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The article discusses the marginal preference model and its applicability in operations research. The article discusses how mathematical models used in operations research are developed and how these models provide measurements that are needed and used to help satisfy human needs. The article discusses measurements, qualitative measurements, and replication. In describing the use of the marginal preference model, the article highlights the preference defined, optimization within constraints, and a test of the model. Discussion of the applicability of the model is also presented.

This paper extends the notion of convex programming with set-inclusive constraints as set forth by Soyster [Opns. Res. 21, 1154-1157 (1973)] by replacing the objective vector c with a convex set C and formulating a dual problem. The primal problem to be considered is (I) [Multiple line equation(s) cannot be represented in ASCII text] where the sets {K[sub j]} are convex activity sets, K(b) is a polyhedral resource set, C is a convex set of objective vectors, and the binary operation + refers to addition of sets. Any feasible solution to the dual problem provides an upper bound to (I) and, at optimality conditions, the value of (I) is equal to the value of the dual. Furthermore, the optimal solution of the dual problem can be used to reduce (I) to an ordinary linear programming problem. [ABSTRACT FROM AUTHOR]

The problem is that of locating a facility in a region, so as to minimize the weighted sum of distances between customers and facility. This note shows that a subregion containing half or more of the total 'customer-weight,' if it obeys an additional restrictive hypothesis, must include at least one optimal location for the facility. Thus the search for an optimal location can be limited to such a subregion, once identified. [ABSTRACT FROM AUTHOR]

This article proposes a refinement of the usual approximation due to Satterthwaite for making a significance test when the test statistic involves a single mean square in the numerator and a linear combination of mean squares in the denominator, that linear combination involving known positive constants. The test procedure is outlined in detail, and its derivation given in a separate section. The development of the technique essentially involves determining, by successive approximations, a function which serves as the test criterion. This function is given through terms in the cubes of the reciprocals of the degrees of freedom involved in the problem, thereby giving a deviation from the advertised significance level which is smaller (in magnitude) than the deviation provided by the Satterthwaite procedure. An expression approximating the power of the test is also developed. [ABSTRACT FROM AUTHOR]

A noisy duel is a zero-sum, two-person game with the following structure. Each player has bullets which he can fire at any time in [0, 1]. If Player i fires at time t, he hits with probability Pi(t). The functions Pi are continuous and nondecreasing with P[sub i](0) = 0 and P[sub i](l) = 1. The number of bullets each player possesses at any time and the functions Pi are known to both. The payoff is I to the sole survivor, otherwise 0. This article states the authors' earlier result on the existence of a value of a noisy duel and presents a detailed discussion of the structure of epsilon-good strategies and criteria for the existence of good first-shot times. We present tables of values and shooting times for noisy duels, which, in some cases, can be used to trace the play of the game. An additional table illustrates how large an arsenal is necessary to overcome the effects of an opponent's superior accuracy. [ABSTRACT FROM AUTHOR]

Cochran's Q test for differences between related-sample percentages or proportions has generally been incorrectly presented in secondary sources. The most common mistake results from failure to recognize that rows containing only 1's or only O's, i.e., only successes or only failures, do not affect the value of Q. The F test, however, is affected by such rows. The probabilities from the x[sup 2] and F approximations are compared with the exact probabilities in three sets of data. A rule of thumb, based on extensive study of the distribution of Q in small samples, is given as an aid in judging when the x[sup 2] approximation is satisfactory for practical purposes. [ABSTRACT FROM AUTHOR]

A multiple-choice item is called ideal if all its alternatives are equally attractive to every person who cannot answer the item correctly without guessing. This paper discusses reasons for attempting to construct ideal items, develops methods for testing whether items are ideal or at least more nearly ideal than other items, and presents examples of both ideal and nonideal items. [ABSTRACT FROM AUTHOR]

Where Youden's extreme rank sum test is used, an early decision is often possible by performing the trials in sequence with the following method. After each trial is completed, the greatest lower bound and least upper bound of both extreme rank sums are calculated for all remaining trials. If the critical regions cover either or both intervals of the statistics or the intervals lie completely outside the critical regions, the round-robin test is terminated with the acceptance of the proper hypothesis. [ABSTRACT FROM AUTHOR]

Copyright of Revue Française de Sociologie is the property of Presses de Sciences Po 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.)

The article focuses on the curriculum design of elementary mathematics. The success of this teaching allegedly lies on the right use of skill of the learners; it concludes attentive interest, virility, and steadiness of thought. As a teaching aid, an outline for discussion and study for Grades I to IV is suggested. It proposes an activity which could arouse the mathematical reasoning of every student. In this activity, the students are made to discover utmost bend capacity of the sticks of varied kinds, such as pine, ash, hemlock, hickory, elm, red oak and white oak, the determination of weight that could break the certain stick, as well as the bend for each load before the stick breaks. In this way, the students will be able learn number fact and they are taught to answer by measurement.

The article discusses a mathematical model constructed to explain the observed state of an economy, as an equilibrium resulting from the interaction of agents with partially conflicting goals. A reference is made only to the concept of Walrasian equilibrium for an exchange economy with a finite set of private commodities. The tools for the solution of the existence problem were provided by algebraic topology in the form of fixed point theorems. It is sufficient to find economies with commodities and consumers having no pathologies which exhibit a continuum of equilibria.

This article focuses on a study which illustrated the application of a matrix algebra formulation and solution to the problem of calculating standard prime cost variances. If the total material and labor price, mix, and quantity variances for all components are desired, these may be obtained by accumulating the relevant variances for all individual components. If there are a larger number of individual components involved in the manufacture of a single product, certain efficiencies in the computation of these variances may be achieved by setting up the basic data in matrix form and using simple matrix operations to perform the arithmetic. There are several advantages to be gained from the expression of accounting procedures, such as the calculation of standard cost variances, in mathematical form. In the first place, the explicit statement of the variables to be used in the analysis and the mathematical derivation of the formulas involved make it possible for the cost accountant to see clearly what the key elements in the analysis are and how the computational rules which an accountant later follows automatically were arrived at.

In building a curriculam for any school, the educational objective of the school and the character and extent of the educational preparation possessed by the entering students, invariably dominates the process. Since graduate schools of business administration have been excluded from consideration, one can say that the mental equipment and training of the average high-school graduate determine the ability of the student of a collegiate school of business. Three courses have been found to be satisfactory instruments for the student in collegiate schools of business. The first is designed to give a mastery of those mathematical principles and methods which must be used in business, finance, and management calculations, if such calculations are to be made effectively. Other courses are, Course In General Mathematics For Business Students and Elementary Business Mathematics and Advanced Mathematics of Business Management, and Planning and Forecasting. For these 60 hour courses, the tools developed in General Mathematics Course are most helpful.

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 analyzes priority rules that are mixtures of preemption and postponable rules. Whether a preemption occurs is made to depend on some factor in addition to priority class; dependence on the completed portion of service (age) of the lower-priority customer in service and the number of prior preemptions of the lower-priority customer in service are each considered. The stochastic model (without priorities) is that of the M/G/1 queue. The paper obtains first-moment expressions (e.g., expected number of customers in the system) in the steady-state case for each priority class as a function of the particular factor being considered. It then introduces a linear cost model that is a function of expected waiting time and expected number of preemptions, and formulates the problem of finding an optimal rule from each class by considering a parametric class of rules determined by each factor. In each case, conditions are sought for the global optimality of a rule over a class of rules, but results are obtained only after restrictions (e.g., monotone failure rates) on service distributions are imposed. [ABSTRACT FROM AUTHOR]

This paper presents two algorithms for targeting strikes in a lines-of-communication (LOC) network. The LOCs are represented by a network of nodes and directed arcs. It is assumed that the user of the LOCs is attempting to achieve a circulation flow at minimum cost, a very general goal that includes, as special cases, maximizing flow between two points, meeting required flows between two points at minimum cost, and combinations of these two. The algorithms presented here attempt to make such costs as large as possible over time when the effect of targeting strikes is to increase arc-cost functions and decrease arc capacities for a given period of time. The first algorithm treats the situation where arc costs are linear functions of flow; the second treats the situation where arc costs are piecewise linear functions of flow with one break point. [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]

This paper considers an efficient algorithm for finding the optimal design of a module under a special set of circumstances that prevail in the design of a module for logistical applications. The method is based on primal-dual relations between generalized polynomial minimization and its quasi dual. [ABSTRACT FROM AUTHOR]

A certain class of integer programming problems, called asymptotic or steady-state, has been shown by GOMORY to be cost equivalent to a group-optimization problem. This paper extends the algebraic characterization by demonstrating that there are cost-equivalent group problems for all integer programming problems. Finally, the result is interpreted from the viewpoint of dynamic programming, and this provides the turnpike theorem. [ABSTRACT FROM AUTHOR]

This paper presents computational algorithms for the solution of a clam of stochastic programming problems. Let z and y represent the decision and state vectors, and suppose that x must be chosen from some set K and that p is a linear function of both x and an additive random vector ξ. If y is uniquely determined once z is chosen and ξ is observed, we say that the problem has simple recourse. The algorithms presented apply, e.g., when the preference functions h(x) and g(y) are convex, and continuously differentiable, K is a convex polytope, ξ has a distribution that satisfies mild convergence conditions, and the objective is to minimize the expectation of the sum of the two preference functions. An illustrative example of an inventory problem is formulated, and the special ease when p is asymmetric, quadratic, and separable is presented in detail to illustrate the calculations involved. [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 describes an algorithm, based on a recently proposed method due to D.D. Morrison, for solving constrained optimization problems, and shows that it compares favorably with existing methods in several examples. [ABSTRACT FROM AUTHOR]

The article presents a study which dealt with the use of optimum preventive maintenance policies when immediate detection of system failure is uncertain. The authors mention that in the derivation of preventive maintenance policies it is generally believed that system failure are detected and repaired immediately. In connection to this, the authors state that the study aims to develop the preventive maintenance schedule that will optimize system performance when immediate detection or repair failures are not assured. They added that the study showed that even for exponential failure rates, optimum preventive maintenance schedule exist.

The paper considers two-person zero-sum game. Let B be an arbitrary positive real number and let &b.Theta; be a real number between zero and one. First player chooses a number, t1, with t1 ranging between 0 to B+1. Second player chooses a number, t2, with t2 ranging between 0 to B. The pay-off function, &b.Theta, which specifies the amount the first player receives from second player, is given in the article. If &b.Theta; were continuous, it would be known that these two numbers are equal and hence the game would have a well-determined value. However, the pay-off function considered here is not continuous and this standard theorem cannot be applied. It should be clear that the optimal strategies for first player and second player are not unique.

This paper is an extension of previously published work by Bernard O. Koopman to the general case of any number of tasks and any effect function. A systematic method for the numerical calculation of the maximum effect and its corresponding optimum distribution is presented in a form which is also suitable for solution on an automatic digital computer. For the special case of additive returns which saturate, a special graphical or numerical method for any number of tasks is presented with an example worked out in detail A similar method for multiplicative effects is sketched. [ABSTRACT FROM AUTHOR]

The article considers the use of sub-optimization to solve operations research problems. The reason why operations researchers have to sub-optimize is because it is so frequently impossible, either in principle or more frequently in practice, to calculate the consequences of any given action in terms of the appropriate high level criteria. The three classes of sub-optimizations are: those in which there is a one-dimensional objectives function; those in which the objectives function is multi-dimensional; and those which are partial in that objectives which are known to be important are left out because they are not subject to quantitative analysis. The article also provides examples of criterion problem which is simplest in industrial operations research.

A fundamental theorem of mathematical demography states that two closed populations sharing the same extended history of net fertility, no matter how variable, have the same age composition. In consequence, when in any population net fertility has long followed a purely repetitive cycle, age composition must also be repetitive with the same cycle length. Under these conditions annual births follow a path that is an exponential multiplied by a periodic time-function. If the time variation of fertility is a small amplitude sinusoidal oscillation, the periodic component of the birth sequence is also sinusoidal. The relative amplitude and timing of fertility oscillations and the consequent birth fluctuations are functions of the duration (or frequency) of the fertility cycle; the nature of the functions is determined by the age structure of net fertility. Any time sequence of fertility variation over an extended period of time can be treated as if part of a repetitious cycle of very long duration. By Fourier analysis the fertility sequence can be expressed as the sum of a series of sinusoidal terms; and finally the sinusoidal components of the resultant birth sequence can be derived. The calculated birth sequence closely approximates the actual. [ABSTRACT FROM AUTHOR]

Copyright of Demography (Springer Nature) is the property of Springer Nature 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.)

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.

There are two main reasons why an accountant should study mathematics. First, the use of mathematics in problem solving requires a consistent logical approach. This second reason is that certain areas of mathematics have useful applications in the study and in the practice of accounting. Accountants have found, for example, practical applications of certain topics in calculus e.g., profit-volume analysis when the total revenue and total cost functions are nonlinear. The basic reasons for studying computers are parallel to those for studying mathematics. First and foremost, of course, the computer is extremely useful in the solution of many problems confronting accountants and businessmen generally. However, study of computers, and particularly computer programming, also stimulates careful analysis of problems and approaches to their solution and it fosters the habit of organized problem solving. A computer user may call upon canned programs and subroutines for standardized mathematical and statistical calculations without even having to write the programs himself.

The article reports on the process of group discussion regarding the study of functions. The concept of function is described to be a central part of a mathematical thought and can be used specifically to illustrate problems of teaching. The function concept is also illustrated to be in a similar status as the class concept. The functions allows the student of mathematics to define what algebra means and geometry. It also gives fundamental mathematical tools in several areas of mathematics. Moreover, functions are considered to give fundamental building blocks in the study of mathematics.

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 reports on the concept of functions in the study and learning of mathematics. Functions are mathematical entities, designated by many other names that are associated to the different branches of mathematics. One of the characteristics of functions is that it acts upon and combines with certain objects and converting them into unique objects of the same kind. It was through the study of geometry that the functions were first detected. Examples of functions were also accumulated gradually and was not numerous until the start of the previous century.

The article studies a computer model which simulates a Daphnia species, subject to predation, and grazing upon a single-celled algal population. The model was successful in demonstrating that simple biological processes, acting and interacting simultaneously, can generate a great deal of biological complexity. Students may also learn from this model that the computer is a good analytical tool for dissecting and understanding a complex system. To understand the workings of the model requires little mathematical sophistication. Daphnia is a small fresh water crustacean, commonly called the water flea.

Results are developed for play-the-winner sampling for choosing the better of two binomial populations when the maximum number of tests is specified. It is shown that for a fixed number of tests the probability of correct selection with alternating assignment exceeds that for play- the-winner sampling. However, when the probability of correct selection is fixed, neither sampling method is uniformly better than the other as measured by the expected number of tests on the poorer population, or on the total expected number of tests. [ABSTRACT FROM AUTHOR]

We investigate the problem of finding the expected value of functions of a random variable X of the form f(X) = (X + A)[sup -n] where X + A > 0 a.s. and n is a non-negative integer. The technique is to successively integrate the probability generating function and is suggested by the well-known result that successive differentiation leads to the positive moments. The technique is applied to the problem of finding E[1/(X + A)] for the binomial and Poisson distributions. [ABSTRACT FROM AUTHOR]

This paper deals with a model in which Poisson events in fixed time periods are recorded with probability a and left to accumulate into the succeeding period with probability 1-α. The distribution of number of events recorded is obtained, together with its mean, variance, and generating function. [ABSTRACT FROM AUTHOR]

The article deals with the use of a unified algorithm for solving some network-programming problems. The author states that hydraulic and mechanical analogues for the problems discussed in this section are useful in explaining the nature of the solution-process to some whose physical intuition is stronger than their mathematical background. The author also mentions that acquaintance with the studies discussed here will enable the reader to modify the methods for the case where the variable x are restricted to be integers.