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Showing papers on "Stochastic programming published in 1974"


Journal ArticleDOI
TL;DR: The paper surveys the basic results and nonresults for decision rules in stochastic programming and exhibits some of the difficulties encountered when trying to restrict the class of acceptable rules to those possessing specific functional forms.
Abstract: The paper surveys the basic results and nonresults for decision rules in stochastic programming. It exhibits some of the difficulties encountered when trying to restrict the class of acceptable rules to those possessing specific functional forms. A liberal dosage of examples is provided which illustrate various cases. The treatment is unified by making use of the equivalence of various formulations which have appeared in the literature. An appendix is devoted to the P-model for stochastic programs with chance constraints.

132 citations


Journal ArticleDOI
01 Jul 1974
TL;DR: In this paper, a review of the recent literature within the power systems field can be found in Section 5.1. The authors point out some specific areas where more work needs to be done.
Abstract: Important power system planning and operation problems have been formulated as mathematical optimization problems. Such problems as the economic dispatch, in many of its facets; var scheduling and allocation; pollution dispatch; maximum interchange; hydrothermal unit commitment and dispatch; generation, transmission, and distribution expansion planning; maintenance scheduling and substation switching, have been formulated and solved. Modern mathematical optimization techniques, such as nonlinear, quadratic, linear, integer and dynamic programming and their many combinations and extensions, have been exploited. Some of the formulations and solutions to these problems as presented in the recent literature within the power systems field are reviewed. The large number of papers available is a measure of the current immense activity in this area. Attempts are made to point out some specific areas where more work needs to be done.

127 citations


Journal ArticleDOI
TL;DR: This paper formulates models of defense problems that are convex programs having the mathematical properties treated in the previous papers, including several strategic-force-planning models and two general-purpose-force planning models.
Abstract: Bracken and McGill have discussed the theory, computations, and an example of mathematical programming models with optimization problems in the constraints [Opns. Res. 21, 37-44 1973], and have presented a computer program for solving such models with nonlinear programs in the constraints [Opns. Res. 22, 1097-1101 1974]. Bracken, Falk, and McGill have given a procedure for transforming mathematical programs with two-sided optimization problems in the constraints into mathematical programs with nonlinear programs in the constraints [Opns. Res. 22, 1102-1104 1974], thus enabling their solution by the computer program. This paper formulates models of defense problems that are convex programs having the mathematical properties treated in the previous papers. The models include several strategic-force-planning models and two general-purpose-force planning models.

81 citations


Journal ArticleDOI
01 Nov 1974
TL;DR: In this paper, the problem of decentralized control of stochastic discrete-time dynamic systems with one-step-delay sharing information structure is treated, and the problem can be decomposed into several static team problems.
Abstract: This paper treats problems of decentralized control of stochastic discrete-time dynamic systems with one-step-delay sharing information structure. It is shown that, by applying dynamic programming technique, the problem can be decomposed into several static team problems. For LQG case, this approach gives a solution which clearly shows the relation between estimation and control functions in the optimal control policy. Also the form of this solution is convenient for numerical computation of the optimal control.

75 citations


Journal ArticleDOI
TL;DR: An example is given which demonstrates that using a decision theory analysis for the basic chance-constrained model of stochastic linear programming may lead to an apparent dilemma, namely, 0 > EVSI > EVPI.
Abstract: An example is given which demonstrates that using a decision theory analysis for the basic chance-constrained model of stochastic linear programming may lead to an apparent dilemma, namely, 0 > EVSI > EVPI. The problem is discussed and a resolution suggested.

32 citations


Journal ArticleDOI
TL;DR: In this paper, an optimization model is studied in which a convex functional, giving expected cost subject to convex constraints, is minimized over a class of measurable recourse functions describing decisions that depend non-anticipatively on a sequence of observations of random variables.

26 citations


Journal ArticleDOI
TL;DR: Computing costs were reduced and system performance was improved with the use of the alternate stochastic optimization technique described and suggested as an improvement.
Abstract: Stochastic optimization techniques that are used in determining reservoir operation are presented. An alternate stochastic optimization technique is then described and suggested as an improvement. Feasible use of the alternate is possible since observations on planning horizons are employed in computation reduction. For a simple reservoir system, the techniques are applied and compared. Computation costs were reduced and system performance was improved with the use of the alternate.

22 citations


Journal ArticleDOI
TL;DR: The subject of this paper is the application of stochastic control theory to resource allocation under uncertainty in the context of the general problem of allocating resources to repair machines where it is possible to perform a limited number of diagnostic experiments to learn more about potential failures.
Abstract: The subject of this paper is the application of stochastic control theory to resource allocation under uncertainty. In these problems it is assumed that the results of a given allocation of resources are not known with certainty, but that a limited number of experiments can be performed to reduce the uncertainty. The problem is to develop a policy for performing experiments and allocating resources on the basis of the outcome of the experiments such that a performance index is optimized. The problem is first analyzed using the basic stochastic dynamic programming approach. A computationally practical algorithm for obtaining an approximate solution is then developed. This algorithm preserves the "closed-loop" feature of the dynamic programming solution in that the resulting decision policy depends both on the results of past experiments and on the statistics of the outcomes of future experiments. In other words, the present decision takes into account the value of future information. The concepts are discussed in the context of the general problem of allocating resources to repair machines where it is possible to perform a limited number of diagnostic experiments to learn more about potential failures. Illustrative numerical results are given.

21 citations


Journal ArticleDOI
TL;DR: A stochastic version of the standard nonlinear programming problem is considered, and it is indicated that the approach is quite versatile, and can be a useful tool for systematic Monte-Carlo optimization of constrained systems, a much-neglected area.
Abstract: A stochastic version of the standard nonlinear programming problem is considered. A function f(x) is observed in the presence of noise, and we seek to minimize f(x) for x \in C = {x:q^{i}(x) \leq 0} , where q^{i}(x) are constraints. Numerous practical examples exist. Algorithms are discussed for selecting a sequence X n which converges wp 1 to a point where a necessary condition for optimality holds. The algorithms use, of course, noise-corrupted observations on the f(x) . Numerical results are presented. They indicate that the approach is quite versatile, and can be a useful tool for systematic Monte-Carlo optimization of constrained systems, a much-neglected area. However, many practical problems remain to be resolved, e.g., investigation of efficient one-dimensional search methods and of the tradeoffs between the effort spent per search cycle and the number of search cycles.

16 citations


Journal ArticleDOI
TL;DR: In this article, the optimal performance of linear-quadratic stochastic systems with instantaneous output feedback was studied and the optimal cost sensitivity matrices were derived, and no special computations were required to obtain the sensitivity matrics.
Abstract: Problems of sensitivity of the optimal performance of linear-quadratic stochastic systems with instantaneous output feedback is studied. Optimal-cost sensitivity matrices are derived. Once the optimization problem is solved, no special computations are required to obtain the sensitivity matrices.

9 citations


Journal ArticleDOI
TL;DR: Structural optimization problems which can be transformed to geometric programming problems can be easily solved by a further simple transformation to convex programming problems.



Journal ArticleDOI
TL;DR: The modified application of dynamic programming is made for a single reservoir system illustrating the technique and the achievement of near optimum performance.
Abstract: Reduction of computation in reservoir operation optimization problems can be made through a modification of the optimization technique instead of limiting development of the system models. Considerations are presented herein which lead to the development of a modified application of deterministic optimization techniques. The modification enables reduction of computation to take place while achieving results that approximate the optimum. The modified application of dynamic programming is made for a single reservoir system illustrating the technique and the achievement of near optimum performance.

Journal ArticleDOI
TL;DR: A cost optimization study of factory type structures is described, which finds those elements that provide the greatest variation in cost due to different structural forms and various available material products.
Abstract: A cost optimization study of factory type structures is described. Investigations centre around those elements that provide the greatest variation in cost due to different structural forms and various available material products. A mathematical model of factory costs is constructed for the shell of the building and includes constraints on the design variables of both a structural and a practical nature. The resulting mathematical programming problems are solved by means of the Geometric Programming technique, sample results are presented, and general conclusions on the usefulness of the study are drawn.

Journal ArticleDOI
TL;DR: A technique is presented by which one can apply deterministic optimization techniques, for example, the maximum principle of Pontryagin, to stochastic optimal control problems formulated around linear systems with Gaussian noises and general cost criteria.
Abstract: A technique is presented by which one can apply deterministic optimization techniques, for example, the maximum principle of Pontryagin, to stochastic optimal control problems formulated around linear systems with Gaussian noises and general cost criteria. Using this technique, the stochastic nature of the problem is suppressed but for two expectation operations, the optimization being deterministic. The use of the technique in treating problems with quadratic and nonquadratic costs is illustrated.

Journal ArticleDOI
TL;DR: A very fast nongradient procedure for function optimization which provides an optimum with a very small number of function evaluations and appears to be very robust and reliable.
Abstract: A very fast nongradient procedure for function optimization is described. The procedure is based on the ideas of Rosenbrock [1] and Swann [2]. These were modified and refined to obtain an algorithm which provides an optimum with a very small number of function evaluations. This algorithm, compared with recently reported algorithms by Lawrence and Steglitz (L-S) [3], and Beltrami and Indusi (B-I) [4], appears to be very robust and reliable. Constrained optimization problems can be handled and a special method for handling optimization with linear constraints is presented.

Journal ArticleDOI
TL;DR: The problem of selecting a fixed dimensional output which will lead to the best instantaneous output-feedback is solved for linear stochastic systems with quadratic cost criterion.
Abstract: The problem of selecting a fixed dimensional output which will lead to the best instantaneous output-feedback is solved for linear stochastic systems with quadratic cost criterion.

Book ChapterDOI
01 Jan 1974
TL;DR: In this article, the sensitivity of the numerical solution with respect to changes in these parameters is explored, and the problem becomes a stochastic programming problem when these variations are of a random nature, the coefficients should be thought of as probability distributions rather than numbers.
Abstract: There are three groups of parameters in a linear programming problem: the “technological” coefficients, a ij (representing, for example, machine time per unit of product); the constant terms on the right-hand sides of the restrictions, b i (e.g., capacity limits); and the coefficients in the linear preference function, c j (for example, unit profits). In practical applications of linear programming it is important to explore the sensitivity of the numerical solution with respect to changes in these parameters1. Some of them may be subject to known variations in time — prices or cost elements change, machine times are reduced and capacities increased because of rationalization or technological change, output stipulations vary from period to period, etc. — or it may not be possible to determine them exactly but only within certain intervals. (When these variations are of a random nature, the coefficients should be thought of as probability distributions rather than numbers and the problem becomes a stochastic programming problem.)

Journal ArticleDOI
TL;DR: The main conclusion is that any corporate financial decision rule based on mathematical programming under uncertainty contains a limited and potentially suboptimal view of risk.
Abstract: A substantial number of papers in recent years have been devoted to various programming models for making optimal financial decisions under conditions of uncertainty. 1 The purpose of this paper is to: 1. 1. Examine the suitability of the major stochastic programming models proposed for solving the capital budgeting problem. 2. 2. Consider the relative advantages and disadvantages of employing the stochastic dominance criteria to the same problem. 3. 3. Suggest additional areas for investigation. The main conclusion is that any corporate financial decision rule based on mathematical programming under uncertainty contains a limited and potentially suboptimal view of risk. In contrast, financial decision rules employing stochastic dominance criteria, though subject to some inconvenience of application, never provide an incorrect evaluation of the risk of a set of projects. Our references make no effort to cover even a majority of the papers related to the subject, but rather are limited to relatively few articles that have been most helpful to us in gaining our current perspective.


Journal ArticleDOI
TL;DR: CurCurley as discussed by the authors describes an experiment in which the Monte Carlo method is applied to the problem of evaluating alternative life insurance strategies, and family wealth is observed during a forty year life cycle under a variety of assumptions concerning life insurance and other financial decisions.
Abstract: This paper describes an experiment in which the Monte Carlo method is applied to the problem of evaluating alternative life insurance strategies. A hypothetical family is modeled and family wealth is observed during a forty year life cycle under a variety of assumptions concerning life insurance and other financial decisions. The basic objective is exploration of methodological adequacy for evaluating life insurance strategy. The model is used to gather general insights as to preference for different strategies under stochastic dominance ordering rules. A methodology for estimating the cost of life insurance protection is also explored. The evaluation of life insurance strategy is an important part of the problem of consumer choice. Viewed in the framework of time-state preference,1 the insurance decision is a significant factor in determining uncertain wealth outcomes. This is clearly evident in the increasing attention devoted to such variables as uncertainty of lifetime and bequest motivation in models of consumer choice.2 But theoretical models are difficult to operationalize. In view of the variety of available life insurance programs, with complex and time-variant costs and benefits, realistic insurance models are mathematically intractable. Operational techniques for solving insurance models are also elusive. Stochastic dynamic programming, for example, is an attractive and logical framework for choice models. But algorithms are not available for extended time horizons and data deficiencies are severe. Cross-section panel data exist but individual time series of consumption, savings and wealth do not. In view of the mathematical and empirical problems involved, simulation is a promising alternative methodology. This paper discusses the construction, operation and testing of a Monte Carlo insurance model. It introduces Anthony J. Curley, Ph.D., C.P.A., is Associate Professor of Finance in The Pennsylvania State University. His earlier teaching was at St. Joseph's College and The Wharton School. This paper was submitted in June, 1973. This study was made possible by a research grant from the American Risk and Insurance Association. Additional support and computer resources were made available by the P.S.U. Center for Research of the College of Business Administration. The author is indebted to Richard Parli for research assistance, to R. Burr Porter for useful comments on an earlier draft, and to participants at the 1973 Risk Theory Seminar for their comments and encouragement. 'See Arrow [1], Debrew [5] and Hirshleifer [11]. 2Insurance has been considered in theoretical choice models by, among others, Fama [6], Hakansson [9], Meade [15], Merton [16], Samuelson [21] and Yaari [24, 25].


Journal ArticleDOI
01 Sep 1974-Calcolo
TL;DR: The method suggested here is based on the utilization of the generalized inverse of a matrix: it allows a fast and simple solution of parametric problems and has several advantages over the classical parametric methods.
Abstract: In this paper we are concerned with parametric programming problems. The main results are two: the first one is an explicit representation of the general optimal solution of particular parametric programming problems; the second one is an unified approach to general parametric programming problems.

Journal ArticleDOI
TL;DR: In this paper, the authors compare dual programs of stochastic programs with recourse and explain why the discrepancy exists between two such dual programs recently appearing in the literature, and present an example which illustrates the difference.
Abstract: This short paper compares dual programs of stochastic programs with recourse. It explains why the discrepancy exists between two such dual programs recently appearing in the literature. An example is presented which illustrates the difference.

Book ChapterDOI
01 Jul 1974
TL;DR: Very many optimization problems, as related with system development, have a dynamic character and they are to be solved under uncertainty when for the part of initial information the probable description is neither known exactly nor available at all.
Abstract: Very many optimization problems, as related with system development, have a dynamic character and they are to be solved under uncertainty when for the part of initial information the probable description is neither known exactly nor available at all.

Journal ArticleDOI
TL;DR: In this paper, the optimal control of a linear system subject to random actions is considered, where the system's phase coordinates are connected by nonconvex constraints which are necessarily also stochastic.

Journal ArticleDOI
TL;DR: In this article, the duality conditions of linear programming in the determination of optimal investment programs have definitively clarified the question of the correct discount rate in the deterministic case (Chames, Cooper, Miller, 1959).
Abstract: The interpretation of the duality conditions of linear programming in the determination of optimal investment programmes has definitively clarified the question of the ‘correct’ discount rate in the deterministic case (Chames, Cooper, Miller, 1959). A similar total analysis of the multiple expectations case facilitates superior indications of the nature of the present value calculation for a piecemeal approach to project appraisal. A controversial issue is the question of whether the expected values of net cash flows should be discounted with a ‘risk-adjusted’ rate or whether such flows should first be adjusted for risk and then be discounted at a ‘risk free’ rate.