Search

The article presents abstracts of contributed papers submitted for presentation at the Chicago Meeting. "Some Recent Contributions to the Lanchester Theory of Combat," by Ralph E. Bach, Laislav Dolansky and Harlod L. Stubbs explains that since the original formulation of Lanchester's equations pertaining to the combat of two opposing forces, the theory has been extended, organized and applied by many scientists. Certain more recent extensions of this theory, which have been developed under Project Numerics, will be described in this paper. Another paper "Single-Shot Kill Probability As a Measure of Bombing Effectiveness," by Albert M. Johnson and Vincent A. Ciminera points out advantages of using single-shot kill probability as a measure of bombing effectiveness in evaluating weapon systems. Historically the circular probable error has been employed for this purpose. However, with compressed reaction tunes made possible by future systems and the large effective yields of nuclear weapons, it is more desirable to be able to predict the probability that a single bomb will impact within a lethal distance of its intended target. The computation of this statistic, the single shot kill probability, is accomplished for values of the lethal radius and parameters of the distribution which characterize the bombing system.

Copyright of International Journal of Production Research is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper the traditional capital asset pricing model is reformulated as a system of simultaneous equations in which returns on similar securities are treated as endogenous variables and in which pertinent financial data for particular firms and a market factor are treated as exogenous variables. Such a system is estimated, and serious questions are raised concerning the tenability of the simple linear model so often used to explain capital asset prices under uncertainty. This paper offers a robust test of the capital asset pricing model (e.g., Sharpe [12] and [13] and Fama [3]) assumption which asserts that all of the inter- dependencies among security returns are accounted for solely by the relationship between a single security and a common market index. Also, it examines the relationship of security returns and corporate operating data to determine the extent to which the beta of the capital asset pricing model is simply a summary, surrogate measure for them. The proposed test is based on a simultaneous equation model. Two goals are sought through this research which, first, serves as a direct test of important implications of the capital asset pricing model and which, second, will provide approximations of the magnitude and direction of any biases that may exist in estimates of beta obtained from single index models. [ABSTRACT FROM AUTHOR]

This article presents a note on the paper "Optimal Growth Portfolios When Yields are Serially Correlated." The author offers a solution to finding the optimal amount of money to invest in a given investment opportunity when there is an optimal myopic policy. The author provides several equations that help in this determination process.

The multi-index transportation problem is defined and a summary of the algorithm described in an earlier paper is given. This paper discusses the theorems justifying the use of the algorithm and gives a necessary condition for the existence of a solution. It also describes the formulation of three special-structure linear-programming problems as examples of multi-index problems. The three problems discussed are the capacitated Hitchcock problem, transportation where there is more than one method of transport available, and the transformation of one type of multi-index problem into another. A final section describes problems that have restrictions in the form of inequalities. [ABSTRACT FROM AUTHOR]

This paper develops solutions to extensions of F. W. LANCHESTER'S classical equations of 'modern warfare' (frequently referred to as aimed-fire equations) for combat between two homogeneous forces. In these extensions the lethality of the fire (as expressed by the Lanchester attrition-rate coefficient) depends on time. When the dependence is arbitrary, the solution is an infinite series of recursively related integrals; in special cases, more convenient representations (including representation in terms of tabulated functions) are available. Solutions are obtained in the following cases: (1) the lethality of each side's fire proportional to a power of time and both lethalities initially zero, and (2) the lethality of each side's fire linear with time, but only one side's lethality initially zero. The latter case models the constant-speed approach between forces whose weapons have different maximum effective ranges. [ABSTRACT FROM AUTHOR]

"Speed Words" uses an analogy between the psychomotive force of the dialectic field and the electromotive force of the magnetic field to formulate a conjecture which might be the subject of investigation. Using the term, "meaning time," which is explained, the paper introduces the time dimension as a function of word value. Accepted laws of an electric system are used to suggest parallel laws for the dialectic system. As a result, understanding speed of words is expressed by an equation WS = MT × WF, where WS is the relative speed of a word in terms of its understandability, MT is the meaning time in years of word use, and WF is the word frequency per million words used by a stated audience. Experimental use of this equation and method suggests that there may be as much meaning in a few dozen stable words, of greater meaning age than numbers, as there is in a few dozen digits in the decimal system - used as the basis of science and mathematics. This could lead to revealing an even more basic or universal language. If these points can be stressed, speed words are then only part of a larger concept. There could be a field of thought above, and yet related, to known physical fields. If such a field is postulated and searched for its analogical equivalents, language could, in a mean sense, become the thought field constant, the relationship of ideas, field units; time, the field denominator. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to extend the loop-technique of the stepping-stone algorithm to the generalized transportation problem. The main result (Theorem and Corollary of §6) is, that passing from a basic feasible solution to another one may always be carried out by constructing a simple symmetrical or a double loop (as defined in §2) and computing new values for the variables only along this path. The amount of computations needed for this turns out to be substantially reduced as compared to the usual way of solving the system of equations relating the new basis to the old one. [ABSTRACT FROM AUTHOR]

One of the problems which occupies the work study engineer is that of determining the number of observations necessary in order to estimate the work content of a job with a prescribed accuracy. A new equation is presented for this purpose. [ABSTRACT FROM AUTHOR]

This paper is concerned with the solution of linear and linear goal programming problems in which the values of the right-hand side parameters are not fixed constants. Specifically, we are concerned with linear optimization problems in which the right-hand sides of the constraining equations are free to vary subject to a set of linear constraining equations. By formulating a relaxed linear program wherein the right-hand sides are treated as variables, we show how it is possible to solve one larger linear program that yields as a solution not only the optimal values for the decision variables, but also the optimal values for the right-hand sides. [ABSTRACT FROM AUTHOR]

In this paper we examine the effects of the policies of wage and price restraint that have at various times been employed in Britain since 1945. We have taken the two-equation model that has been studied extensively in the context of data for both the United Kingdom and the United States,[2] and have assumed that, although far from perfect, this model will be a good enough statistical description of wage and price inflation to allow it to catch any major influence of wage and price restraints. In order to see how the potential effects of incomes policies should be specified in this two-equation model, we are forced to examine the derivation of the equations in some detail. In this process we discover that shift dummies which have been used by other investigators[3] to catch the effects of incomes policies are inappropriate and that their use can give rise to misleading results. After conducting tests more satisfactory than those employing shift dummies, we conclude that the data are not inconsistent with the view that wage and price restraints have usually been ineffective in restraining inflation, and also that the restraints have sometimes actually had the effect of raising the rate of inflation above what it would otherwise have been. This perverse effect is very noticeable in the most recent periods of "restraint" since 1966. [ABSTRACT FROM AUTHOR]

THIS PAPER reports on an annual econometric model of import duties which was developed for explanatory and forecasting purposes. In terms of invoices filed with Customs in fiscal year 1968, 59 per cent of merchandise imports were subject to ad valorem duties, 25 per cent were free of duty, 15 per cent were subject to a specific duty and 1 per cent were subject to quota. A tariff can be said to be equivalent to a specified quota if, when substituted for the quota, it gives rise to the same level of importable production;[1] tariffs and quotas are, of course, nonequivalent in terms of their revenue effect. [ABSTRACT FROM AUTHOR]