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Showing papers on "Stochastic programming published in 1976"


Book
01 Jan 1976
TL;DR: In this paper, the authors present a model for renewable-resource harvesting based on the Schaefer model with a focus on the one-dimensional control problem and its application to policy problems.
Abstract: Introduction. 1. Elementary Dynamics of Exploited Populations. 1.1 The Logistic Growth Model. 1.2 Generalized Logistic Models: Depensation. 1.3 Summary and Critique. 2. Economic Models of Renewable-Resource Harvesting. 2.1 The Open-Access Fishery. 2.2 Economic Overfishing. 2.3 Biological Overfishing. 2.4 Optimal Fishery Management. 2.5 The Optimal Harvest Policy. 2.6 Examples Based on the Schaefer Model. 2.7 Linear Variational Problems. 2.8 The Possibility of Extinction. 2.9 Summary and Critique. 3. Capital-Theoretic Aspects of Resource Management. 3.1 Interest and Discount Rates. 3.2 Capital Theory and Renewable Resources. 3.3 Nonautonomous Models. 3.4 Applications to Policy Problems: Labor Mobility in the Fishery. 4. Optimal Control Theory. 4.1 One-Dimensional Control Problems. 4.2 A Nonlinear Fishery Model. 4.3 Economic Interpretation of the Maximum Principle. 4.4 Multidimensional Optimal Control Problem. 4.5 Optimal Investment in Renewable-Resource Harvesting. 5. Supply and Demand: Nonlinear Models. 5.1 The Elementary Theory of Supply and Demand. 5.2 Supply and Demand in Fisheries. 5.3 Nonlinear Cost Effects: Pulse Fishing. 5.4 Game-Theoretic Models. 5.5 Transboundary Fishery Resources: A Further Application of the Theory. 5.6 Summary and Critique. 6. Dynamical Systems. 6.1 Basic Theory. 6.2 Dynamical Systems in the Plane: Linear Theory. 6.3 Isoclines. 6.4 Nonlinear Plane-Autonomous Systems. 6.5 Limit Cycles. 6.6 Gause's Model of Interspecific Competition. 7. Discrete-Time and Metered Models. 7.1 A General Metered Stock-Recruitment Model. 7.2 The Beverton-Holt Stock-Recruitment Model. 7.3 Depensation Models. 7.4 Overcompensation. 7.5 A Simple Cohort Model. 7.6 The Production Function of a Fishery. 7.7 Optimal Harvest Policies. 7.8 The Discrete Maximum Principle. 7.9 Dynamic Programming. 8. The Theory of Resource Regulation. 8.1 A Behavioral Model. 8.2 Optimization Analysis. 8.3 Limited Entry. 8.4 Taxes and Allocated Transferable Quotas. 8.5 Total Catch Quotas. 8.6 Summary and Critique. 9. Growth and Aging. 9.1 Forestry Management: The Faustmann Model. 9.2 The Beverton-Holt Fisheries Model. 9.3 Dynamic Optimization in the Beverton-Holt Model. 9.4 The Case of Bounded F. 9.5 Multiple, Cohorts: Nonselective Gear. 9.6 Pulse Fishing. 9.7 Multiple Cohorts: Selective Gear. 9.8 Regulation. 9.9 Summary and Critique. 10. Multispecies Models. 10.1 Differential Productivity. 10.2 Harvesting Competing Populations. 10.3 Selective Harvesting. 10.4 A Diffusion Model: The Inshore-Offshore Fishery. 10.5 Summary and Critique. 11. Stochastic Resource Models. 11.1 Stochastic Dynamic Programming. 11.2 A Stochastic Forest Rotation Model. 11.3 Uncertainty and Learning. 11.4 Searching for Fish. 11.5 Summary and Critique. Supplementary Reading. References. Index.

2,449 citations


Book
01 Jan 1976
TL;DR: In this article, the authors present a model for single-stage SLP models with Probability Functions, Quantile Functions, Value at Risk, Models Based on Expectation, Models Built with Deviation Measures, Modeling Risk and Opportunity, Risk Measures.
Abstract: Basics.- Introduction.- Linear Programming Prerequisites.- Nonlinear Programming Prerequisites.- Single-stage SLP Models.- Introduction.- Models involving Probability Functions.- Quantile Functions, Value at Risk.- Models Based on Expectation.- Models Built with Deviation Measures.- Modeling Risk and Opportunity.- Risk Measures.- Multi-stage SLP Models.- The General SLP with Recourse.- The Two-stage SLP.- The Multi-stage SLP.- Algorithms.- Models with Probability Functions.- Models with Quantile Functions.- Models Based on Expectation.- Models with Deviation Measures.- Two-stage Recourse Problems.- Multi-stage Recourse Problems.- Modeling Systems for SLP.- Bibliography.

663 citations


Book
01 Jan 1976
TL;DR: A major revision of the second volume of a textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization.
Abstract: A major revision of the second volume of a textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequential decision making under uncertainty, and discrete/combinatorial optimization. The second volume is oriented towards mathematical analysis and computation, and treats infinite horizon problems extensively. New features of the 3rd edition are: 1) A major enlargement in size and scope: the length has increased by more than 50%, and most of the old material has been restructured and/or revised. 2) Extensive coverage (more than 100 pages) of recent research on simulation-based approximate dynamic programming (neuro-dynamic programming), which allow the practical application of dynamic programming to large and complex problems. 3) An in-depth development of the average cost problem (more than 100 pages), including a full analysis of multichain problems, and an extensive analysis of infinite-spaces problems. 4) An introduction to infinite state space stochastic shortest path problems. 5) Expansion of the theory and use of contraction mappings in infinite state space problems and in neuro-dynamic programming. 6) A substantive appendix on the mathematical measure-theoretic issues that must be addressed for a rigorous theory of stochastic dynamic programming. Much supplementary material can be found in the book's web page: http://www.athenasc.com/dpbook.html

606 citations


Book
01 Jan 1976

147 citations



Journal ArticleDOI
TL;DR: This bibliography contains references to publications, reports, and articles dealing with stochastic programming in terms of their contents: formulation, applications, theory and computation, books and surveys.
Abstract: About 800 publications, reports, and articles dealing with stochastic programming are included in this bibliography. The references are classified in terms of their contents: formulation, applications, theory and computation, books and surveys.

83 citations


Journal ArticleDOI
TL;DR: Optimal harvest rates for mixed stocks of fish are calculated using stochastic dynamic programming, which is shown to be superior to the best methods currently described in the literature.
Abstract: Optimal harvest rates for mixed stocks of fish are calculated using stochastic dynamic programming. This technique is shown to be superior to the best methods currently described in the literature. The Ricker stock recruitment curve is assumed for two stocks harvested by the same fishery. The optimal harvest rates are calculated as a function of the size of each stock, for a series of possible parameter values. The dynamic programming solution is similar to the fixed escapement policy only when the two stocks have similar Ricker parameters, or when the two stocks are of equal size. Normally, one should harvest harder than calculated from fixed escapement analysis.

67 citations


Journal ArticleDOI
TL;DR: In this article, a two-stage stochastic programming problem with recourse is studied in terms of an extended Lagrangian function which allows certain multipliers to be elements of a dual space (i?00)*, rather than an ϊ£λ space.
Abstract: A two-stage stochastic programming problem with recourse is studied here in terms of an extended Lagrangian function which allows certain multipliers to be elements of a dual space (i?00)*, rather than an ϊ£λ space. Such multipliers can be decomposed into an i^-component and a "singular" component. The generalization makes it possible to characterize solutions to the problem in terms of a saddle-point, if the problem is strictly feasible. The Kuhn-Tucker conditions for the basic duality framework are modified to admit singular multipliers. It is shown that the optimal multiplier vectors in the extended dual problem are, in at least one broad case, ideal limits of maximizing sequences of multiplier vectors in the basic dual problem.

42 citations


Book ChapterDOI
01 Jan 1976
TL;DR: Conditions under which the problem can be solved approximately, or in the limit, by solving a sequence of linear programming problems in R n by approximating the given random vectors by simple random vectors are presented.
Abstract: Multistage stochastic programming with recourse has been formulated as linear programming in an Lp space. This paper presents conditions under which the problem can be solved approximately, or in the limit, by solving a sequence of linear programming problems in R n . Each of these problems is obtained by approximating the given random vectors by simple random vectors.

34 citations


Journal ArticleDOI
TL;DR: Multistage stochastic programming with recourse is defined recursively as a natural extension of two-stage stochastics with recourse, and some existing results for two- stage problems are examined.
Abstract: Multistage stochastic programming with recourse is defined recursively as a natural extension of two-stage stochastic programming with recourse. Some existing results for two-stage problems are ext...

29 citations


Journal ArticleDOI
TL;DR: Multistage stochastic programming with recourse has been formulated in terms of a recursive sequence of parameterized, finite-dimensional mathematical programming problems.
Abstract: Multistage stochastic programming with recourse has been formulated in terms of a recursive sequence of parameterized, finite-dimensional mathematical programming problems. It has also been formula...

Journal ArticleDOI
B. Bereanu1
TL;DR: In this article, it is proved a sufficient condition that the optimal value of a linear program be a continuous function of the coefficients, in the sense that, if it is not imposed, then examples with discontinuous optimal-value function may be found.
Abstract: It is proved a sufficient condition that the optimal value of a linear program be a continuous function of the coefficients. The condition isessential, in the sense that, if it is not imposed, then examples with discontinuous optimal-value function may be found. It is shown that certain classes of linear programs important in applications satisfy this condition. Using the relation between parametric linear programming and the distribution problem in stochastic programming, a necessary and sufficient condition is given that such a program has optimal value. Stable stochastic linear programs are introduced, and a sufficient condition of such stability, important in computation problems, is established.

Journal ArticleDOI
TL;DR: A rigorous definition of multistage stochastic programming with fixed linear recourse is shown to avoid the possibility that the optimal value of a multi-stage programming problem may be ill-defined and the recursion defining the problem may fail, so the problem itself is not even defined.
Abstract: Certain measure-theoretic issues raise the possibility that (a) the optimal value of a multistage stochastic programming problem may be ill-defined and (b) the recursion defining the problem may fail, so the problem itself is not even defined. The first difficulty is illustrated by example. A rigorous definition of multistage stochastic programming with fixed linear recourse is shown to avoid this difficulty. In the context of the new definition, certain measurability, convexity, and lower-semicontinuity assumptions on the objective function preclude the second possibility.


Journal ArticleDOI
TL;DR: The importance of instantaneous and future shop loads for assigning due-dates in a one-machine shop, with constant interarrivals and exponential service times, is shown.
Abstract: The due-date assignment problem occurs when due-dates are assigned within, rather than outside, a job shop. This study explores the importance of instantaneous and future shop loads in setting due-dates in shops operating under due-date dependent queue discipline. The assignment of due-dates to arriving jobs in an m-machine shop is formulated as a stochastic dynamic programming problem in the first part of this study. A computational experiment using dynamic programming is performed in the second part and due-dates are developed for specific instantaneous load conditions in a simulated one-machine shop. The importance of instantaneous and future shop loads for assigning due-dates in a one-machine shop, with constant interarrivals and exponential service times, is shown.

Book ChapterDOI
01 Jan 1976
TL;DR: The aim of this work is to prove the existence of Lagrange multipliers associated with the information constraints and with the phase constraints.
Abstract: The multistage problems of concave stochastic programming are studied in the paper. The aim of this work is to prove the existence of Lagrange multipliers associated with the information constraints and with the phase constraints.

Journal ArticleDOI
TL;DR: The optimization models presented here represent a synthesis between input-output analysis and mathematical programming models for environmental pollution control and the theory of optimization with relative bounded variables in nonlinear programming.


Journal ArticleDOI
TL;DR: In this paper, the authors consider the problem of determining the cumulative distribution function and/or moments of the optimal solution value of a nonlinear program dependent upon a single random variable and provide an algorithm to solve the distribution problem in the linear case based on extensions of the methods of parametric linear programming.
Abstract: We consider the problem of determining the cumulative distribution function and/or moments of the optimal solution value of a nonlinear program dependent upon a single random variable. This problem is difficult computationally because one must in effect determine the optimal solution to an infinite number of nonlinear programs. Bereanu [Bereanu, B., G. Peeters. 1970. A ‘Wait-and-See’ problem in stochastic linear programming. An experimental computer code. Cashiers Centre Etudes Rech. Oper. 12 (3) 133–148.] has provided an algorithm to solve the distribution problem in the linear case based on extensions of the methods of parametric linear programming. (See also [Bereanu, B. 1967. On stochastic linear programming, distribution problems: stochastic technology matrix. Z. f. Wahrscheinlichkeitstheorie u. oerw. Gerbieter 8 148–152; Bereanu, B. 1971. The distribution problem in stochastic linear programming: the Cartesian integration method. Center of Mathematical Statistics of the Academy of RSR, Bucharest, 71...

Journal ArticleDOI
TL;DR: The network equilibrium problem, the network design model, and the stochastic transportation problem are analyzed.

Journal ArticleDOI
TL;DR: The multiperiod optimal control problem is formulated and solved using dynamic programming and it is shown that the solution to this problem can be derived from classical programming methods.
Abstract: The multiperiod optimal control problem is formulated and solved using dynamic programming.

Proceedings ArticleDOI
01 Dec 1976
TL;DR: In this article, a dual control optimization problem for a stochastic system with constant but unknown parameters over a finite horizon is considered, and the expected value of a quadratic scalar performance index, with respect to the prior statistics of the parameters of the system, is minimized.
Abstract: The problem of controlling a stochastic system containing constant but unknown parameters over a finite horizon is considered. The expected value of a quadratic scalar performance index, with respect to the prior statistics of the parameters of the system, is minimized. Due to the complexity of this dual control optimization problem we propose to fix the structure of the estimator-controller and choose the feedback gain, the parameter estimates, and filter gain such that the performance index is minimized. We develop a design procedure for optimizing the constant parameters of this controller. This procedure is attractive when the horizon is short but it also incorporates adaptation to long term changes in the statistics of the plant parameters.

DOI
01 Jan 1976
TL;DR: In this paper, a mathematical programming model is presented to determine the optimal water resource allocation and pricing policy for Salt Lake County, by maximizing the sum of consumer and producer surplus (the difference between total willingness-to-pay and total cost).
Abstract: Using a conceptual model of a water supply firm, the necessary conditions for production and market efficiency are derived when renovated wastewater is considered as a potential water resource. The nature and extent of the supply augmentation due to recycled reuse is demonstrated using classical optimization techniques. Three stages of short-run supply corresponding to no recycling, partial recycled reuse and complete recycling of all reclaimable water are identified through appropriate Lagrangian Multipliers as well as graphical techniques. A mathematical programming model is structured to determine the optimal water resource allocation and pricing policy for Salt Lake County. By maximizing the sum of consumer and producer surplus (the difference between total willingness-to-pay and total cost) economically efficient equilibria arc derived. The feasibility of recycled reuse for Illunicipal purposes is examined in a planning context. The impact of higher water quality discharge standards on the attractiveness or water recycling option is studied. To ensure social acceptability of renovated wastewater for culinary purposes, blending restrictions arc imposed, which stipulate that the amount of water for reuse be less than a fixed percentage of the water from other sources. The effect of such a constraint on the prices and water allocation are delineated. The hydrologic uncertainty in water supply is treated using stochastic programming techniques. Application of the concepts of single and joint chance-constrained programming are illustrated. The resulting changes in pricing and allocation policies are discussed.

Proceedings ArticleDOI
01 Dec 1976
TL;DR: A suboptimal procedure that preserves the essential features of stochastic dynamic programming is developed and is measured in terms of the improvement in the performance index when the action resources are allocated subsequently with more accurate, even though still imperfect, information.
Abstract: This paper presents a performance adaptive algorithm for the allocation of information gathering (probing) resources and action resources in a time-varying environment. A suboptimal procedure that preserves the essential features of stochastic dynamic programming is developed. The information gathering resources are allocated using the prior probability density function of the subsequent observations in order to evaluate the value of future information. This value is measured in terms of the improvement in the performance index when the action resources are allocated subsequently with more accurate, even though still imperfect, information.

Journal ArticleDOI
TL;DR: In this article, a reformulation of the problem as an integer transportation problem with a convex separable cost function is presented, which demonstrates the relationship between some statistical optimization problems and mathematical programming procedures.
Abstract: Presented here is a reformulation of the problem as an integer transportation problem with a convex separable cost function. This representation demonstrates the relationships between some statistical optimization problems and mathematical programming procedures.

Journal ArticleDOI
TL;DR: In this paper, the problem of allocating customers of different types to various channels of a service system is considered, and the objective is to find the optimal allocation of customers to channels, xij, such that the expected net gain, revenue minus losses, is maximized.
Abstract: The problem of allocating customers of different types to various channels of a service system is considered. Service times are assumed to be independent identically distributed random variables whose distribution functions depend on the type of customers as well as the service channel. The total loading time of each channel consists of the sum of service times of all customers which were allocated to it and is thus a random variable also. If the loading time of a given channel exceeds falls short its nominal capacity, an overtime idle time penalty is incurred. Penalties are assumed to be proportional to the time lapse involved. There is also a revenue gain which is proportional to the number of customers served. The objective is to find the optimal allocation of customers to channels, xij, such that the expected net gain, revenue minus losses, is maximized. It is shown that the distribution function of a loading time depends on the choice of the xij and hence that, in general, no claims can be made with respect to desirable convexity properties of the objective function. It is further shown that if the service times are assumed to be normally distributed, then the objective function depends also on the means and the variances of the loading times. The mathematical properties of the program are utilized to ascertain that the solution obtained via a suggested algorithm is global. The nonlinear program is reduced to a possibly iterative solution of a linear program by using previous results obtained by the first author.

Journal ArticleDOI
TL;DR: The role of the 'wait and see' model in planning is discussed, and a method of analysis based on the minimax and maximax decision criteria is proposed which requires the solution of a special class of non-linear programming problems.
Abstract: A number of methods of obtaining the distribution of the optimum of the ‘wait and see’ stochastic programming model have been proposed, but computational experience for these is currently limited to the solution of small problems. The purpose of this paper is to discuss the role of the ‘wait and see’ model in planning, and to propose a method of analysis based on the minimax and maximax decision criteria. The approach requires the solution of a special class of non-linear programming problems. Computational results to date suggest that it will be possible to analyse practically sized problems in this way.

Proceedings ArticleDOI
01 Dec 1976
TL;DR: In this paper, the authors present a method of converting a stochastic optimal control problem into a deterministic one, where probability distributions on the state space of the deterministic model are taken as states in the deterministic model, and relations between policies and rewards of the two models are given.
Abstract: This paper presents a method of converting a stochastic optimal control problem into a deterministic one, where probability distributions on the state space of the stochastic model are taken as states in the deterministic model. Relations between policies and rewards of the two models are given and counterparts to known deterministic results are developed for the stochastic model. A novel feature of our framework is the enlargement of the set of admissible control laws to include universally measurable policies rather than only Borel measurable policies. This feature together with a new measurable selection theorem allow us to dispense with the notions of p-optimality of Blackwell and Strauch [11,6] and the notion of p-essential infimum of Striebel [12], and obtain all results in a form comparable to that for deterministic problems.


Posted Content
TL;DR: In this article, about 800 publications, reports, and articles dealing with stochastic programming are included in a bibliography, classified in terms of their contents: formulation, applications, theory and computation, books and surveys.
Abstract: About 800 publications, reports, and articles dealing with stochastic programming are included in this bibliography. The references are classified in terms of their contents: formulation, applications, theory and computation, books and surveys.