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This article derives bounds on a wide class of moments of the underlying distribution from data grouped in intervals when the mean of each group is given. The extremal distributions are constructed yielding the upper and lower bounds to moments of the form Integral of h(x)dF(x), where h(x) is convex and F(x) is concave. To illustrate the results, bounds on the variance and Gini index are presented for two theoretical distributions. [ABSTRACT FROM AUTHOR]

This paper is concerned with a linear fractional problem of the form: max[sub x] min[sub y] F(X, Y) = (cX + dY + α)/(fX + gY + β), subject to AX + BY less than or equal to b; X, Y greater than or equal to O. This problem represents a generalization of a problem considered in the literature in which F(X, Y) is assumed to be linear. A number of results for the linear case are extended; and, in particular, it is shown that this fractional max-min problem is equivalent to a quasi-convex programming problem whose optimal solution lies at a vertex of the feasible region. Using these results, we develop an algorithm for solving this problem. The paper concludes with a numerical example. [ABSTRACT FROM AUTHOR]

This article considers two examples of bivariate extremal distributions when the margins follow the first asymptotic distribution of the largest values. The variables are assumed to be reduced and each distribution contains only one parameter indicating the association between the extremes. The probability and the density functions of these distributions at the characteristic value, median, and mode have been analyzed. A procedure has been developed to estimate the single parameter of the distributions. A criterion for distinguishing between the two bivariate extremal distributions has been worked out. Finally, the various theories developed are applied to a numerical example. [ABSTRACT FROM AUTHOR]

The objective of this paper is the construction of a branch-and-bound algorithm for computing minimum cost flows in capacitated networks when the cost of passing a flow over an arc is concave. The method is based on the equivalence of the general network flow problem to a network flow problem in a bipartite network of a special form. An optimal flow is found by implicit enumeration of the set of extremal flows in that network. [ABSTRACT FROM AUTHOR]

Numerous alternatives are available in the kinds of studies which can be elected in the market research which should precede the introduction of a new product. This gives rise to a possible network interpretation and treatment by an associated chance-constrained programming characterization and analysis. The resulting model, called DEMON (Decision Mapping Via Optimum GO-NO Networks), which was discussed in [6], is here given a new formulation in terms of an extremal equation. A general analytic characterization is achieved and then replaced by more special ones. Means for effecting study decisions and inferences are discussed along with the sensitivity analyses that we associate with GO and NO preemptions, relative to profit and payback constraints. Payback (in a constraint) is here distinguished from its use as a criterion for choice (or objective), the latter being here oriented toward MEMP (maximizing expected maximum profit). A chart is provided for interpreting these and other aspects of policy which bear on the problems of marketing a new product. [ABSTRACT FROM AUTHOR]

Several techniques in mathematical programming involve the constrained optimization of an extremal-value function. Such functions are defined as the extremal value of a related parameterized optimization problem. This paper reviews and extends the characterization of directional derivatives for three major types of extremal-value functions. The characterization for the completely convex case is then used to construct a robust and convergent feasible direction algorithm. Such an algorithm has applications to the optimization of large-scale nonlinear decomposable systems. [ABSTRACT FROM AUTHOR]

This paper shows that the Lagrange multiplier method suggested by H. Everett does not have 'Fail-Safe' properties when applied to simple situations with nonconvexity only in the functional. Although each Lagrange multiplier problem for these situations has immediate solutions no means of combining them to obtain a solution to any reasonable approximation appears to be visible. [ABSTRACT FROM AUTHOR]

A solution to the feed-mix problem is presented that treats the problem as a part of a decision-making system. Three basic approaches are utilized to solve the problem of continual reformulation of many feeds in order to follow market price fluctuations. The resulting system can produce 20 to 30 new formulations in an hour on an IBM 650. Extension of the system to faster computers would make the system more flexible and responsive to grain market fluctuations. [ABSTRACT FROM AUTHOR]

The calculational aspects of solving certain classes of location-allocation problems are presented. Both exact extremal equations and a heuristic method are presented for solving these problems. Directions for further investigation are also indicated because of the need for methods to shorten the total amount of calculation involved. [ABSTRACT FROM AUTHOR]

Let Gi, ,Gr be groups of n1, , nr workers on a production line, all members of G1 performing identical operations in the time t2, on entities drawn (repeatedly) from a pool P. When the production line starts all members of G1 are put to work at the time T1, and some time thereafter all members of G2 are put to work at the time T2, etc. We assume that n1/t1 = =nr/tr  R Let dj = g c d (nj-1, nj) We prove the theorem Let Tj-1=0 Then Tj = (nj-1+nj-dj)/R is the earliest time at which Gj can be put to work so that supply for Gj is at any time greater than or equal to demand (j=2, ,r). [ABSTRACT FROM AUTHOR]

A deterministic production planning problem with limited backlogging, inventory and production capacity constraints is considered. The model also includes a certain type of production cost function which is neither convex nor concave. A characterization of the extreme points is provided and an algorithm is suggested for the problem with equal production capacities. It is also shown how initial inventory can easily be incorporated into the model. [ABSTRACT FROM AUTHOR]

A class of optimization problems is investigated in which some of the functions, continuous in all their arguments, have continuous right- and left-hand derivatives but are not equal at a point called the corner. For this nonclassical problem, a set of first order necessary conditions for stationarity is determined for an optimal path which may have arcs lying on a corner for a nonzero length of time. Enough conditions are provided to construct an extremal path. This, in part, is achieved by noting that the corner defines a manifold in which the derivatives of all the functions are uniquely defined. Three examples, two of which represent possible aggregate production and employment planning models, illustrate the theory. [ABSTRACT FROM AUTHOR]

The article presents mathematical problems and solutions.