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This note presents some comments on BONDER'S paper on the Lanchester attrition-rate coefficient, which indicate that a valid prediction of average attrition is obtained by using the harmonic mean of the variable attrition rates rather than the arithmetic mean. This change results in a constant Lanchester attrition-rate coefficient being defined as the reciprocal of the expected time to kill a target. An alternate and more general method for obtaining the constant coefficient is presented and some comparative results are displayed. An appendix indicates the conditions for which it is appropriate to use the harmonic and arithmetic means of rates in general. [ABSTRACT FROM AUTHOR]

Some discrepancies in an earlier paper describing a bulk service queuing situation with customer balking or reneging are pointed out. Necessary modifications to make the model more valid are incorporated in a reformulation and an approach for developing the state-time probabilities of the system is suggested. [ABSTRACT FROM AUTHOR]

Léon Wairas' "Correspondence and Related Papers," edited by W. Jaffé is the source book on the birth of mathematical economics. He himself was first to succeed in breaching the wall of the scornful opposition to the application of mathematics to economics, only at the high cost of forty years of a much-resented exile and of endless struggles with this correspondence as a weapon. Still more important, "Correspondence" provides a fascinating example of the social process of discovery with feedbacks through colleagues engaged in similar endeavors. Such records are of special interest for those blessed periods in the history of a science when ideas have ripened to the point where several scientists discover the same things at the same time. This was certainly the case of economics around the 1870's when ten persons independently discovered marginal utility and its relation to relative prices, and around the 1880's when only a slightly smaller number of economists discovered the similar relation for marginal productivities.

Optimization is rightly claimed to be the most significant factor distinguishing the modern approach to machining processes from the orthodox one. Practical results can be obtained from the application of mathematical modelling and optimization techniques.
The paper presents a procedure for solution of machining process optimization problems, with the use of theory of graphs and Bellman's optimum principle.
The finite graph G=(N, A) (where N denoted a set of nodes and A the set of arcs) here presents the set of feasible solutions. Each arc represents a corresponding machining operation and each path the feasible machining process.
A number can be associated with each are the increment of criterion for optimality. Using the optimum principle we can find the shortest possible path in the graph, thus solving given problems of choice for the optimal machining process.
There is a variety of ways in which the performance criterion can be formulated. In this paper only those performance measures having sufficient economical justification are considered. We may minimize the costs of machining processes, or optimize economical effectiveness of capital engaged.
The method presented can be applied with every additive criterion, as well as with some non-additive ones. A practical example illustrates the field of possible application of this method. [ABSTRACT FROM AUTHOR]

The article presents the seventeen illustrative written activities for the enrichment program for mathematics that although, are self-administering, should still be followed by teacher-pupil discussion. The author states that the activities are not designed for a particular grade level, but can be adapted for use at various grade levels.

The primary objectives of this article will be to reconcile the several lease or buy models and identify points where different choices will lead to different conclusions. However, the immediate motivation is the recent article by Johnson and Lewellen on the lease-or-buy decision in this journal. They state, "We will first indicate our disaffections with extant models of this process and then suggest an alternative--allegedly superior--model." For ease in comparing the results of this paper with those of Johnson and Lewellen (hereafter referred to as J & L), to the extent it is feasible, the same set of symbols and equations will be used. [ABSTRACT FROM AUTHOR]

The article presents a discussion about dialectic materialism and modern science. It discusses the conditions in which dialectic materialism creates for scientists and for scientific pursuits. Dialectic materialism holds that internal contradiction are inherent in all things and phenomena of nature, and treats reality being in constant flux and change. The relationship and the contributions of dialectic materialism in physics, theory of relativity, mathematics, and quantum theory are also discussed.

The author comments on the article "A Simultaneous Equation Approach to Financial Planning." He states that in terms of mathematical connotations, "Simultaneous Equation" is an overstatement and that it is pretentious to call a series of equations "simultaneous" because they are accounting identities. He suggests that the authors should have compared their pro forma model with other models in more details. He states that other pro forma models allow for greater flexibility and have users specify several categories of cost separately a function of variables and fixed values.

The article focuses on the random walk theory of stock price behavior which posits that past stock-price movements cannot be used to predict future market prices that would allow traders to profit from the predictions. If stock price movements were to become predictable enough that a profit were possible, proponents of the random walk theory argue that enough market participants would quickly recognize and exploit the pattern. These market participants compete enough to make all non-random fluctuations so small that they cannot be exploited for a profit. As a result, the trader would be as well off with a buy and hold strategy as he would with a mechanical decision rule based upon past price changes.

This paper presents a review of the exact formulae for control limits for P charts and C charts. Also presented are appropriate graphical methods so that these limits may be easily evaluated. The use of the exact methods, given appropriate tables and/or curves, is no more difficult than the approximate methods which are prevalent in the literature. This note is not intended to criticize the approximate techniques which have been used; rather it is intended to illustrate the use of existing theory whereby the errors of approximation may be eliminated. [ABSTRACT FROM AUTHOR]

The article presents the report of the president of the Operations Research Society of America (ORSA) in the U.S. to the membership. He outlines the problems and activities of the society including the amendment to eliminate associate membership, affiliation with the division of mathematics of the national research council, commemorative plaque for the Lanchester prize, consideration of employment of full-time staff member, quality of presentations at ORSA meetings, plans for an international conference on operations research and management sciences and participation in management of the society by members from industry.

Several forms of citation index were compiled with the aid of punched card techniques from 11,000 citations appearing in a coherent body of scientific literature which contained more than 740 citing papers. Preliminary statistics on citation patterns are given. The potential uses of various types of citation indexes are discussed and are related to problems in recording and standardizing data. [ABSTRACT FROM AUTHOR]

This paper considers the case of a product consisting of several components, each of which is batch manufactured. It assumes that the product demands occur singly, and that the components are manufactured in equal-batch quantities in a reorder level-batch quantity system. The paper is concerned with the optimal phasing of the components in order to minimize the variance of holding cost for the product. It shows that the optimal policy is independent of the order of sequencing of the components and is given when the phase lag between consecutive components in the cycle is equal to [(Ai+Aj)/∑all i Ai. (q/2), where Ai, Aj are the unit values of the components, and q is the batch quantity. A specific example is included to illustrate the three-component case and the discrete practical solution for any number of components is indicated. [ABSTRACT FROM AUTHOR]

Assignment problems arise whenever elements of a finite set have to be paired with elements of another finite set in such a way as to maximize a certain function of the pairing. In this paper three different formulations of such a problem are given. They are analyzed and a method for obtaining a low-cost solution is developed. [ABSTRACT FROM AUTHOR]

This paper contains a brief résumé of a mathematical foundation for construction and analysis of accelerated life tests The effects, on distribution of time to failure, of several special methods of accelerating life are studied A special type of accelerated life test for capacitors is examined in detail Three methods for estimating the parameter of the original distribution, from data gathered from the accelerated tests, are indicated if the original distribution is negative exponential [ABSTRACT FROM AUTHOR]

This paper applies residual analysis to build up improved forecasts from exponential smoothing models. The resulting model is not unknown, but the method of achieving it is more straightforward and intuitive than existing methods. The paper also shows that the model is identical to IMA(k, k) forecasting models. [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]

This paper presents an approach, similar to penalty functions, for solving arbitrary mathematical programs. The surrogate mathematical program is a lesser constrained problem that, in some cases, may be solved with dynamic programming. The paper deals with the theoretical development of this surrogate approach. [ABSTRACT FROM AUTHOR]

This paper gives general conditions for the convergence of a class of cutting-plane algorithms without requiring that the constraint sets for the subproblems be sequentially nested. Conditions are given under which inactive constraints may be dropped after each subproblem. Procedures for generating cutting-planes include those of KELLEY, CHENEY AND GOLDSTEIN, and a generalization of the one used by both ZOUTENDIJK and VEXNoTT. For algorithms with nested constraint sets, these conditions reduce to a special case of those of ZANGWILL for such problems and include as special cases the algorithms of Kelley, Cheney and Goldstein, and Veinott. Finally, the paper gives an arithmetic convergence rate. [ABSTRACT FROM AUTHOR]

This paper introduces a generalization of the frequently discussed problem of finding the optimum redundancy that maximizes the reliability of a network of components. Past work has restricted consideration to arrangements of redundant components called series-parallel networks. This paper allows a much broader class of arrangements called series-parallelseries networks. It is important to consider such arrangements for realistic situations in which components have more than one failure mode, or the combination of parallel paths introduces a failure probability. A dynamic programming algorithm is used to solve the more general problem for the case in which there are no constraints on the optimum solution. The algorithm is extended to handle multiple constraints using dominance and a variety of elimination methods to reduce the storage required in a compurer implementation of the algorithm. Problems with as many as 15 serial components and three constraints have been solved with reasonable digital computer computation times. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

The article reports on the discussion of the study concerning the learning of mathematics. The discussion contains arguments regarding the paper written by professor Stone about functions. One of the arguments that is given attention to, is the concept of function being connected with the primitive concepts of pure logic, nearly unanalyzable and must be grasped by a psychological act of direct perception. This argument is also related to the child's development as the notion of grasping and perception are described to occur at some point in the development.

The article is a comment on an article "Matrix Theory and Cost Allocation," by researchers T.H. Williams and C.H. Griffin, published in the July 1964 issue of the journal "The Accounting Review." According to the author, Williams and Griffin were the first to select this topic as an illustration of the application of matrix algebra to accounting problems. The model presented by Williams and Griffin is a matrix formulation of the popular simultaneous equations method of past years. It was pointed out that the aggregate cost of service departments after allocation in the Williams and Griffin model is more than the combined direct cost before allocation. The scope of this paper has two dimensions: first, to attempt to clarify the matrix algebra approaches that have already been posed and place them in perspective; second, to present a new matrix model of reciprocal service cost allocation and relate it to those previously presented. It would be assumed that each service department will have some of its cost allocated to some of the producing departments.

Randomly-generated linear programming problems of three different types and five different sizes were solved by the criss-cross method and by the simplex method. One hundred problems of each type and size were solved, and the results are overwhelmingly favorable to the criss-cross method. An improvement to the criss-cross method used in these tests is given, and the extension of the results of the paper to variations of the criss-cross and simplex methods is discussed. [ABSTRACT FROM AUTHOR]

In this paper the dual method and the poly-ω technique are specialized for the generalized transportation problem. A simple procedure is obtained for solving the parametric version of this problem, i.e. for passing from a solution optimal for given values of the parameters, to solutions optimal for other values of the parameters. This procedure is then extended to the case when not only the parameters change, but additional constraints appear. Finally, the procedure may be used as a general method for solving the usual (non-parametric) generalized transportation problem, and for this case a way is described for finding an initial (dual-feasible) solution. [ABSTRACT FROM AUTHOR]

This paper describes an algorithm for the solution of mathematical programming problems having a linear objective function and non-linear constraints. The algorithm is basically an adaptation of the simplex method to the case of non-linear constraints. Certain complications are, however, introduced through non-linearity in the constraints, and it is shown how these can be overcome. [ABSTRACT FROM AUTHOR]

The duration of time between two successive births or between marriage and first birth is an indicator of the level of fertility of a couple. Potter and Parker (1964) and Singh (1961, 1967) have suggested the Type I Geometric as a distribution appropriate Or representing the length of interval to first conception leading to a live birth. Potter and Parker estimated the parameters of this distribution with the help of the first two moments. Majumdar and Sheps (1970) pointed out the limitations of these moment estimates and gave a method to Obtain maximum likelihood estimates, based on formulas which are too involved for solution without the help of a computer. Singh proposed a continuous probability distribution based on another set of assumptions for the above situation. He outlined a method to obtain best asymptotically normal estimates of the parameters. These estimates are obtained after several iterations starting from any set of consistent estimates. The objective of this paper is to show that it is relatively easier to obtain maximum likelihood estimates of the parameters of the continuous model, which describes the data on duration to first conception as well as does the discrete model. Simple expressions for the moment and maximum likelihood estimates with the corresponding covariance matrices are obtained. Application is made to three sets of data. [ABSTRACT FROM AUTHOR]

Place-of-birth-by-residence data, tabulated by age and sex for the same areal units in two successive censuses, have been used to estimate intercensal net migration flows. However, a fuller use of the same data permits the estimation of place-to-place flows. This paper describes a method for estimating intercensal migration streams from place-of-birth- by-residence data and illustrates its application with data on the white female native population of the United States. [ABSTRACT FROM AUTHOR]

For solving the flow-shop scheduling problem, this paper examines elimination techniques that reduce the set of solutions to a subset that must contain the optimal solution being sought. The paper shows (1) that the elimination method of SZWAKC [Naval Res. Log. Quart. 18, 295–305(1971)] removes at least as many solutions as any other method, and is therefore optimal, and (2) how to construct a general counterexample to any procedure that removes more sequences than this optimal method. [ABSTRACT FROM AUTHOR]

This paper describes and discusses some search problems, starting with the case of no false contacts, to provide a foundation for developing a search theory in the presence of false contacts. Important properties of the search plan are defined and illustrated by examples. After a general description of false-contact generators and alternative actions that may be used when contacts are made, the problem is formulated for the case in which false contacts are generated by real stationary objects that are investigated when contacted. It is shown that the formulation and solution of the standard optimization functionals are contingent on the number of false targets found, in general, and possibly on the locations and times of contact as well. The optimization functional is difficult to write and more difficult to solve. The formulation is made for the expected-time functional when the number of false targets is bounded. Finally, the paper outlines a procedure for ending the solution and illustrates it with an example. [ABSTRACT FROM AUTHOR]

This paper considers an n-phase generalization of the typical M/M/1 queuing model, where the queuing-type birth-and-death process is defined on a continuous-time n-state Markov chain. It shows that many models analyzed in the literature can be considered special cases of this framework. The paper focuses on the steady-state regime, and observes that, in general, closed-form results for the limiting probabilities are circuit to obtain, if at all possible. Hence, numerical methods should be employed. For an interesting special case, explicit results are obtained that are analagous to the classical solutions for the simple M/M/1 queue. [ABSTRACT FROM AUTHOR]