programming Problem
Authors: Glover Fred
Published: November 2008

Following a line of approach recently applied to the 0-1 integer programming problem with some success by Egon Balas, the algorithm of this paper is based upon an underlying tree-search structure upon which a series of tests is superimposed to exclude large portions of the tree of all possible 0-1 solutions from examination. In our method, the specific design of the enumeration and tests, supplemented by the use of a special type of constraint called a “surrogate constraint,” results in an algorithm that appears to be quite efficient in relation to other algorithms currently available for solving the 0-1 integer programming problem. Early indications of efficiency must, however, be regarded as suggestive rather than conclusive, due to the limited range and size of problems so far examined. Following the analytical development of the method, three example problems are solved in detail with the Multiphase-Dual Algorithm to illustrate various aspects of its application. An extension of the algorithm to the general integer programming problem in bounded variables is briefly sketched in a concluding section.
Chance Constrained Programming with Joint Constraints
Authors: Miller Bruce L. , Wagner Harvey M.
Published: November 2008

This paper considers the mathematical properties of chance constrained programming problems where the restriction is on the joint probability of a multivariate random event. One model that is considered arises when the right-handside constants of the linear constraints are random. Another model treated here occurs when the coefficients of the linear programming variables are described by a multinormal distribution. It is shown that under certain restrictions both situations can be viewed as a deterministic nonlinear programming problem. Since most computational methods for solving nonlinear programming models require the constraints be concave, this paper explores whether the resultant problem meets the concavity assumption. For many probability laws of practical importance, the constraint in the first type of model is shown to violate concavity. However, a simple logarithmic transformation does produce a concave restriction for an important class of problems. The paper also surveys the “generalized linear programming” method for solving such problems when the logarithmic transformation is justified. For the second type model, the constraint is demonstrated to be nonconcave.
A Mathematical Model of Supply Support for Space Operations
Authors: Freeman Raoul J. , Gogerty David C. , Graves Glenn W. , Brooks Robin B. S.
Published: November 2008

This paper develops a methodology to evaluate various aspects of logistics supply support of space bases. It is assumed that there exists at the space base a schedule of operations that reflects the day-to-day living, build-up, and scientific experimental activities that are to be carried on. These activities, in turn, set a series of demands or requirements for products over a time spectrum. The supply system must deliver products so as to meet the amounts and times of the product requirements. Each product or module has an earliest and latest time by which it must be delivered. A mathematical model is developed that plans a series of trips, the dates at which each is to be sent, and the composition of the cargoes on each trip that satisfy the series of requirements over a time spectrum imposed by the activities at the space base. The series of trips are an expression of an efficient plan that simultaneously considers demands for different products at different future times and observes the various constraints of the system (e.g., cargo capacity of spaceships). The mathematical formulation of this scheduling problem is a simple nonlinear discrete programming problem. An algorithm has been developed for its solution, and a description thereof is presented. The model is illustrated by showing how it would supply a long-term lunar base. Various uses of the model are described.
Administrative Control of Multiple-Channel Queuing Systems with Parallel Input Streams
Authors: Young John P.
Published: November 2008

Two stochastic models of general theoretical interest and applicability are presented. Both models consider the introduction of decision and control into parallel channel queuing systems with mixed input streams. In the “rate control” model, arrivals are composed of a random, Poisson distributed input superimposed on selected constant rates of input. In the “adaptive control” model, arrivals are composed of a random, Poisson distributed input superimposed on an input controlled by means of instantaneous information feedback as to the state of the system. For both models steady-state probability distributions are derived, together with expressions for the expected value and system variance. The decision-maker exercises control over the system variance and the expected number in the system through the use of decision rules dealing with the arrival process. The models are generalizable to many situations where one is confronted with a demand for service that has both random and scheduled elements.
Two-Link Material Handling Systems
Authors: Morgan John T.
Published: November 2008

This paper considers the steady-state behavior of two-link material handling systems with intermediate storage. Round trip times for carriers in either link are assumed to be random variables. We require the mean rate of flow through the system and the mean number of carriers waiting. Systems with a single carrier in the first link are considered initially, and the desired quantities are found by solving a set of simple linear equations. Since the number of equations increases with the number of carriers in the system, an approximation is examined for systems with a large number of carriers. Finally similar methods are seen to be appropriate for analyzing systems with several carriers in the first link provided the trip times are exponentially distributed.
General Symmetric Dual Programs
Authors: Mehndiratta S. L.
Published: November 2008

Duality and symmetry of nonlinear programs are considered. The duality theorem of this paper assures that if the primal problem is solvable at a certain point of its domain of definition then the dual problem is also solvable at the same point and vice versa.
Mean Value Estimation from Digital Computer Simulation
Authors: Gafarian A. V. , Ancker C. J.
Published: November 2008

Terminating and nonterminating stochastic processes are studied. If digital simulation is used, either a time-slicing or an event-sequencing technique may be used to obtain an estimate of some measure (mean value in our case) of system performance. We consider the variance of the estimate to be the basic measure for determining the goodness of the estimate. Three points are examined: (1) unbiasedness of the estimate, (2) efficiency of the estimate, and (3) variance reduction techniques. For the nonterminating case a large class of steady-state processes having a negative exponential covariance function is studied and curves and specific examples are derived. Replication is shown to be generally superior either to increasing the length of a run or to reducing the sampling interval. For the terminating case, a general expression for efficiency is derived and replication is shown to be superior to decreasing the sampling interval. All results are equally valid for discrete or continuous processes and do not consider the cost trade-offs.
A Second Look at Hanssmann's Inventory Control Model with Special Reference to the Central Store/Sub Store Problem
Authors: Lampkin W.
Published: November 2008

In a paper published in Opns. Res. 7, 483–498 (1959), F. Hanssmann puts forward a model for inventory control of single stores, unbranching chains of stores, and finally branching chains of stores. In particular the model can be used for the problem of a central store supplying sub stores. Hanssmann's model is unrivalled in its versatility, but is derived in an intuitive, heuristic manner, and is open to some criticism on these grounds. The present author has tried to correct these deficiencies and in most cases has verified Hanssmann's intuition. A few of Hanssmann's results appear to be inaccurate, however, and alternatives are put forward to replace these.
Redundancy in Decision-Making Systems
Authors: Rau John G.
Published: November 2008

Decision-making systems consisting of n independent decision devices and designed to include a simple voting redundancy scheme are discussed. It is shown how to determine the threshold level or minimum number of votes that must be received so as to minimize the probability of the system making an incorrect decision. Applications of such systems can be found in the areas of target detection and fault isolation of electronic equipment.
Establishing Objectives, Measures, and Criteria for Multiphase Complementary Activities
Authors: Firstman Sidney I. , Stoller David S.
Published: November 2008

Many diverse types of systems phenomena may be represented by a time-phased sequence of complementary activities. These models are characterized by the requirement that, in general, the initiation of an activity in any given time phase is dependent upon the completion of several complementary activities in preceding time phases. In order to translate over-all system objectives into operationally meaningful concepts for planning and evaluation, it is necessary to establish subobjectives for each of the phases of a multiphase activity, and also for each of the complementary activities within each phase. Subobjectives for each phase should support the achievement of the system objectives, and the complementary subobjectives within each phase should combine to yield the phase subobjectives. Within each phase and activity, depending on the subobjectives, primary and secondary measures and criteria are constructed to ascertain progress toward (or retrogression from) the achievement of the subobjectives. Two particularly appropriate classes of measures and criteria are defined by a (1) time-limit-probability structure and a (2) within-limits structure. It is not always possible to structure subobjectives so that the within-phase and within-activities measures and criteria are concordant and commensurable. Examples of the process and concepts described above are given in the context of generalized countdown and launch activities.
Queuing Systems with Bounded Waiting-Line Length
Authors: Votaw D. F. , Stover A. M.
Published: November 2008

Equations have been developed for the various state probabilities associated with queuing systems having a finite number of sources, waiting places, and service stations. Units that need servicing are generated in the sources. If a service station is free when a unit arrives from a source, the unit's service starts immediately; otherwise, the unit waits in a waiting place, or if there are none available, the unit waits in a source, thus temporarily blocking it from generating additional units. The chemical plant production process is an illustration of such a system. In that process reactors correspond to sources, holding tanks to waiting places, and stills to service stations. The reactors generate batches that correspond to units. It is assumed in this paper that generation of units in an unblocked source follows a Poisson distribution. State probabilities under the condition of statistical equilibrium are given for the following kinds of systems: (1) at each service station the service time is exponential; (2) there is one source and one service station, and the service time is constant.
Letter to the Editor—Signal Flow Graphs and Analog Computation in the Analysis of Finite Queues
Authors: Gue Ronald L.
Published: November 2008

The signal flow graph has been shown to be a useful device for displaying and analyzing discrete state, continuous time, finite Markov processes (3, 4, 5, 6). The one-to-one correspondence between the flow graph and the wiring diagram for an analog computer is discussed. These concepts are summarized and used to outline a framework for the transient analysis of finite queues. Applications are discussed, including cases with non-Poisson arrivals and nonexponential service.
Labor Assignment as a Dynamic Control Problem
Authors: Nelson Rosser T.
Published: November 2008

A problem of labor assignment in a labor and machine limited production system is formulated as a dynamic control problem. The criterion function employed is total in-process inventory cost over a time period [O, T]. The Pontryagin maximum principle is applied to obtain necessary and sufficient conditions for the optimal control. Specifications defining the admissible set of control vectors leads directly to the constrained optimal solution that is found to be a time-dependent control determined by both the queue lengths and transitions among production centers. Some examples are given to illustrate the nature of the resulting priority policies in tandem and network type systems. A number of limiting assumptions and omissions that facilitated analytical resolution of the problem are discussed to suggest challenging possibilities for extensions of the model.