bluuebunny/crossref_metadata_2025 huggingface dataset:
Lower Bounds for the Quadratic Assignment Problem Based upon a Dual Formulation
Authors: Hahn Peter , Grant Thomas
Published: November 2008

A new bounding procedure for the Quadratic Assignment Problem (QAP) is described which extends the Hungarian method for the Linear Assignment Problem (LAP) to QAPs, operating on the four dimensional cost array of the QAP objective function. The QAP is iteratively transformed in a series of equivalent QAPs leading to an increasing sequence of lower bounds for the original problem. To this end, two classes of operations which transform the four dimensional cost array are defined. These have the property that the values of the transformed objective function Z′ are the corresponding values of the “old” objective function Z, shifted by some amount C. In the case that all entries of the transformed cost array are nonnegative, then C is a lower bound for the initial QAP. If, moreover, there exists a feasible solution U to the QAP, such that its value in the transformed problem is zero, then C is the optimal value of Z and U is an optimal solution for the original QAP. The transformations are iteratively applied until no significant increase in constant C as above is found, resulting in the so called Dual Procedure (DP).

Several strategies are listed for appropriately determining C, or equivalently, transforming the cost array. The goal is the modification of the elements in the cost array to obtain new equivalent problems that bring the QAP closer to solution. In some cases the QAP is actually solved, though solution is not guaranteed. The close relationship between the DP and the Linear Programming formulation of Adams and Johnson is presented. The DP attempts to solve Adams and Johnson's CLP, a continuous relaxation of a linearization of the QAP. This explains why the DP produces bounds close to the optimum values for CLP calculated by Johnson in her dissertation and by Resende, et al. in their Interior Point Algorithm for Linear Programming.

The benefit of using DP within a branch-and-bound algorithm is described. Then, two versions of DP are tested on the Nugent test instances from size 5 to size 30, as well as several other test instances from QAPLIB. These compare favorably with earlier bounding methods.
Order-Fulfillment Performance Measures in an Assemble-to-Order System with Stochastic Leadtimes
Authors: Song Jing-Sheng , Xu Susan H. , Liu Bin
Published: November 2008

We study a multicomponent, multiproduct production and inventory system in which individual components are made to stock but final products are assembled to customer orders. Each component is produced by an independent production facility with finite capacity, and the component inventory is controlled by an independent base-stock policy. For any given base-stock policy, we derive the key performance measures, including the probability of fulfilling a customer order within any specified time window. Computational procedures and numerical examples are also presented. A similar approach applies to the generic multi-item make-to-stock inventory systems in which a typical customer order consists of a kit of items.
(s, S) Continuous Review Models for Products with Fixed Lifetimes
Authors: Liu Liming , Lian Zhaotong
Published: November 2008

We analyze an (s, S) continuous review perishable inventory system with a general renewal demand process and instantaneous replenishments. Though continuous review systems seem more amenable to optimization analysis than do periodic review systems, the existing literature addressing this type of model is rather limited. This limitation motivated us to seek greater understanding of this important class of inventory models. Using a Markov renewal approach, we obtain closed-form solutions for the steady state probability distribution of the inventory level and system performance measures. We then construct a closed-form expected cost function. Useful analytical properties for the cost function are identified and extensive computations are conducted to examine the impact of different parameters. The numerical results illustrate the system behavior and lead to managerial insights into controlling such inventory systems.
A Simple Heuristic for m-Machine Flow-Shop and its Applications in Routing-Scheduling Problems
Authors: Averbakh Igor , Berman Oded
Published: November 2008

We consider the routing-scheduling version of the flow-shop problem, where n jobs located at different nodes of a transportation network must be executed by m machines (servers) travelling between the jobs. The objective is to minimize the makespan. For this problem, we present a simple heuristic and analyze its worst-case performance.
Applying Experimental Design and Regression Splines to High-Dimensional Continuous-State Stochastic Dynamic Programming
Authors: Chen Victoria C. P. , Ruppert David , Shoemaker Christine A.
Published: November 2008

In stochastic dynamic programming (SDP) with continuous state and decision variables, the future value function is computed at discrete points in the state space. Interpolation can be used to approximate the values of the future value function between these discrete points. However, for large dimensional problems the number of discrete points required to obtain a good approximation of the future value function can be prohibitively large. Statistical methods of experimental design and function estimation may be employed to overcome this “curse of dimensionality.” In this paper, we describe a method for estimating the future value function by multivariate adaptive regression splines (MARS) fit over a discretization scheme based on orthogonal array (OA) experimental designs. Because orthogonal arrays only grow polynomially in the state-space dimension, our OA/MARS method is accurately able to solve higher dimensional SDP problems than previously possible. To our knowledge, the most efficient method published prior to this work employs tensor-product cubic splines to approximate the future value function (Johnson et al. 1993). The computational advantages of OA/MARS are demonstrated in comparisons with the method using tensor-product cubic splines for applications of an inventory forecasting SDP with up to nine state variables computed on a small workstation. In particular, the storage of an adequate tensor-product cubic spline for six dimensions exceeds the memory of our workstation, and the run time for an accurate OA/MARS SDP solution would be at least an order of magnitude faster than using tensor-product cubic splines for higher than six dimensions.
Large-Scale Convex Optimization Via Saddle Point Computation
Authors: Kallio Markku , Rosa Charles H.
Published: November 2008

This article proposes large-scale convex optimization problems to be solved via saddle points of the standard Lagrangian. A recent approach for saddle point computation is specialized, by way of a specific perturbation technique and unique scaling method, to convex optimization problems with differentiable objective and constraint functions. In each iteration the update directions for primal and dual variables are determined by gradients of the Lagrangian. These gradients are evaluated at perturbed points that are generated from current points via auxiliary mappings. The resulting algorithm suits massively parallel computing, though in this article we consider only a serial implementation. We test a version of our code embedded within GAMS on 16 nonlinear problems, which are mainly large. These models arise from multistage optimization of economic systems. For larger problems with adequate precision requirements, our implementation appears faster than MINOS.
Designing Portfolios of Financial Products via Integrated Simulation and Optimization Models
Authors: Consiglio Andrea , Zenios Stavros A.
Published: November 2008

We analyze the problem of debt issuance through the sale of innovative financial products. The problem is broken down to questions of designing the financial products, specifying the debt structure with the amount issued in each product, and determining an optimal level of financial leverage. We formulate a hierarchical optimization model to integrate these three issues and provide constructive answers. Input data for the models are obtained from Monte Carlo simulation procedures that generate scenarios of holding period returns of the designed products.

The hierarchical optimization model is specialized for the problem of issuing a portfolio of callable bonds to fund mortgage assets. The upper level optimization program is multimodal, and a tabu search procedure is developed for its solution. Empirical results illustrate the efficacy of the developed models in designing the appropriate structure of the callable bonds and making optimal allocations of equity and debt among the designed products. Computational results with the implementation of tabu search—on both serial and parallel computers—are also presented.
Incorporating Competence Sets of Decision Makers by Deduction Graphs
Authors: Li Han-Lin
Published: November 2008

This paper proposes an optimization model of incorporating competence sets of group decision makers to maximize the total benefit of the whole group. Such an incorporation model is formulated as finding a deduction graph linked from the nodes of existing competencies to the nodes of desired competencies. Compared with other methods treating competence set problems (Yu and Zhang 1991, Li and Yu 1994, and Shi and Yu 1996), the proposed model can solve problems involving multiple decision makers; in addition it allows the network to be cyclic and to contain compound nodes.
Structural Analysis of a Queueing System with Multiclasses of Correlated Arrivals and Blocking
Authors: Xu Susan H.
Published: November 2008

In assemble-to-order production systems, and others of a similar flavor, it is often the case that orders for components of various types are placed simultaneously, but that these components are manufactured or assembled at separate facilities. The order process introduces correlation among the jobs at separate facilities. The purpose of this paper is to study the effect of this correlation on a variety of system performance measures.

Consider a system that consists of s parallel servers, where each server has a finite buffer and is dedicated to a separate job type. Multiple classes of customer orders arrive to the system, where each class is composed of one or more unique job types. Upon the arrival of an order, each job in the order is separately routed to its designated buffer; if the buffer is full, that job is blocked and lost; otherwise, it enters the buffer and is served according to the FCFS discipline. Under Markovian assumptions, we systematically examine the impact of arrival correlations on system-based performance measures such as the queue length vector and the workload vector and class-based performance measures such as the waiting time vector and the order response time. Among other things, we establish several stochastic orders between performance vectors with different degrees of arrival correlations. We also show that greater arrival correlation can stochastically improve the worst component in a performance vector (e.g., the longest queue, the heaviest workload), reduce the expected sum of the j longest queues, 1 ≤ j ≤ s, and, for any given order type, increase its entering probability and reduce its order response time. Our results can also be extended to the compound Poisson arrival process, where each order contains multiple units of several job types.
Random Yield and Random Demand in a Production System with Downward Substitution
Authors: Hsu Arthur , Bassok Yehuda
Published: November 2008

In this paper, we present and solve a single-period, multiproduct, downward substitution model. Our model has one raw material as the production input and produces N different products as outputs. The demands and yields for the products are random. We determine the optimal production input and allocation of the N products to satisfy demands. The problem is modeled as a two-stage stochastic program, which we show can be decomposed into a parameterized network flow problem. We present and compare three different solution methods: a stochastic linear program, a decomposition resulting in a series of network flow subproblems, and a decomposition where the same network flow subproblems are solved by a new greedy algorithm.
A Method for Strategic Asset-Liability Management with an Application to the Federal Home Loan Bank of New York
Authors: Seshadri S. , Khanna A. , Harche F. , Wyle R.
Published: November 2008

Strategic asset-liability management is a primary concern in today's banking environment. In this paper, we present a methodology to assist in the process of asset-liability selection in a stochastic interest rate environment. In our approach, a quadratic optimizer is embedded in a simulation model and used to generate patterns of dividends, market value and duration of capital, for randomly generated interest rate scenarios. This approach can be used to formulate, test, and refine asset-liability strategies. We present results of applying this methodology to data from the Federal Home Loan Bank of New York.
Bounds and Policies for Dynamic Routing in Loss Networks
Authors: Bertsimas Dimitris , Chryssikou Thalia
Published: November 2008

We consider the problem of maximizing a weighted sum of expected rewards in steady-state in multiclass loss networks under dynamic routing and admission control, with Poisson arrivals and exponentially distributed holding times. By aggregating the underlying Markov decision process, we derive linear programming relaxations that contain the achievable performance region under all admissible policies and lead to a series of progressively tighter upper bounds. These relaxations allow stronger bounds at the expense of higher computational times. We further propose a series of routing and admission control policies from the relaxations that outperform, in computational experiments, other heuristic policies, such as the dynamic alternative routing with trunk reservation and the least busy alternative routing, variations of which are used in practice. The suboptimality guarantees defined as best bound/best policy range from 0 to 2.5% under symmetry conditions (symmetric network topology, arrival rates, link capacities, rewards), and from 4% to 10% under asymmetry conditions. We discuss the qualitative behavior of these policies and obtain insights about their performance.
Dynamic Vehicle Dispatching: Optimal Heavy Traffic Performance and Practical Insights
Authors: Gans Noah , van Ryzin Garrett
Published: November 2008

We analyze a general model of dynamic vehicle dispatching systems in which congestion is the primary measure of performance. In the model, a finite collection of tours are dynamically dispatched to deliver loads that arrive randomly over time. A load waits in queue until it is assigned to a tour. This representation, which is analogous to classical set-covering models, can be used to study a variety of dynamic routing and load consolidation problems. We characterize the optimal work in the system in heavy traffic using a lower bound from our earlier work (Gans and van Ryzin 1997) and an upper bound which is based on a simple batching policy. These results give considerable insight into how various parameters of the problem affect system congestion. In addition, our analysis suggests a practical heuristic which, in simulation experiments, significantly outperforms more conventional dispatching policies. The heuristic uses a few simple principles to control congestion, principles which can be easily incorporated within classical, static routing algorithms.
Optimal System Design with Multiple Decision Makers and Possible Debt: A Multicriteria De Novo Programming Approach
Authors: Shi Yong
Published: November 2008

This paper applies multicriteria de novo programming to formulate and solve problems of system design that involve multiple decision makers and a possible debt. In the framework of the system design model, each involved decision maker has his or her own preference for the budget availability level associated with multicriteria under consideration. If the possible debt occurs in the design time, the model allows flexibility for decision makers to borrow additional money from a bank with a fixed interest rate so as to keep the production process feasible. A contingency plan therefore can be constructed to deal with the debt situation. A solution procedure is developed to design the optimal system with a certain range of budget availability levels. Numerical examples are used to illustrate the procedure.
Analysis of Lagrangian Lower Bounds for a Graph Partitioning Problem
Authors: Adil Gajendra K. , Ghosh Jay B.
Published: November 2008

Recently, Ahmadi and Tang (1991) demonstrated how various manufacturing problems can be modeled and solved as graph partitioning problems. They use Lagrangian relaxation of two different mixed integer programming formulations to obtain both heuristic solutions and lower bounds on optimal solution values. In this note, we point to certain inconsistencies in the reported results. Among other things, we show analytically that the first bound proposed is trivial (i.e., it can never have a value greater than zero) while the second is also trivial for certain sparse graphs. We also present limited empirical results on the behavior of this second bound as a function of graph density.
A Facet Generation Procedure for Solving 0/1 Integer Programs
Authors: Parija Gyana , Gadidov Radu , Wilhelm Wilbert
Published: November 2008

This paper presents the Facet Generation Procedure (FGP) for solving 0/1 integer programs. The FGP seeks to identify a hyperplane that represents a facet of an underlying polytope to cut off the fractional solution to the linear programming relaxation of the integer programming problem. A set of standard problems is used to provide insight into the computational characteristics of the procedure.
The Simultaneous Planning of Production, Capacity, and Inventory in Seasonal Demand Environments
Authors: Bradley James R. , Arntzen Bruce C.
Published: November 2008

Manufacturing managers often address capacity and inventory decisions separately, thus ignoring the interaction between capacity and inventory within a manufacturing system. The separation of these two decisions can lead to an imbalance of capacity and inventory investment. We develop a model that simultaneously plans capacity investment, inventory investment, and the production schedule using return on assets as the objective to maximize. An algorithm is developed that optimizes a fractional objective function for a mixed-integer program. The model was applied at an electronics manufacturer and at a manufacturer of office supplies.
Rendezvous Search on the Line with Limited Resources: Maximizing the Probability of Meeting
Authors: Alpern Steve , Beck Anatole
Published: November 2008

Two players are placed on a line at a distance dwhich is drawn from a known distribution F. The players have no common notion of direction on the line, and each has a resources bound on the total distance he can travel. If Fis bounded and the resources are sufficiently large, then the players can ensure a meeting. The expected time minimization problem in that case has been studied by the authors in a previous paper. Aside from that case the most the players can do is maximize the probability that they meet. This is the problem studied here, for general and specific distributions. This problem generalizes that of Foley et al. (1991), where one of the players is stationary (zero resources).
Optimal Reliability Allocation with Discrete Cost-Reliability Data for Components
Authors: Majety Subba Rao V. , Dawande Milind , Rajgopal Jayant
Published: November 2008

This paper addresses the optimal allocation of reliability among components that are to be assembled into a system. While it is a generally accepted notion that a component's cost is an increasing function of its reliability, most research to date adopts exponentially increasing, closed-form functions to relate cost and reliability. However, in practice such functions are often unknown or difficult to construct, and it is often more reasonable to describe cost-reliability relationships via discrete data sets. We consider such situations, where each component is available at several reliability levels with corresponding costs. The design optimization problem results in a nonlinear integer program. Because every system configuration has an equivalent representation as either a series connection of parallel subsystems or a parallel connection of series subsystems, we provide formulations, linear relaxations, and algorithms for these two.
The Nonpreemptive Priority MAP/G/1 Queue
Authors: Takine Tetsuya
Published: November 2008

This paper considers the nonpreemptive priority queue with MAP(Markovian Arrival Process) arrivals. Since MAPis weakly dense in the class of stationary point processes, it is a fairly general arrival process. Service times of customers of each priority class are independent and identically distributed according to a general distribution function that may differ among priority classes. Using both the generating function technique and the matrix analytic method, we derive various formulas for the marginal queue length distribution of each class. Further, we provide the delay cycle analysis of the waiting time distribution of each class and characterize its Laplace-Stieltjes transform.
Decentralized Adaptive Flow Control of High-Speed Connectionless Data Networks
Authors: Vázquez-Abad Felisa J. , Mason Lorne G.
Published: November 2008

We introduce a permit-based adaptive control scheme for regulating traffic admission in high-speed connectionless data networks, such as the internet. Permits are awarded to potential customers arriving from outside and travel with them towards their destinations, where the permits are assigned to the local controllers. The controllers randomly distribute the permits among the entry gates at the nodes. Customers from outside are not allowed to enter the network unless there are permits available at the entrance node, thus the model is that of a closed queueing network if we model the dynamics of the permits. The goal is to find the permit distribution strategy that maximizes network performance subject to the restrictions of the network topology. A traffic balance approach is used to establish nonuniqueness of the optimal distribution probabilities for the decentralized operation. We exploit nonuniqueness introducing the concept of the automata actions, focusing on two strategies for the actions. For each strategy, a learning automaton is implemented at the controllers using the Kuhn–Tucker conditions for optimality. Our first learning algorithm converges weakly to a unique limit point, which is optimal, while the limit behaviour of our second learning algorithm may be suboptimal. We illustrate our results using computer simulations in order to compare the two strategies for the same network.
Restricted-Recourse Bounds for Stochastic Linear Programming
Authors: Morton David P. , Wood R. Kevin
Published: November 2008

We consider the problem of bounding the expected value of a linear program (LP) containing random coefficients, with applications to solving two-stage stochastic programs. An upper bound for minimizations is derived from a restriction of an equivalent, penalty-based formulation of the primal stochastic LP, and a lower bound is obtained from a restriction of a reformulation of the dual. Our “restricted-recourse bounds” are more general and more easily computed than most other bounds because random coefficients may appear anywhere in the LP, neither independence nor boundedness of the coefficients is needed, and the bound is computed by solving a single LP or nonlinear program. Analytical examples demonstrate that the new bounds can be stronger than complementary Jensen bounds. (An upper bound is “complementary” to a lower bound, and vice versa). In computational work, we apply the bounds to a two-stage stochastic program for semiconductor manufacturing with uncertain demand and production rates.
Operations Research in a Public Corporation
Authors: Edie Leslie C.
Published: November 2008

I am sure you have all heard quite a good deal about operations research in the military, in business, and in industry, and perhaps some about operations research in government. Tonight I would like to take a look at operations research in a somewhat different area—generally that of public corporations and specifically that of The Port of New York Authority. The types of problems in that area are somewhat different from those in business and industry, just as those in business and industry are somewhat different from the problems in the military, from which operations research sprang. The motivations are also different in these different areas. But, the essential unity of operations research is such that the methods, the approach, the principles, the philosophy, personnel, and other attributes of operations research are the same in all of its areas of application. The results too, I think, are somewhat the same, and sometimes they border, as you know, on the spectacular.
The Effect of Departures from Assumption when Manufacturing to a Specification
Authors: Page E. S. , Muris Shirley
Published: November 2008

When manufacturing to a specification articles of which some dimension varies by chance, the best conditions of manufacture can be found theoretically when the distribution of the dimension is known, often a normal distribution is assumed for this purpose. It is shown that even considerable departures from normality cause little change in the optimum conditions, and thus the theoretical calculations based on the normal distribution can be applied in practice over a wider class of situations.
Résumé of Useful Formulas in Queuing Theory
Authors: Saaty Thomas L.
Published: November 2008

This paper is intended as a convenient summary of some results in queuing, which in the author's opinion would be of value to investigators applying the theory to operational problems. The paper is neither intended as an elementary introduction, nor is it an exposition of the techniques used in deriving the results. The main purpose is to present results and briefly point out fields of activity to which the theory has been applied. The basic ideas of the subject of waiting lines will be introduced by means of the following example.
Some Industrial Applications of Military Operations Research Methods
Authors: Kimball George E.
Published: November 2008

Those of US who after the end of World War II invaded the field of industrial operations research bolstered our courage with the thought that there was enough similarity between military and industrial operations so that the methods used to solve military problems might be used in the analysis of industrial problems as well. In retrospect, it is not entirely obvious that this has been the case. To a casual glance there seem to be many differences, particularly in the measures of effectiveness by which the success of operations is judged.
Salvo Hit Probabilities for Offset Circular Targets
Authors: Groves Arthur D. , Smith Ed S.
Published: November 2008

A method, with necessary graphs, is furnished for estimating the probability of at least one hit per salvo round of n missiles for different values of standard deviation for aiming errors of the rounds and ballistic errors or dispersions of the n missiles about their center of impact for the round. The method permits the solution of the problem when the center of impact of the missiles is offset from the center of the target, by expressing the missiles distribution in terms of the distance from the center of the target instead of from the center of impact. Also presented, as of related interest, are approximations of the single-missile round-hit probability for offset circular targets.
Gradient Methods for Constrained Maxima
Authors: Arrow Kenneth , Hurwicz Leonid
Published: November 2008

This paper deals with the application of certain computational methods to evaluate constrained extrema, maxima or minima. To introduce the subject, we will first discuss nonlinear games. Under certain conditions, the finding of the minimax of a certain expression is closely related to, in fact identical with, the finding of a constrained minimum or maximum. Let us consider then a game (in a generalized sense) where player 1 has the choice of a certain set of numbers x1, …, xm that are constrained to be nonnegative for present purposes and player 2 selects numbers y1, …, yn also constrained to be nonnegative but otherwise unrestricted. The payoff of the game, the payment made by player 2 to player 1, will be a function of the decisions made by the two players, the x's and the y's. This payoff will be designated by φ(x1, …, xm, y1, …, yn). To play the game in an ideal way is to find the minimax solution, we know this solution exists under certain conditions. That is, we arrive at a choice of strategies by the two players where player 1 is maximizing his payoff given the strategy of player 2, and player 2 is minimizing the payoff, given the strategy of player 1.
A Possible Solution to the Shortage of Scientists
Authors: Taylor Jean G. , Balloch John
Published: November 2008

An operations-research approach to the problem of the growing shortage of scientists is described. Of the many factors contributing to the shortage, the one chosen for pilot experiment concerns the high-school students' interest in and attitude toward science. High school students were given an opportunity to observe scientists at work, get to know scientists and how they think, and actually to complete an operations-research study. Although the success of the program, in terms of its ultimate aim to motivate students toward a science career, cannot be measured for many years, certain qualitative evaluations can be made in terms of changing student attitude, educational advantage, and the research product.
Evaluating Health Screening Procedures
Authors: Blumberg Mark S.
Published: November 2008

The various objectives and means used in screening populations for disease conditions are briefly presented. Detailed consideration is given to the evaluation of screening done primarily to improve the health status of the screened community. Alternative numerical methods of measuring health benefits are given. The many variables that are subject to control by authorities directing the screening program are listed. A model is formulated for determining the optimum level at which the result of a test should be considered as positive (resulting in recall of the screened person for further diagnostic study). The proposed model is compared with other evaluation methods in use. Data from a diabetes survey are used as an example. The optimum level for screening is shown to depend not only on the biological characteristics of the test, but also on (1) the relative health value to the screened community of true and false positives and negatives, and (2) the prevalence of the disease condition in the population screened.
An Operations-Research Study of Sales Response to Advertising
Authors: Vidale M. L. , Wolfe H. B.
Published: November 2008

This paper presents the results of studies for major industrial concerns on the sales response to advertising. A simple model of the interaction of advertising and sales is described that is consistent with the results of controlled experiments performed on a large number of products and several media. The model is based on three parameters Sales Decay Constant, Saturation Level, and Response Constant. It has proved useful for analyses of advertising campaigns and for allocations of advertising appropriations.
The Mechanical Blackboard
Authors: Machol Robert E.
Published: November 2008

A device has been constructed to aid in solving problems of optimum distribution (the assignment problem, the transportation problem, the traveling-salesman problem, etc). It does not mechanize the algorithm, and therefore, is not a computer, rather, it mechanizes the tedious operations that one is forced to perform in manipulating such problems on a blackboard. While it may be used to solve certain problems, and to demonstrate methods of solution, its primary value is as an aid in the development of new algorithms. It is suggested that building special-purpose mechanical blackboards rather than special-purpose computers may prove a valuable approach in the solution of many comparable problems.
Letter to the Editor—Military Applications of Operational Research
Authors: Abrams John W.
Published: November 2008

Organized military operational research was initially applied by the Royal Air Force at the very outset of the 1939–45 war. Its worth to the armed services was rapidly appreciated, and it was not long before operational research sections appeared throughout the British Services and in those of the United States and Canada.
Letter to the Editor—Possible Motivation for a Stated Concept of Defense
Authors: Walsh John E.
Published: November 2008

Many military operations-research studies are concerned with defense problems. The procedures used to solve these problems are nearly always closely related to the over-all concept of defense. For a specified over-all concept, an understanding of considerations that motivate this concept can be helpful in performing defense studies. This paper presents a possible motivation for an authoritatively stated concept of defense of the United States against strategic attack.
Errata
Authors: Vazsonyi Andrew
Published: November 2008

In my paper, Economic-Lot-Size Formulas in Manufacturing, appearing in the February 1957 issue of Operations Research (pp. 28–44), the cuts for Figs 2 and 8 should be interchanged, similarly, the cuts for Figs 3 and 9 should be interchanged.
On the Construction of a Multi-Stage, Multi-Person Business Game
Authors: Bellman Richard , Clark Charles E. , Malcolm Donald G. , Craft Clifford J. , Ricciardi Franc M.
Published: November 2008

The subject of this paper is a multi-stage, multi-person business game which will be used for executive training purposes by the American Management Association. A discussion of the basic philosophy of game play, and of the many analytical, computational, and conceptual difficulties encountered in the construction of business games, is followed by a description of the game in question, as actually constructed and played, with particular attention to four features which, it is felt, merit consideration: (1) Absence of an explicit criterion function; (2) Principle of marginal change; (3) Hidden formulas; (4) Minimal computation. The game (which, in a number of preliminary plays with top management participating, has met with a favorable reception) is outlined in some detail with a view to showing how it circumvents or overcomes a number of the obstacles described.
The Practical Calculation of Reorder Points
Authors: Marshall Byron O. , Boggess William P.
Published: November 2008

Patterns of demand for an item are usually found to be approximated very well by the Poisson distribution, provided that the sizes of individual sales are taken into account. A method is given that derives the effective sales size from historical data, thus permitting the determination of the proper Poisson parameter. Fitting this distribution to the data permits forecasting of usage and the determination of accurate reorder points. A chart employing the Poisson distribution is given for the simplified reorder-point determination.
A Model for Optimum Control of Stochastic Sampled-Data Systems
Authors: Bishop Albert B.
Published: November 2008

A model is developed for a sampled-data feedback control system for processes having randomly-distributed outputs or involving measurement techniques that introduce a significant component of variance in the measured values of the controlled variable. The principal development concerns a simple proportional control system with fixed proportionality constant. An acceptable range for the constant is determined from stability criteria for the case of a normally-distributed output with constant process variance and is observed to coincide with well-known servo-mechanism design principles. The method of derivation involves successive operations on the normal probability density function. The effects on system response (time constant), oscillatory tendencies, and system variance of various values of the constant (within the acceptable range) are discussed. Finally, two classes of criterion functions are mentioned, from which optimum values of the proportionality constant can be determined. The first involves fixed tolerances on individual items of output, and the second treats costs that are functions of the deviation between desired and actual outputs.
Letter to the Editor—The Data-Enrichment Method
Authors: Lewis Henry R.
Published: November 2008

The following remarks are intended as a nontechnical exposition of an interesting method which has been proposed (not by the present author) to improve the quality of inferences drawn from a set of experimentally obtained data.
Letter to the Editor—The Operations Research Society of Japan
Authors: Fry Macon
Published: November 2008

I thought that your publication might like to have an informal first-hand report on the organization meeting of the Operations Research Society of Japan, which was held at Keio University (Mita Campus), Tokyo, June 15 and 16, 1957.
Minimum Cost Decision-Feedback Systems for Detecting Signals Perturbed by Additive Gaussian Noise
Authors: Harris B. , Hauptschein A. , Schwartz L. S.
Published: November 2008

This paper is concerned with achieving reliable communications at minimum cost. It studies a means of accomplishing this in the form of a decision-feedback system. In this system binary signals are transmitted and three decisions are permitted at the receiver (1) the decision to record the presence of a signal, (2) the decision to record the absence of a signal, and (3) the decision to withhold recording a statement about the signal. Because of noise, the first decision may result in a false alarm and the second in a miss. By withholding judgment in doubtful cases, the risk of a wrong decision may be reduced providing two conditions are met (1) natural (i.e., language) or artificial (i.e., coding) constraints can be utilized within the message to interpret doubtful observations and/or (2) the transmitter can be required to repeat the signal corresponding to the doubtful observation. The latter is the method of decision feedback. The objectives of this paper are two-fold (1) to develop a theory of decision-feedback systems by means of which the optimum conditions of operation in the least cost sense can be specified and (2) to demonstrate that the method of artificial constraints for interpreting doubtful observations is less efficient in its use of the fundamental communication cost parameters, power, bandwidth, and time than decision feedback.
Determination of Optimal Capacities of Service for Facilities with a Linear Measure of Inefficiency
Authors: Hanssmann Friedrich
Published: November 2008

A service facility Fı always employs an “effort” xı to perform a service xı is called its capacity. If a service requires the minimum effort x ≦ xı for performance, the operation is, in a sense, inefficient. The difference xı − x is used as a measure of wasted effort. If a specified number, m, of facilities with different capacities is to be installed, it is possible, for a specified distribution of x, to determine the optimum capacities xı, …, xm such that the total wasted effort is minimal. A simple iterative procedure for so doing is developed and illustrated.
A Laboratory for Combat Operations Research
Authors: Brooks Franklin C. , Hill Floyd I.
Published: November 2008

The Combat Developments Experimentation Center at Fort Ord, California, has been established to measure the effectiveness of Army organizations and procedures in controlled field experiments. Available are approximately a regiment of troops and 250 square miles of land. A technique of experimentation which requires a previously unattained degree of coordination in the soldier-scientist team has been devised. These experiments are, in essence, Monte Carlo war games played with actual troops and equipment. Only weapons effects are simulated.
Decision Theory and Operations Research
Authors: Arrow Kenneth J.
Published: November 2008

Decision theory, as it has grown up in recent years, is a formalization of the problems involved in making optimal choices. In a certain sense—a very abstract sense, to be sure—it incorporates operations research, theoretical economics, and wide areas of statistics, among others. The formal structure of a decision problem in any area can be put into four parts: (1) the choice of an objective function defining the relative desirability of different outcomes, (2) specification of the policy alternatives which are available to the agent, or decisionmaker, (3) specification of the model, that is, empirical relations that link the objective function, or the variables that enter into it, with the policy alternatives and possibly other variables, and (4) computational methods for choosing among the policy alternatives that one which performs best as measured by the objective function. In the last part, the objective function is maximized subject to the constraints imposed by the model. It is for this reason that decision theory is mathematically, to a great extent, a branch of the theory of constrained maxima.
Operational Requirements for a Collision Warning System
Authors: Pina Eduardo I. , Landau Henry J.
Published: November 2008

In this paper operational requirements are developed for a collision warning system under the assumption of airplanes moving in straight line paths at constant velocities. This assumption is believed to be reasonable during the on-route portion of an airplane's flight, but need not hold when airplanes are in a holding pattern around some airport. The problem is first reduced from a three dimensional problem to one of relative motion in a plane. Then, equations are derived which permit equipment resolution requirements to be established as a function of the radius of a safety sphere around an airplane, relative velocity, required warning range, and range at which first measurement is taken. Finally, with an eye toward minimizing computer storage and data handling, a statistic based on the difference between the first and last ordered statistics is considered, and the probability theory is derived to enable the computation of alarm and false alarm probabilities to be made.
Determining Criteria for Evaluating Man-Machine Links in Weapon System Analysis
Authors: Kurke Martin I.
Published: November 2008

To establish a method for evaluating interactions between operators and equipment in a multi-purpose weapon system, instructional materials from appropriate service schools were examined. An analysis of operations was based on these materials. The analysis was made to determine the number and type of man-machine links, and their significance in establishing a model of the system.
Balance and Stability in Competitive Situations
Authors: Quenzer Hans E.
Published: November 2008

A simple method for analyzing competitive situations quantitatively. The competitive situation is defined by six inputs. Two different measures of effectiveness are developed for the offensive and one for the conservative modes of action. The method provides means for determining optimal distribution of disposable resources between offensive and defensive systems, if input data are well enough established. Although written mainly in military terms, it can be used for the analysis of all kinds of competitive situations.
Letter to the Editor—Note on “Optimum Component Redundancy for Maximum System Reliability”
Authors: Robacker John T.
Published: November 2008

This paper of the above title by Robert Gordon, which appeared in the April 1957 issue of this Journal (vol. 5, pp. 229–243), is somewhat misleading, and the conclusion that arbitrarily high reliability cannot be obtained by duplication of components is in error.
The Crisis in Science and Technology and its Effect on Military Development
Authors: Johnson Ellis A.
Published: November 2008

I want to discuss with you this afternoon the relation of science to war and to human welfare, the new instability that increasing physical knowledge has brought to the management and control of war and of human welfare, and the difficulty of managing development and its supporting applied research. It is in this last area that operations research helps.
Letter to the Editor—Comments on Business Games
Authors: Goldschmidt Karl
Published: November 2008

The discussion and study of business games by Bellman, Clark, Malcolm, Craft, and Ricciardi [Opns Res 5, 469–503 (August 1957)] made very interesting reading. The writer feels that a real contribution has been toward training persons to be executives. However, there seems to be a danger in using such business games for already-successful executives.
Letter to the Editor—Metaphysical Considerations Involved in Choosing a Measure of Effectiveness
Authors: Leibowitz Martin L.
Published: November 2008

What is a measure of effectiveness? Let us not waste time mincing over definitions. A measure of effectiveness is a quantitative expression of the degree to which a system fulfills its objective.
Letter to the Editor—Literature to Turkey
Authors: Camp Glen D.
Published: November 2008

Large strides in engineering and science have been one of the products of the modernization program started in Turkey by Attaturk. Taking advantage of scientific advancement in other countries, and of their own rapidly developing universities, the Turks have produced a rapidly growing number of high quality engineers and scientists.
Letter to the Editor—Das Geschutenwerkes Werdebuke
Authors: Reiland Robert F.
Published: November 2008

I shall be most pleased and honored to have mein Geschutenwerkes Werdebuke in Operations Research. Enclosed you well find a copy of the Buke and some cartoons drawn by Mr. Hank Schoenfeldt, one of our illustration artists.
Letter to the Editor—Whither ORSA?
Authors: McCloskey Joseph F.
Published: November 2008

I am disturbed about the Operations Research Society. The only thing I am not disturbed about is the Journal. I would like to propose that the committee for the next annual meeting allow some additional time for the business meeting in order to afford the members some opportunity to voice their thoughts on some rather specific points.
Solution of the Quota Problem by a Successive-Reduction Method
Authors: Votaw D. F.
Published: November 2008

This paper gives a description and illustrations of a general method of solution of the so-called “quota problem” in personnel assignment. The introduction gives a formulation of the problem and an outline of the method of solution. In the following section, general solutions and illustrations are given for the cases of two and three job categories. An illustration for the case of five job categories is given in the concluding section. The quota problem is treated in reference 3, pp 28-35, and reference 4, pp 15-17. The results in this paper are extensions of results in those references. The problem is similar to a special case of the personnel classification problem, reference 5, and similar to a special case of the transportation problem, reference 1, pp 281-298, and reference 2.
Traffic Dynamics: Studies in Car Following
Authors: Chandler Robert E. , Herman Robert , Montroll Elliott W.
Published: November 2008

The manner in which vehicles follow each other on a highway (without passing) and the propagation disturbances down a line of vehicles has been investigated. Experimental data is presented which indicates that the acceleration at time t of a car which is attempting to follow a leader is proportional to the difference in velocity of the two cars at a time (t − Δ), Δ being about 1.5 sec and the proportionality constant being about 0.37 sec−1. It is shown theoretically that the motion of a long line of vehicles becomes unstable when the product of the lag time and the proportionality constant exceeds one-half. The experimental data implies that driving is done on the verge of instability. A variety of other laws of following is analyzed theoretically.