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Showing papers on "Stochastic programming published in 1981"


Journal ArticleDOI
TL;DR: In this paper, the optimal behavior of a single dealer who is faced with a stochastic demand to trade (modeled by a continuous time Poisson jump process) and facing return risk on his stock and on the rest of his portfolio was examined.

1,416 citations


Journal ArticleDOI
TL;DR: In this paper, the authors unify the concepts of caution and probing put forth by Feldbaum [14] with the mathematical technique of stochastic dynamic programming originated by Bellman [5].
Abstract: The purpose of this paper is to unify the concepts of caution and probing put forth by Feldbaum [14] with the mathematical technique of stochastic dynamic programming originated by Bellman [5]. The decomposition of the expected cost in a stochastic control problem, recently developed in [8], is used to assess quantitatively the caution and probing effects of the system uncertainties on the control. It is shown how in some problems, because of the uncertainties, the control becomes cautious (less aggressive) while in other problems it will probe (by becoming more aggressive) in order to enhance the estimation/identification while controlling the system. Following this a classification of stochastic control problems according to the dominant effect is discussed. This is then used to point out which are the stochastic control problems where substantial improvements can be expected from using a sophisticated algorithm versus a simple one.

156 citations


Journal ArticleDOI
TL;DR: In this paper, a stochastic dynamic programming model was developed to obtain optimal acquisition and sale strategies for the U.S. oil reserve, and the model incorporates quota or tariff policies which may be used in conjunction with the stockpile policy.
Abstract: This article develops a stochastic dynamic programming model which may be used to obtain optimal acquisition and sale strategies for the U.S. oil reserve. The model incorporates quota or tariff policies which may be used in conjunction with the stockpile policy. Although the main focus is on U.S. stockpile policy, a joint consumer country policy is also considered. The analysis indicates the importance of the degree of oil supply response in determining the effectiveness of a stockpile policy.

117 citations


Journal ArticleDOI
TL;DR: In this paper, the authors compare CCP to stochastic programming with recourse SPR and conclude that CCP is seriously deficient as a modeling technique and of limited value as a computational device.
Abstract: Some important conceptual problems concerning the application of chance constrained programming CCP to risky practical decision problems are discussed by comparing CCP to stochastic programming with recourse SPR. We expand on Garstka's distinction between mathematical equivalence and economic equivalence showing that much of practical usefulness is lost in the transition between SPR and CCP. By examining the literature on CCP applications we conclude that there is little evidence that CCP is used with the care that is necessary. Finally we conclude that CCP is seriously deficient as a modeling technique and of limited value as a computational device.

90 citations


01 Jan 1981
TL;DR: For two simple versions of this two-stage hierarchical scheduling problem, heuristic solution methods are described and shown that their performance is asymptotically optimal both in expectation and in probability.

50 citations


Journal ArticleDOI
TL;DR: In this paper, the stochastic maximum principle is applied to solve eight different control problems with special structure and the main thrust of the work is to show that some completely observable control problems can be solved quite quickly and easily using the maximum principle.
Abstract: The stochastic maximum principle is applied to solve eight stochastic control problems. Four have been solved previously using much more complicated methods, but the last four are new. The main thrust of the work is to show that some completely observable stochastic control problems with special structure can be solved quite quickly and easily using the maximum principle.

49 citations


Journal ArticleDOI
TL;DR: This paper reviews a number of data-based applications of optimization methods to pest management and the comparative advantages of alternative optimization methods are discussed.
Abstract: Pest management is a multistage decision process in a stochastic and observable system. A control model of a pest ecosystem is characterized by discontinuous cost functions and nonlinear, stochastic state equations describing the interactions among a large namber of ecosystem components. Dynamic programming has been the optimization technique which has been most widely applied to pest management analysis, but several other optimization methods have also proven useful. This paper reviews a number of data-based applications of optimization methods to pest management. The comparative advantages of alternative optimization methods are discussed.

41 citations


Journal ArticleDOI
TL;DR: This paper shows how state space models for human resource planning may be extended from linear and goal-programming formulations to cover the case where manpower demands and available resources for future periods are not known with certainty.
Abstract: This paper shows how state space models for human resource planning may be extended from linear and goal-programming formulations to cover the case where manpower demands and available resources for future periods are not known with certainty. Under reasonable assumptions, the problem can be treated as a multi-period stochastic program with simple recourse. Normal and Beta probability distributions are fitted to the right hand sides, and the equivalent determinstic programme solved using convex separable programming. An application of this methodology to a military human resource planning problem is described. Solution times for the stochastic model compare favourably with those for a goal-programming model of the same human resource system.

38 citations


Journal ArticleDOI
TL;DR: It is shown that many prominent problems in the nonlinear programming literature can be viewed as optimal control problems, and for these problems, modern dynamic programming methodology is competitive with respect to processing time.
Abstract: Dynamic programming techniques have proven to be more successful than alternative nonlinear programming algorithms for solving many discrete-time optimal control problems. The reason for this is that, because of the stagewise decomposition which characterizes dynamic programming, the computational burden grows approximately linearly with the numbern of decision times, whereas the burden for other methods tends to grow faster (e.g.,n 3 for Newton's method). The idea motivating the present study is that the advantages of dynamic programming can be brought to bear on classical nonlinear programming problems if only they can somehow be rephrased as optimal control problems. As shown herein, it is indeed the case that many prominent problems in the nonlinear programming literature can be viewed as optimal control problems, and for these problems, modern dynamic programming methodology is competitive with respect to processing time. The mechanism behind this success is that such methodology achieves quadratic convergence without requiring solution of large systems of linear equations.

33 citations


Journal ArticleDOI
George J. Anders1
TL;DR: In this paper, two probabilistic reliability criteria are represented: deterministic constraints on the reserve margin or loss of load probability (LOLP) criterion, in addition to real power flows in the transmission lines are introduced and solution procedures for the resulting chance constrained stochastic programming problems are also discussed.
Abstract: The generation expansion models described in the literature are, in a majority of cases, formulated as deterministic optimization problems. The reliability criteria, if present, are represented as deterministic constraints on the reserve margin or, in some cases, as a loss of load probability (LOLP) criterion. In this paper, two probabilistic reliability criteria are represented. In addition to the LOLP criterion, the probabilistic constraints on real power flows in the transmission lines are introduced. The solution procedures for the resulting chance constrained stochastic programming problems are also discussed. The basic concepts developed in this paper are applied to a small system to demonstrate the influence of power flow constraints on the selection process.

27 citations


Journal ArticleDOI
TL;DR: In this article, a method is proposed to optimize the discharge of the hydro reservoirs over a period of one year. Explicit Stochastic Dynamic Programming (ESDD) is employed to deal with the M-stage stochastic return function, the random inflows to the reservoirs and the bounded nature of the system constraints.
Abstract: The operation planning of a hydro-thermal power system involves the coordination of the production schedule of various types of generation, including hydro. A good model is needed to minimize the system energy production costs over a given period in the mid-range time frame. A method is proposed to optimize the discharge of the hydro reservoirs over the period of one year. Explicit Stochastic Dynamic Programming (ESDD) [1] is employed to deal with the M-stage stochastic return function, the random inflows to the reservoirs and the bounded nature of the system constraints. Aggregation of the reservoir and hydro plant sub-systems is used to reduce the dimensionality of the problem, permitting a; realistic modeling of the hydro portion of the power system. The cost of operation for various valve loadings, the scheduled downtime for various unit maintenance activities, the predicted partial and total forced outages, and the stochastic river inflows to the reservoirs are input requirements to the program which yields the monthly hydro energy scheduling for the most economic loading over a one year period

Journal ArticleDOI
Moshe Sniedovich1
TL;DR: In this article, a simple deterministic dynamic programming model is used as a general framework for the analysis of stochastic versions of three classical optimization problems: knapsack, traveling salesperson, and assembly line balancing problems.

Journal ArticleDOI
TL;DR: In this paper, the authors compare the properties of the suboptimal dual adaptive stochastic control with those of the optimal control when plant dynamic contain multiplicative white noise parameters.
Abstract: The purpose of this paper is to compare analytically the properties of the suboptimal dual adaptive stochastic control with those of the optimal control, when plant dynamic contain multiplicative white noise parameters. A simple scalar example is used for this analysis.

Journal ArticleDOI
TL;DR: An optimization procedure utilizing stochastic dynamic programming is described, and optimal feedback strategies for a wolf-ungulate system in Alaska are estimated, revealing that stability properties depend on predator search efficiency.

Dissertation
01 Nov 1981
TL;DR: Results are reported of testing the approximate solution technique developed for the general model, ordinary linear programming ignoring all the stochastic elements in the problem, and two other approximate techniques, by replicative simulation, which suggest that the penalty incurred by ignoring the stoChastic nature of the problem is significant, but that first order deviations from optimal decisions may lead only to second order penalties.
Abstract: Exact solutions to stochastic, capacitated, multi-commodity, multi-stage production/inventory models are in general computationally intractable. The practical application of such models is therefore inhibited. In this thesis a general stochastic, capacitated, multi- commodity, multi-stage production/inventory model with linear cost structure is proposed. Under convexity conditions it is a stochastic linear program. A good computationally efficient approximate solution technique is developed and some numerical results reported. It is important to assess the merit of approximate techniques and this is done statistically by replicative simulation. But the accuracy of this method improves only as the square root of the number of simulation trials made, so it is important to eliminate any unnecessary variability in each trial. It is proposed that this be done by the use of control statistics. Several novel control statistics are developed, the most powerful being a martingale control statistic constructed independently for each trial from information provided by the approximate technique being tested. Results are reported of testing the approximate solution technique developed for the general model, ordinary linear programming ignoring all the stochastic elements in the problem, and two other approximate techniques, by replicative simulation. These suggest that the penalty incurred by ignoring the stochastic nature of the problem is significant, but that first order deviations from optimal decisions may lead only to second order penalties. This is a desirable feature of the stochastic models, for it indicates that approximate solution techniques to stochastic programs may be more reliable than would be supposed from the approximations made.

Journal ArticleDOI
TL;DR: In this article, a family of problems obtained by a small arbitrary perturbation of the parameters of linear programming problems is associated with the linear programming problem, and the main result is to obtain the necessary and sufficient conditions for stability of these problems.
Abstract: WITH the linear programming problem is associated a family of problems obtained by a small arbitrary perturbation of the parameters. The main result is to obtain the necessary and sufficient conditions for stability of linear programming problems. For unstable problems, a method of regularization is described, which does not go outside the framework of linear programming.

Journal ArticleDOI
TL;DR: In this article, a special working group was established to investigate the problems involved with the solvency of insurers, and the capacity of risk carriers is one of the problems dealt with, and it will be preliminarily reviewed in this paper.
Abstract: The Ministry of Social Affairs and Health, being the Supervising Office of Insurance in Finland, has established a special working group to investigate the problems involved with the solvency of insurers. A report will be compiled in a near future. The capacity of risk carriers is one of the problems dealt with, and it will be preliminarily reviewed in this paper. The problem was treated by the working group parallelly by means of 1. an empirical approach observing actual fluctuations in underwriting gains of insurers, and 2. a theoretical approach, constructing a stochastic-dynamic model and studying its behaviour, especially its sensitivity to numerous background factors. First the methods of investigation are described and their application is then demonstrated using some numerical data. Because a comprehensive report will be published by the working group separately, only the main schedule is given. For the same reason the consideration is limited here to stochastic risks, omitting the fact that the solvency of an insurer is also jeopardized by numerous “non-stochastic” risks such as failure in investments, political interference of the authorities, mismanagement of the company, or misappropriation of its property.


Journal ArticleDOI
01 Apr 1981
TL;DR: In this article, a class of optimization problems is introduced which contains the stop-loss problem from risk theory as a special case, and two abstract optimization models, viz. linear programming in normed vector spaces, and Tchebycheff systems, are presented, and it is shown how to solve the initial problems by methods derived from the general models.
Abstract: A class of optimization problems is introduced which contains the stop-loss problem from risk theory as a special case. Two abstract optimization models, viz. linear programming in normed vector spaces, and Tchebycheff systems, are presented, and it is shown how to solve the initial problems by methods derived from the general models.

Book ChapterDOI
S. Vajda1
01 Jan 1981
TL;DR: This chapter considers cases where the constant terms in the constraints are not precisely known; the authors know only their probability distributions.
Abstract: Until now, when we have been dealing with linear programming, we have always assumed that the constants in the objective function, and those in the constraints, were precisely known. In many practical applications this is not so. We shall now consider cases where the constant terms in the constraints are not precisely known; we know only their probability distributions.

Journal ArticleDOI
TL;DR: The study demonstrates the use of fuzzy expectation values in problems of multistage optimization under uncertainty by presenting a practicable procedure for the case where the optimization objective can be decomposed into a series of single-stage decision goals.

Journal ArticleDOI
TL;DR: In this article, the authors study the behavior of a purely competitive firm in a market in which traders' plans may not be realized each period and compare the situation in which plans are always realized to the situation where markets are not cleared each period, and shortages may arise with the realization of plans being in doubt.
Abstract: The objective of this paper is to study the behavior of the purely competitive firm in a market in which traders' plans may not be realized each period. The emphasis of the study is motivated by a desire to introduce explicit price-makers into the theory of competitive markets. The method of introducing price-makers may lead to situations in which markets are not cleared each period and shortages may arise with the realization of plans being in doubt. In this environment traders learn to adjust decisions to offset periodic disappointment. Multiperiod models are introduced to analyze the decision process of the competitive firm in the market and stochastic dynamic programming methods are used to obtain characteristics of optimal plans. Results are compared to the situation in which plans are always realized.

Journal ArticleDOI
TL;DR: In this article, the optimal control problem is transformed into one of mathematical programming by a Raleigh-Ritz-type procedure, which is essentially a penalty function approach which penalizes the given performance index for not satisfying the differential constraints.
Abstract: Introduction O PTIMAL control problems with bounded controls reduce to two-point boundary-value problems which are difficult to handle by conventional methods of calculus of variations. Pontryagin's maximum principle and Bellman's dynamic programming are the other methods for solving such problems. In this paper the optimal control problem is transformed into one of mathematical programming by a Raleigh-Ritz-type procedure. This is essentially a penalty function approach which penalizes the given performance index for not satisfying the differential constraints. The resulting mathematical programming problem is then solved by SWIFT—Sequential Weightage Increasing Factor Technique developed by the authors. The method is illustrated by obtaining the thrust angle history of a probe for an Earth-to-Mars orbit transfer in minimum time. Good comparison of the time obtained by this method with the actual time taken by the Viking-2 spacecraft is extremely interesting. Other methods' do not show such a good comparison.


Book ChapterDOI
01 Jan 1981
TL;DR: The mixed strategy solutions, the possibility of informational improvement and search, and statistical testing of the LP model viewed econometrically are studied.
Abstract: Conventional methods of introducing risk and uncertainty into a linear programming (LP) model, where some parameters are random generally ignore the following cases: (a) the mixed strategy solutions, (b) the possibility of informational improvement and search, and (c) statistical testing of the LP model viewed econometrically.

Journal ArticleDOI
TL;DR: The thermal units scheduling problem is considered from both its aspects: the selection of units to be placed in operation, and the load distribution among them, by considering two separate, but mutually dependent optimization problems.

Journal Article
TL;DR: In this article, the authors presented a method for the collapse load analysis of prefabricated panels in plane, taking the uncertainty of joint material characteristics into consideration, and numerical results showed that an error on the detriment of safety is committed by assuming given, constant material characteristic values.
Abstract: The hehaviour of huildings composed of prefabricated panels is largely influenced hy displacements of the joints made on the site. The joints are the most delicate and the weakest parts of the buildings, therefore it is very important to determine the forces acting on them. They are decisive in the strength calculation, mainly in determining the collapse load of panel structures. But strength characteristics of joints made in field assembly may differ considerably from each other. For the sake of simplicity, the method to he presented for the collapse load analysis of panel structures in plane will take the uncertainty of joint material characteristics into consideration. This method is more complicated than the usual one, but numerical results sho'w that an error on the detriment of safety is committed by assuming given, constant material characteristic values. The uncertainties of construction are reckoned 'with by taking the yield points as random variahles.

ReportDOI
01 Aug 1981
TL;DR: Criteria of optimization, classical methods of optimized, numerical methods, and optimal search procedures are discussed and methods of optimization with special applications to simulation are discussed.
Abstract: : Simulation techniques utilize methods of optimization in several aspects. Validation of simulation models, estimation of models and design of simulation experiments require optimization. Methods of optimization are discussed with special applications to simulation. Criteria of optimization, classical methods of optimization, numerical methods, and optimal search procedures are discussed. (Author)

Book ChapterDOI
01 Jan 1981
TL;DR: In this article, the authors introduce a measure theoretic structure on top of the topological structure, and the resulting interplay brings a new set of questions interesting on their own as well.
Abstract: This final chapter deals with a class of stochastic optimization problems. For this purpose we introduce a measure theoretic structure on top of the topological structure, and the resulting interplay brings a new set of questions interesting on their own as well. The measure theory is nonclassical in that the measures are only finitely additive on the field of cylinder sets, the canonical example being the Gauss measure. The notion of a weak random variable suffices for the stochastic extension of the control problems of the previous chapter, a crucial notion being that of “white noise,” leading to a treatment that is novel with this book, of filtering and control problems embracing in particular linear stochastic partial differential equations. Important tools in the development are the Krein factorization theorem and the Riccati equation. For nonlinear operations we develop a “nonlinear” white noise theory in which the notion of a physical random variable plays a crucial role, as in the calculation of the Radon-Nikodym derivative of finitely additive Gaussian measures. Within the scope of the present work we can but touch upon the general theory of nonlinear stochastic differential equations.

Journal ArticleDOI
TL;DR: In this article, the problem of bounding Pr {X > Y, when the distribution of X is subject to certain moment conditions and Y is known to be of convexconcave type, is treated in the framework of mathematical programming.
Abstract: Problems of bounding Pr {X > Y}, when the distribution of X is subject to certain moment conditions and the distribution of Y is known to be of convexconcave type, are treated in the framework of mathematical programming. Juxtaposed are two programming methods; one is based on the notion of weak duality and the other on the geometry of a certain moment space.