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This paper considers the problem of assigning n facilities, or departments, to locations so that the maximum of the rectilinear distances between departments is minimized. The locations are considered to be points in a lattice. It develops a simple explicit expression for the minimum value of the objective function for all values of n; this expression has as a corollary a necessary and sufficient condition for an assignment, or a configuration, to be minimax; the paper also develops a simple geometrical procedure for constructing minimax configurations. Some related problems are also examined briefly. [ABSTRACT FROM AUTHOR]

This paper compares the waiting times of customers under three priority rules: the order-of-arrival rule, the shortest processing time (within a generation) first, and the longest processing time (within a generation) first. In particular, the covariance matrix of the trivariate distribution of the equilibrium waiting times is obtained explicitly. [ABSTRACT FROM AUTHOR]

Integer programs may have constraints which are redundant or else nonbinding. They may also have variables which are extraneous in the sense that there is some optimal program in which they are nonpositive. Thompson, Tonge and Zionts [1] have discussed the topics of redundant constraints and extraneous variables in linear programs. This paper extends their results to integer programs, and provides new proofs of the original results. [ABSTRACT FROM AUTHOR]

Assembly line balancing consists of assigning work elements, which are subject to sequencing restrictions, along an assembly line in an optimal manner. The procedure presented in this paper leads to optimal line balances by operation on a matrix of zeros and ones called a "Precedence Matrix." A nine element problem is used to illustrate the method in detail and comparisons with other procedures are made. Several balances obtained by applying the FORTRAN program appended to the paper to actual and sample problems are also shown. [ABSTRACT FROM AUTHOR]

MILLER and WAGNER have shown that a deterministic equivalent of a joint chance-constrained programming model with independent random right-and-side elements is a concave programming problem. This paper obtains similar equivalents for chance-constrained programming models with coefficient matrices whose elements are normally distributed and with dependent random right-hand-side elements. [ABSTRACT FROM AUTHOR]

The preceding article by Professors De Fleur and Quinney goes beyond mere coding of the verbal statements contained in the theory of differential association. It reveals hitherto unexpressed relationships in the theory and also shows how Sutherland's propositions are linked with more general sociological and social psychological principles. Further, the article demonstrates that "the theory" of differential association consists of all its first six propositions, and the section on empirical verification shows the tremendous number of hypotheses the theory generates. The work points the way to the ordering of criminological data and to the computerizing of criminological research. [ABSTRACT FROM AUTHOR]

Deterministic linear scheduling problems can often be formulated as linear programs with staircase coefficient matrix structure in which the linking blocks are identity matrices, since the activities that link successive time periods represent storage of goods. The solution technique proposed in this paper can be viewed as a nested decomposition approach in which primarily as well as dual-variable information is transmitter between master and subproblems. [ABSTRACT FROM AUTHOR]

In this paper the solution to the problem of placing n connected points (or nodes) in r-dimensional Euclidean space is given. The criterion for optimality is minimizing a weighted sum of squared distances between the points subject to quadratic constraints of the form X'X = 1, for each of the r unknown coordinate vectors. It is proved that the problem reduces to the minimization of a sum or r positive semidefinite quadratic forms which, under the quadratic constraints, reduces to the problem of finding r eigenvectors of a special "disconnection" matrix. It is shown, by example, how this can serve as a basis for cluster identification. [ABSTRACT FROM AUTHOR]

The problem considered in this paper is that of consistently rounding off the elements of a matrix and its row and column sums. It is shown that a class of rounding problems of this kind is equivalent to a class of problems of determining flows through networks having arbitrary lower as well as upper bounds on edge flows. An existence theorem first proved by Hoffman for flows in such networks is used to show that an important subclass of the matrix rounding problems considered is always soluble. An algorithm for the entire class is illustrated by a numerical example. [ABSTRACT FROM AUTHOR]

This paper deals with a multivariate extension of Friedman's chi[sup 2, sub tau]-test. A rank permutation distribution and the large sample properties of the criterion are studied. The asymptotic relative efficiency (A.R.E.) for a sequence of translation alternatives is studied and bounds are given for certain special cases. It is shown that, under specified conditions, the A.R.E. of this test with respect to the likelihood ratio test is largest, when the block dispersion matrices differ and can be greater than unity when the differences are large. [ABSTRACT FROM AUTHOR]

The article discusses empirical results concerning the testing of the significance of a correlation matrix using the Barlett's test. The problem in a matrix is to determine the probability of rejecting the null hypothesis. Thus, the sample correlation matrix could be considered to have arisen when sampling from a multivariate population of ten variables. The power of Barlett's test appears to be quite high that future factor analysts will see fit to include the test as an automatic first step for sampling correlation matrix.

The standard matrix method for calculating higher transition probabilities in a Markov process is briefly reviewed in the introduction This method is extended to path multiplicities Then a new matrix method for calculating both first arrival probabilities and multiplicities of first arrival paths is presented The matrix method is also suitable for enumerating paths and for obtaining the diameter of a graph An example illustrates these methods [ABSTRACT FROM AUTHOR]

The differences of full vs. reduced rank and principal vs. transformed components solutions are defined. It is shown that the equation X1 = Z B1 (B1/ B1B)-1, where B1 is the component pattern matrix, is correct for computing component scores corresponding to any legitimate pattern. Computational advantages of avoiding unnecessary storage of large matrices and of the inversion of relatively small matrices with large determinants are illustrated. [ABSTRACT FROM AUTHOR]

A discussion of the importance of a direct method in obtaining all the solutions of a transportation problem, and in obtaining solutions of more general problems, is followed by a discussion of methods of reduced matrices in which the transportation matrix is reduced, by a series of subtractions from rows and columns, to a transformed matrix to which the orthogonality condition is applicable. The direct method proceeds in a series of simple steps to the determination of zero terms having associated xi, values which eventually satisfy the row and column equations. Formal and informal versions are presented and application is made to several general problems. [ABSTRACT FROM AUTHOR]

The article describes a procedure to maximize a strictly concave quadratic function subject to linear constraints in the form of inequalities. First the unconstrained maximum is considered; when certain constraints are violated, maximization takes place subject to each of these in equational (rather than inequality) form. The constraints which are then violated are added in a similar way to the constraints already imposed. It is shown that under certain general conditions this procedure leads to the required optimum in a finite number of steps. The procedure is illustrated by an example while also a directory of computations is given. [ABSTRACT FROM AUTHOR]