Showing papers by "Abraham Charnes published in 1966"
TL;DR: In this article, a stochastic warehousing problem is defined and solved, first by backwards induction, then by means of a forward working algorithm, and the influence of holding costs and discount rates on forecasting horizons is illustrated.
Abstract: Analytic decision rules and horizon rules are developed for the warehousing problem. A stochastic warehousing problem is defined and solved, first by backwards induction, then by means of a forward working algorithm. The influence of holding costs and discount rates on forecasting horizons is illustrated.
64 citations
TL;DR: In this paper, the authors consider a multi-modality distribution of the unexpected demands with low probability of occurrence but high resource demand when they do occur, and propose a real-time adjustment process for the initial plan to take into account the actual regular demands and availability.
Abstract: Funding of research projects is considered as encompassing three stages: 1 an initial short run plan for funding based upon projected regular demands and availability subject to random deviations; 2 adjustment of the initial plan to take into account the actual regular demands and availability and the funding of significant break-throughs which occur at random intervals preempting other demands; and 3 a plan for longer-run availability and demands which constitute a “posture” desired subsequent to the funding adjustments of 2. The essence of the distribution of the unexpected demands is multi-modality with low probability of occurrence but high resource demand when they do occur. This approach represents a substantial departure from the usual planning model development which produces only an optimal plan based on forecasted developments without provision for adjustment when the forecasted events actually materialize and additional unexpected demands are placed on resources. The adjustment process explored here---which provides the mechanism for optimal implementation of the original plan or control of resource allocation-enables optimal response to information received in “real-time” avoiding the frequently observed over-or under-response to receipt of such information without reference to the impact of the interim decision on future capabilities.
55 citations
TL;DR: Although it is related to previous work in chance constrained programming, DEMON evidently also effects a further development and extension of these ideas by reference to the fact that here the statistical distributions are only partially known and the chance constraints are also expressed in terms of conditional distributions which in turn may be altered by the choices that are made.
Abstract: In this paper a dynamic, adaptive model, called DEMON,4 is interpreted in terms of a network. The latter is here employed to reduce the problem of selecting optimal decision procedures so that these can be interpreted in terms of a conditional sequential designation of links from such a network. More is involved, however, than is immediately apparent from the network possibilities only. Thus, in the DEMON applications to new product marketing—as discussed in the present paper—it is necessary to comprehend additional chance and deterministic constraints such as (1) payback, or breakeven, conditions that may be specified for fulfillment over a given time horizon, (2) minimum expected level of profits required and (3) study budget limits which should not be exceeded. By means of preemptions or over-rides, which also form a part of DEMON, however, it is possible to relate these additional constraints to the network as we also show by means of a development via ideas associated with the right inverse of an inc...
33 citations
TL;DR: The generalized network problem and the closely related restricted dyadic problem are two special model types that occur frequently in applications of linear programming as mentioned in this paper, and they can be easily implemented algorithms that provide an optimum in one pass through the network.
Abstract: The generalized network problem and the closely related restricted dyadic problem are two special model types that occur frequently in applications of linear programming. Although they are next in order after pure network or distribution problems with respect to ease of computation, the jump in degree of difficulty is such that, in the most general problem, there exist no algorithms for them comparable in speed or efficiency to those for pure network or distribution problems. There are, however, numerous examples in which some additional special structure leads one to anticipate the existence of algorithms that compare favorably with the efficiency of those for the corresponding pure cases. Also, these more special structures may be encountered as part of larger or more complicated models. In this paper we designate by topological properties two special structures that permit evolution of efficient algorithms. These follow by extensions of methods of Charnes and Cooper and of Dijkstra for the corresponding pure network problems. We obtain easily implemented algorithms that provide an optimum in one "pass" through the network. The proofs provided for these extended theorems differ in character from those provided or not provided in the more special "pure" problem algorithms published.
26 citations
21 Jul 1966
TL;DR: Network characterizations are developed for effecting contacts between accounting and mathematical programming altered and related to suitable generalizations of classical network ideas such as the Kirchhoff node conservation laws.
Abstract: : Network characterizations are developed for effecting contacts between accounting and mathematical programming. En route to these objectives some of the customary uses of double entry accounting are altered and related to suitable generalizations of classical network ideas such as the Kirchhoff node conservation laws. Extensions of the usual node-link incidence relations provide a basis for effecting these contacts. Concrete illustrations are supplied including a goods-flow-funds-flow model which is preceded by a simpler example involving a PERT-Critical Path application. The latter is examined in the context of a uni-dimensional physical flow involving time only while the former suggests how double entry can be extended to flows that involve a variety of different dimensions. A possibility for joint coordinated uses of programming and accounting of management planning is indicated and amplified and some of the implications for alterations in accounting practice are then examined. Suggestions for further extensions include probabilistic formulations and multi-dimensional objectives.
22 citations
TL;DR: In this paper, a model of situations in which individuals are faced with multiple activities among which they must allocate their effort is postulated, and optimal allocations are found for four assumed motivational structures, i.e., profit maximization, performance goals in each of the activities, and relationships between the various motivation structures are explored.
Abstract: Models of situations in which individuals are faced with multiple activities among which they must allocate their effort are postulated. Optimal allocations are found for four assumed motivational structures---profit maximization and three involving performance goals in each of the activities. Heuristic approximations to the optimal allocations are developed. Also, the relationships between the various motivation structures are explored.
18 citations
TL;DR: An extension to the theory of linear programming over generalized networks is presented which replaces the generalized Kirchoff node conditions by chance constraints, motivated by a class of problems in sanitary and chemical engineering in which the nonzero entries in the generalized incidence matrix may be random variables.
Abstract: An extension to the theory of linear programming over generalized networks is presented which replaces the generalized Kirchoff node conditions by chance constraints. The extension is motivated by a class of problems in sanitary and chemical engineering in which the nonzero entries in the generalized incidence matrix may be random variables. Duality relations are established for appropriate pairs of such chance-constrained programming problems by showing that their deterministic equivalents consist of a deterministic generalized network problem and its dual. It is also shown how these duality relations may be exploited in order to obtain actual solutions to chance-constrained generalized network problems.
9 citations
TL;DR: In this article, the authors deal with a certain specialization of their theory of duality on the case where the objective function is simple continuously differentiable and convex on the set of the admissible solutions and the constraint functions defining $K$ are continuous and concave.
Abstract: The authors deal with a certain specialization of their theory of duality on the case where the objective function is simple continuously differentiable and convex on the set $K$ of the admissible solutions and the constraint functions defining $K$ are continuously differentiable and concave. Further, a way is shown how to generalize the account to the case where the constraint functions of the problem are simple piecewise differentiable and concave. The obtained conditions can be considered as a generalization of Kuhn-Tucher's theorem.
9 citations
01 Sep 1966
TL;DR: In this paper, it was shown that the problem of planning for liquidity in a savings and loan association can be reduced to one of solving n rather simple one-variable nonlinear programming problems.
Abstract: : The paper deals with an n-period E model of chance-constrained programming in which each period j = 1,...,n generates exactly one new constraint. It is shown that there are cases in which the problem can be reduced to one of solving n rather simple one-variable nonlinear programming problems. The results of this paper are illustrated by means of an example giving the solution of a two-period problem of planning for liquidity in a savings and loan association.
8 citations
TL;DR: A mathematical simulation analysis of refuse collection and disposal systems is presented and results are presented in a series of nineteen graphs.
7 citations
TL;DR: A way for dealing with negative terms by a constraint adjunction procedure which yields an associated approximating problem involving only polynomials which can be transformed into a convex programming problem that has only one local (= global) optimum.
Abstract: : Many important problems of engineering and management are of a form which could be represented as geometric programs except that the functional to be minimized as well as the constraints are not confined to posynomials in that some of the coefficients are negative. This paper supplies a way for dealing with such negative terms by a constraint adjunction procedure which yields an associated approximating problem involving only polynomials which can, in turn, be transformed into a convex programming problem that has only one local (= global) optimum. The latter, which is called a convex approximant, has an associated dual. Recourse to the related duality theory then supplies guidance for improving the approximation along lines that are indicated in the paper.
01 Apr 1966
TL;DR: In this article, a special class of constrained generalized median problems, such as Charnes, Cooper, Thompson, and Thompson's generalized generalized median problem, is studied. But the results of A. C. Williams and R. Wets obtained by involved arguments and sophisticated constructs appear, when corrected, as special instances of some of the above results but devoid of the interrelations and interpretations presently adduced.
Abstract: : By means of elementary properties of the absolute value function, important properties of a special class of 'constrained generalized median' problems (and eventually, the most general class, vide Charnes, Cooper, Thompson) such as existence of solutions, gradient and incremented formulae, linear programming and probabilistic interpretations are obtained for all classes of joint distribution functions for which the problems make sense. Results of A. C. Williams and R. Wets obtained by involved arguments and sophisticated constructs appear, when corrected, as special instances of some of the above results but devoid of the interrelations and interpretations presently adduced.