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Comments on various statistical studies , featured in the August 1971 issue of the periodical 'Technometrics.' Estimation of linear parameters in nonlinear regression; Mean square error prediction as a criterion for selecting variables; Method of picking and transforming variables; Difference between integrated mean square error and mean square error.

Organizational research generally does not use experiments or multivariate analysis to verify propositions. This paper indicates four types of designs that characterize such research. Suggestions are advanced for each type of design, which would improve the logical rigor of such research and thus provide better propositions for verification by means of experiments and multivariate analysis. [ABSTRACT FROM AUTHOR]

The article presents discussions by economists on some papers that are published in the May 1, 1970 issue of the journal "American Economic Review." The author states that his comments are directed mainly to the paper by economist R. Radner and L.S. Miller. The author is particularly interested in the data Radner and Miller have assembled on variations in faculty-student ratios among groups of institutions and over time. However, before commenting on that aspect of their paper, the author wants to know how student aid is treated in their analysis. The author cannot tell from the paper itself how this variable has been handled and yet it is clearly of great importance in many cases. To return to the faculty-student ratios, the intriguing question is, of course, related to observed patterns. The difficulty that Radner and Miller have had to-date in finding systematic relationships between faculty-student ratios and other variables, or even in presenting much in the way of conjectures, attests to the complexity of the problem. It also serves as a challenge to economists to come up with some ideas of their own. In this spirit, the author suggests that variations in faculty-student ratios can be understood only in the context of more complete behavioral models for various groups of institutions.

This paper draws attention to the increasing use of the concept of "model" in accounting literature. It distinguishes between economic models and accounting models, defines the latter, demonstrates the presentation of a whole accounting cycle in the mathematically formal way of an accounting model, discusses by way of a practical example the independent and dependent variables in such a system and shows how the structure of accounting models is graphically presentable. It finally gives, with the aid of some balance-sheet-ratios, an example of combining accounting models with economic models and indicates the application of this approach to a prospective area which still can be considered to be the accountant's. The paper, however, intends to be nothing more than an experiment. There is no denial that the conscious and systematic application of mathematical models to certain branches of economic science opened new paths and perspectives, not without enriching our insight into many a problem. It therefore seems to be comprehensible if accountants try to dabble and experiment in this apparently promising field.

This paper discusses the use of unmeasured variables in path models. Problems of estimation of the path coefficients of a path model are explored when unmeasured variables are utilized as both causes and effects (intervening variables). The paper concludes with a discussion of conditions for the identification of a path model containing unmeasured variables and some remarks on the substantive interpretation of unmeasured variables. [ABSTRACT FROM AUTHOR]

The article presents several letters to the editor referencing various articles and topics discussed in previous issues of the journal "Management Science," including comments on Ralph D. Snyder's paper "A Note on the Location of Depots," comments on the storage reduction scheme proposed in an article by Eugene L. Lawler, and a discussion of the article "Redundant Constraints and Extraneous Variables in Integer Programs," by David Rubin.

The paper presents a method for solving the linear programming problems, which is itself a step towards the generalization of the classical Simlex Method. It replaces two basic variables by two non-basic variables at each iteration. Naturally this will reduce the total number of steps to reach the final solution. The paper also includes the solution of one example to illustrate the applicability of the method. [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]

This section presents abstracts of research and articles on general economics and methodology used in economics. G. O. Bierwag and M. A. Grove devote their paper Indifference Curves in Asset Analysis to a geometrical demonstration of the transformation that maps indifference curves from the expected value-variance space to the asset space. The paper then proceeds to discuss the properties of indifference curves in the asset space. Meanwhile, A. F. Chalk shows that Bernard Mandeville's principal work, The Fable of the Bees, is representative product of the so-called transitional stage in the development of economic thought. As such, it contains a mixture of liberal and mercantilist elements which preclude its being categorized as either consistently laissez-faire or interventionist in outlook. Turning to economic analysis, C. Schotta examines the problem of selection of variables in formulating theories and hypotheses concerning social and economic behaviors in the paper Values in Economic Analysis: a Methodological Issue. Schotta argues that while considerable precision is utilized in deriving conclusions from economic models, the degree of precision used in selecting the variables included in the model is very much less.

The author discusses the pattern analysis of variance of sample estimates of plant cover changes as the distance between samples increases. The author mentions the disagreement between his work and the data from the similar studies conducted by Greig-Smith at Bangor. The author argues that variance between samples could often be satisfactorily represented by a linear regression connecting log variance with log spacing; and that in any case such a linear regression would account for by far the major part of the differences in variance observed.

The article discusses the estimation of measurement error using multiple indicators. A number of recent papers have considered various approaches to measurement error by utilizing explicit causal models linking unmeasured variables to their measured indicators. In general, we know that unless there are a large number of measured variables relative to unmeasured variables it will be difficult, if not impossible, to reach definite conclusions, since the existence of unmeasured variables in a causal system introduces a relatively large number of unknowns, thereby necessitating additional assumptions which are often rather implausible. In this article, the author would like to combine selected features of the arguments developed by researchers Herbert L. Costner and David R. Heise, while emphasizing the flexibility of the general approach that is common to both papers. When we study the implications of non- random measurement errors, even where we have multiple indicators and several time periods, we begin to see the importance of careful measurement at the data collection stage, as well as working with large samples that have been carefully designed.

This paper presents a theoretical basis for cost-effectiveness analysis. It is argued that, frequently, a range of effectiveness or cost levels may be acceptable to whoever must ultimately decide which military system (if any) should be acquired. The function of the analyst is to present a schedule of alternatives and not to optimize in the sense that he recommends the selection of a particular alternative. The formulation of the schedule is discussed where the cost and effectiveness associated with each alternative are viewed as random variables. The paper concludes with some general observations relating to military system selection. [ABSTRACT FROM AUTHOR]

The article presents discussions by economists on various papers that are published in the May 1, 1953 issue of the journal "American Economic Review." The discussion based on economist Lyle C. Fitch's paper, which dealt with expenditures of government in the U.S., states that at the beginning of his analysis, Fitch called attention to variables affecting public expenditures. Among them, Fitch listed the size of the population and the amount and the cost per unit of benefits and services provided for each person. He held growth in the national income or product to be an indirect influence tending to increase public expenditures. But Fitch found the effect of these variables impossible to measure. He also pointed out that the distribution of increases is to be considered in any appraisal of their effect. Fitch also stated that an urban community requires greater variety of services. He doubted whether the adjustment of expenditures by a consumer price index necessarily corrects changes in prices, by the government.

This paper is concerned with characterizing decision rules for the sequential E-model of chance-constrained programming. A key feature of our characterization will be a detailed discussion of various interpretations of the probability operator in the chance constraints. Specifically we define two new classes of decision rules by exhibiting those sets of constraints which locally support the corresponding probability requirements. The question of how the probabilistic constraints for future periods are affected by previous decisions and realizations of the random variables is considered in detail. Since we are primarily concerned with the feasibility of decision rules, we deal mainly with the constraints of the model. The procedure for selecting the optimum rule from among a particular class of feasible rules depends on the objective function and is briefly discussed in the final section along with some implications concerning the form of the optimum rule. The application of our proposed rules to a two-period example previously appearing in the literature concludes the paper. [ABSTRACT FROM AUTHOR]

In this paper we study a model that minimizes the sum of production, employment smoothing, and inventory costs subject to a schedule of known demand requirements over a finite time horizon. The three instrumental variables are work force producing at regular-time, work force producing on overtime, and the total work force. Overtime is limited to be not more than a fixed multiple of regular time. The idle portion of the work force and the levels of inventory are resultant variables. We postulate the following shape characteristics for the cost functions production costs are convexlike, smoothing costs are V-shaped, and holding costs are increasing, both the production and holding cost functions need not be stationary. In this paper, we provide upper and lower bounds on the cumulative regular-time plus overtime work force for any sequence of demand requirements. We also give the form of an optimal policy when demands are monotone (either increasing or decreasing). Finally, we derive the asymptotic behavior of optimal policies when demands are monotone and the planning horizon becomes arbitrarily long. All of these results, which convey information about the numerical values of optimal policies, given specific demands and an initial level of inventory, depend only on the shape characteristics of the cost functions. Algorithmic techniques are discussed elsewhere. [ABSTRACT FROM AUTHOR]

This paper considers a class of algorithms for solving quadratic programming problems. An attempt is made to rank the various procedures. Computational results are given and a discussion of the results is presented. [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]

In this paper the results of some new structural estimates of liquidity preference may be found. The justification for presenting them is that they differ from earlier estimates in certain ways. In some cases, the implications of these estimates differ sharply from the implications drawn by other observers on the basis of their estimates. Three broad issues will be raised. The first concerns the question of the existence of a significant relationship between long-term interest rates and the supply of money. Previous interesting studies have led observers to believe that no significant relationship does exist and they have been led to focus upon short-term interest rates instead of long-term interest rates. Here, the evidence indicates that a highly significant relationship does indeed exist between long-term bond yields and the money supply, provided the money supply is defined to include time deposits. The second issue to be discussed concerns one aspect of the form of the regressions—whether the rate of interest variable should be the dependent variable or whether instead the money supply should be the dependent variable. Those who prefer to speak in terms of a Keynesian "liquidity preference" function typically place the interest rate variable on the left side of the equation, while those who like to speak of the "demand for money" prefer instead to place the money supply variable on the left. The correct form, of course, if the purpose of the experiment is to test a theory, depends upon whether the theory indicates that the causal force runs from the money supply to the interest rate, or from the interest rate to the money supply. It is argued below that the rate of interest should be on the left if nominal balances of money are used in the regressions and if the desire is to provide monetary managers with information on the likely impact of their policy actions. If, instead, the money supply appears on the left, it should be measured in terms of... [ABSTRACT FROM AUTHOR]

The article discusses modeling simple dynamic cash balance problems. The author states that scientists have demonstrated the applications of the maximum principle to solve simple dynamic cash balance problems. He explains that scientists brought forth the idea of penalty function to solve the cash balance problem with bounded state variables arising out of disallowing overdrafts and short selling. He states that this resulted in the adjoint equations which contain terms in the state variables x(t) and y(t).

This part of the paper introduces some possible implementations of Self-Scaling Variable Metric algorithms based on the theory presented in Part I. These implementations are analyzed theoretically and discussed qualitatively. A special class of SSVM algorithms is introduced, which has the additional property of being invariant under scaling of the objective function or of the variables. Experimental results are provided for a particular case of this class. This case has been tested in comparison to the DFP algorithm on a variety of functions with up to 50 variables. The results indicate that the new method has substantial advantage for functions with a large number of variables. [ABSTRACT FROM AUTHOR]

The article presents comments of the authors on the review of their article by Professor C. Horack Hamilton. The paper was based on the analysis of net migration rates in the U.S. in 1950-60 by using multiple regression model. Authors of the article suggest that the usage of terms "variables" and "covariable" to identify the independent variables are common and accepted. It is made clear that the mathematical model, employed in the paper, did not include an independent variable to reflect natural increase as it is suggested by Hamilton. And the two educational variables used in the analysis, median years of schooling by persons 25 years of age and over, the percentage of the population 25 years of age and over completing 4 or more years of high school, are closely related. The computation of the overlapping and net effects of each independent covariate helps in determining the highly correlated variables and eliminating those variables from the model, but the overlapping effects provide no information regarding the nature of interactions which may exist and don't show the response surface of interacting variables.

This paper presents an improved stochastic model for the behavior of the daily census and associated waiting variables in general-acute hospitals. The development and form of the distributions derived follow the general approach of a previous paper by Shonick [J. Amer. Statist. Assoc. 65, 1474–1500 (1970)], but greater flexibility is provided for the health-services planner by increasing the number of decision choices available for achieving given outcomes. This increased flexibility is attained via a generalization of the queuing discipline, permitting admissions of elective patients to be suspended when the number of occupied beds reaches a predetermined level (which may be less than the total bed complement). For any emergency-elective mix of the demand for hospitalization, this model permits the computation of many measures of operating efficiency, including expected overfill rate, percentage occupancy, waiting-list length, and loss of emergency patients. A variant of the model permits computation of the expected number of patient days that will be served in ‘nonapproved’ facilities when emergencies arriving during ‘full’ periods are accommodated therein, rather than turned away. [ABSTRACT FROM AUTHOR]

This paper presents a computational procedure for the solution--via reduction to a parametric quadratic program--of the 'minimum-risk problem' associated with a stochastic linear program where costs are random variables with normal multidimensional joint distribution, i.e., for the nonlinear program max[subx&isinX] (c'x--t)/(x'Vx)[sup1/2] where t is a given number, V a positive-definite matrix, and X a given convex polyhedron in n-dimensional Euclidean space R[si[n]. [ABSTRACT FROM AUTHOR]

In earlier papers [Opns. Res. 9, 849-859 (1961), and 11, 863-888 (1963)] the one-dimensional cutting stock problem was discussed as a linear programming problem. There it was shown how the difficulty of the enormous number of columns occurring in the linear programming formulation could be overcome by solving a knapsack problem at every pivot step. In this paper higher dimensional cutting stock problems are discussed as linear programming problems. The corresponding difficulty of the number of columns cannot in general be overcome for there is no efficient method for solving the generalized knapsack problem of the higher dimensional problem. However a wide class of cutting stock problems of industry have restrictions that permit their generalized knapsack problem to be efficiently solved. All of the cutting stock problems that yield to this treatment are ones in which the cutting is done in stages. In treating these practical cutting problems, one often encounters additional conditions that affect the solution. An example of this occurs in the cutting of corrugated boxes, which involves an auxiliary sequencing problem. This problem is discussed in some detail, and a solution described for the sequencing problem under given simplifying assumptions. [ABSTRACT FROM AUTHOR]

One of the most important concepts in value theory or utility theory is the notion of independence among variables or additivity of values. Its importance stems from numerous multiple-criteria procedures used for rating people, products, and other things. Most of these rating procedures rely on the notion of independence (often implicitly) for their validity. However, a satisfactory definition of independence (additivity), based on multidimensional consequences and hypothetical gambles composed of such consequences, has not appeared. This paper therefore presents a definition of independence for cases where the set of consequences X is a product set X1×X2× … ×X each element in X being an ordered n-tuple (x1, The definition is stated in terms of indifference between special pairs of gambles formed from X. It is then shown that if the condition of the definition holds, the utility of each (x1, x2, …, xn) in X can be written in the additive form ϕ(x1, x2, …, xn)=ϕ1(x1)+ϕ2(x2)+…, ϕn(xn), where ϕi is a real-valued function defined on the set Xi i=1, 2, …, n. The development is free of any specific assumptions about ϕ(e.g., continuity, differentiability) except that it be a von Neumann-Morgenstern utility function, and places no restrictions on the natures of the Xi. [ABSTRACT FROM AUTHOR]

The article presents discussions by economists on some papers that are published in the May 1, 1953 issue of the journal "American Economic Review." The author in this article discusses economist Yale Brozen's paper, which covered many aspects of the study of the direction of technological change. The author states that his systematic presentation set the matter in clear perspective. The blend of economic analysis with supporting illustrative data, presented by Brozen, is convincing. The author also states that his remarks largely involve qualifications that he would add to the discussion or matters on which he would place a somewhat different emphasis. The author's comments cover three principal points. The first of these concern Brozen's conclusion that technological change is largely endogenous within the economic system and that, perhaps, economists should incorporate technological change as an endogenous variable in their models. This conclusion could come, in part, from the use of a concept of technological change, which includes both the introduction of known but previously unused techniques when factor supplies become favorable and the development of entirely new techniques. The selection of the best combination of factors from the production function in the light of relative factor costs is, of course, entirely an economic matter and as Brozen implies, has for a long time been a part of economic models.

While social scientists are aware that the relationship between an independent and dependent variable may be spurious, they are much less aware that the absence of relationship may be equally spurious. The chief reason is that the relationship is concealed by a suppressor test factor. This paper supplements earlier discussions of this topic by considering the logical status of suppressor test factors and compensating influences. Examples of antecedent, intervening, and component suppressor variables and of compensating influences are provided. It shows that, in a causal sense, standard test factors and suppressor test factors generate opposite interpretations of spuriousness, but in a formal sense they are the same. Several substantive contributions of suppressor variables to social science are discussed. Suppressor variables are not rarities, but may actually appear as often as standard test factors in research. [ABSTRACT FROM AUTHOR]

This paper extends the results of "Duality in Discrete Programming" [1] to the case of quadratic objective functions. The paper is, however, self-contained. A pair of symmetric dual quadratic programs is generalized by constraining some of the variables to belong to arbitrary sets of real numbers. Quadratic all-integer and mixed-integer programs are special cases of these problems. The resulting primal problem is shown, subject to a qualification, to have an optimal solution if and only if the dual has one, and in this case the values of their respective objective functions are equal. The dual of a mixed-integer quadratic program can be formulated as a minimax problem whose quadratic objective function is linear in the integer-constrained variables, and whose linear constraint set does not contain the latter. Based on this approach an algorithm is developed for solving integer and mixed-integer quadratic programs. [ABSTRACT FROM AUTHOR]

This paper demonstrates the equivalence of several published algorithms for solving the so-called linear fractional programming problem. [ABSTRACT FROM AUTHOR]

In a previous paper, the authors presented the minimax block search strategy for locating the maximum of unimodal functions of one variable by a sequence of simultaneous function evaluations. In the present work the nearly optimal minimax golden block search method is developed which has the advantage that the number of function evaluations need not be specified in advance. For one experiment per block it reduces to the well known golden section method. It is shown that this method is an excellent approximation of the block search strategy and that for a certain marginal resolution the two methods become identical. [ABSTRACT FROM AUTHOR]

The article is a response to comments concerning "Design of Proof in Organizational Research" and "Organizational Effectiveness: An Inventory of Propositions." The research designs of case study, small-sample study, and longitudinal method are mentioned, as well as five ideas to improve the quality of proof in research such as compiling measurement inventories for the major variables and controlling contaminating variables. The author states that comments on his work, the issues raised, and the reported data were not accurately assessed.

This paper presents a framework for evaluating the conflicting claims in the literature on estimation from grouped observations. Attention is restricted to two-variable substantive models. For this case it is shown that random grouping results in unbiased estimators with very low efficiency. Grouping observations by values of the independent variable yields unbiased estimators with relatively high efficiency. Conversely, grouping by values of the dependent variable results in biased estimation. The most interesting case is that in which observations are grouped according to values of some variable which is related to variables in the model but which is not explicitly included in the model. Results on bias are developed for this case. Each of the cases is illustrated with empirical data. [ABSTRACT FROM AUTHOR]

Within the framework of chance-constrained programming, this paper formulates two related stochastic models for players competing in a random-payoff two-person zero-sum game. Under certain assumptions, it shows that a one-to-one correspondence (called stochastic pseudoduality) exists between the two formulations at their optimal values, and, furthermore, exact deterministic equivalents can be obtained for these formulations. The optimal solution for a deterministic equivalent can be found by considering an appropriate class of subproblems. [ABSTRACT FROM AUTHOR]

This paper shows that the final solutions to the executive and divisional programs in a linear fractional decomposition furnish the complete primal and dual solutions; it extends the proofs already presented for the linear decomposition problem. [ABSTRACT FROM AUTHOR]

Each of the main enumerative methods for zero-one programming has a drawback: the branch-and-bound (multi-branch) approach may require an inordinate amount of storage capacity and the backtrack implicit-enumeration (single-branch) approach circumvents this storage problem only by restricting the flexibility of the search. This paper outlines an implicit-enumeration scheme that, while maintaining a low storage requirement, allows the same flexibility in backward branching (backtracking is no longer mandatory) as we commonly have in forward branching. Preliminary computational results are presented. [ABSTRACT FROM AUTHOR]

Several components comprising a system are to be maintained, while service resources are limited. An optimal inspection and repair policy yields minimal losses. Charges are for checking, repair, and lost time elapsed from component's failure to its detection. This paper examines a model of N identical components, possessing exponential failure distributions, operating simultaneously; only one component can be served (checked or repaired) at a time. The solution is based on HOWARD'S method for solving sequential decision processes. Numerical computations indicate that losses by the best feasible policy that disregards the future (i.e., disregards other components of the system) are almost as low as long-run minimal ones. [ABSTRACT FROM AUTHOR]

The paper describes an Irrigation Feasibility Study carried out for a Developing Country. The area considered comprised some 1,000,000 acres of land in Burma and the study was undertaken for the Burmese Government under the auspices of the United Nations. The solution technique used was Mixed Integer Programming, there being approximately 750 continuous variables, 50 integer variables and 250 constraints. The study is of particular interest in that the problem was solved both by conventional methods and by Operational Research methods independently. Therefore, a complete comparison of the relative merits of both approaches exists and is discussed here. [ABSTRACT FROM AUTHOR]

A multi-stage linear program is defined with linking variables that connect consecutive stages. Optimality conditions for the composite problem are partitioned into local and linking conditions. When the Dantzig-Wolfe decomposition scheme is applied with the first stage as the master, the subproblem is also a MLP with one less stage. The same decomposition is then applied to the subproblem, giving rise to a nested decomposition scheme, in which each stage acts as a master for the following stage and a subproblem for the preceding. Optimizing a single stage problem results in satisfying the "local" optimality conditions. A very general rule is given for selecting the next subproblem to optimize, and finite convergence to a solution satisfying all linking conditions is demonstrated. Procedures for extracting the optimal primal solution at the end of the main algorithm and for initialization are given. Particular rules for selecting the next subproblem and for generating additional proposal vectors are discussed. Finally, it is shown how a variety of problems may be restructured as multi-stage linear programs to which this algorithm may be applied, and some computational experience is reported. [ABSTRACT FROM AUTHOR]

This article comments on Arthur Goldberg's critique of the author's article in the "American Economic Review" about paired equation rates for dependency and savings rates. As the data in the accompanying table indicate, the discrepancies are very small, and are well within the margins of accuracy within which anyone views data generated from the national income accounts of the less developed countries. The reason for the disrepancies is given. The main conclusions of the original paper are reiterated and the effect of Goldberg's criticism of them.

The first purpose of this paper is to indicate the circumstances in which path coefficients may be accepted as adequate guides to the relative importance of anterior (causal) variables in a path analysis. It is shown that weights in a regression equation may be regarded as indicators of importance, in the sense of determinants of proportions of variance, if the (projection of the) variate defined by the equation coincides with a principal component of the anterior variables. The second purpose of the paper is to illustrate the usefulness of employing generalized multiple regression (analysis by canonical correlations) as an aid in the interpretation of a path diagram. The discussion is illustrated by reference to the path analysis which appears in `Ability and Achievement' by Professor 0. Dudley Duncan. [ABSTRACT FROM AUTHOR]

This paper is written with three objectives in mind. First, to point out that the problem of grouping, where a larger number of elements n are combined into m mutually exclusive groups (m ~n) should be recognized as a problem in Integer Programming, and that such recognition can help us in avoiding complete enumeration of stages in grouping from n to n - 1 ... to m, and of alternative possibilities in each stage. Second, to formulate mathematically some simple versions of the relevant Integer Programming Problem, so that the available computer codes can solve it. When the grouping attempts to minimize the within groups sums of squares, the so-called string property is proved to be necessary for the minimum (Lemma 1). It is shown that the string property can be exploited to write the non-linear within group sums of squares as a linear function (Lemma 2). An attempt is made to generalize the string property for the higher dimensional case. Third, to give some numerical examples to clarify the mathematical models and to illustrate the advantages of Integer Programming formulation by comparing with the numerical examples appearing in the literature [8], [13 ]. Zero-one programming where the integer variables can take values of zero or one only appears to be most efficient from the limited experience of the author. The paper is divided into three sections which closely correspond to the three objectives noted above. [ABSTRACT FROM AUTHOR]

The principal part of this paper is devoted to the study of the distribution and density functions of the ratio of two normal random variables. It gives several representations of the distribution function in terms of the vivariate normal distribution and Nicholson's V function, both of which have been extensively studied, and for which tables and computational procedures are readily available. One of these representations leads to an easy derivation of the density function in terms of the Cauchy density and the normal density and integral. A number of graphs of the possible shapes of the density are given, together with an indication of when the density is unimodal or bimodal. The last part of the paper discusses the distribution of the ratio (u[sub 1] + ... + u[sub n])/(v[sub I] + ... + v[sub m]) where the u's and v's are independent, uniform variables. The exact distribution for all n and m is given, and some approximations discussed. [ABSTRACT FROM AUTHOR]

The article presents information on a method or algorithm for finding proposals on which all members of a group can agree. The method is confined to situations where the variables can be changed by any "small" amount and, where the group is attempting to decide on a change in the variables from some "existing situation." A possible change in the variables will be called a "proposal." A proposal would be "acceptable" to an individual if it would increase his utility. The problem is not to pick a particular proposal which is acceptable to all individuals.

This paper attempts to integrate theoretically the Bales-Parsons model of small groups and a theory of complex organizations. The organizational positions of the instrumental and expressive leaders are seen as critical variables, affecting both the fulfillment of the functional needs of participant groups and the groups' commitment to organizational goals. Complex organizations are distinguished according to the nature of their goals, power employed. and the level of lower-echelon commitment they require. The relations between the small group and the complex organization are reviewed for each kind. These theoretical consideration are applied to the study and administration of prisons, the "Human Relations" approach in industry, therapeutic mental hospitals, and schools. [ABSTRACT FROM AUTHOR]

MILLER and WAGNER [Opns. Res. 13, 930–945 (1965)] define joint chance-constrained programming by specifying a set of consists that are joint probability measures of the extent to which constraint violations are permitted. For the special case of a random right-hand-side vector whose elements are independent random variables, they show that an equivalent deterministic concave program exists. The purpose of this paper is to generalize this result to a class of nonlinear chance-constrained programming models with joint constraints. [ABSTRACT FROM AUTHOR]

This paper discusses a model for the stochastic motion of the slow-down points of cars behind a bottleneck. The model considered assumes cars to have non-zero length, and employs a simple ‘car-following-slowdown rule.’ The case where ‘gaps’ between cars form a stationary reversible sequence of random variables is discussed, and the main result consists of an explicit expression for the steady-state distribution of the physical length of the stream of cars behind the bottleneck when ‘gaps’ are independent and identically distributed (iid) with exponential tail and atom at the origin. When this atom has zero mass (i.e., the gaps are lid exponential) it turns out that the result yields the steady-state distribution of waiting time in an M/D/1 queue and agrees with the known result. When this atom is nonzero, the main result in the queuing context yields the steady-state distribution of waiting time in an M′/D/1 queue, where M′ denotes an arrival stream with interarrival times being iid with exponential tail and atom at the origin. [ABSTRACT FROM AUTHOR]

This paper derives a general steepest-ascent expression to show that any 'direction' in the function space can be considered to be a steepest ascent direction by selecting a proper distance metric index and/or variable scaling. Several search procedures can be thus considered to be special cases of the method of steepest ascent. An illustrative investigation shows that, in a qualitative sense, most metric indices perform comparably. [ABSTRACT FROM AUTHOR]