scispace - formally typeset
Search or ask a question

Showing papers on "Stochastic programming published in 1983"


Journal ArticleDOI
TL;DR: Stochastic quasigradient methods generalize the well-known stochastic approximation methods for uncnstrained optimization of the expectation of a random function to problems involving general constraints for deterministic nonlinear optimization problems.
Abstract: This paper systematically surveys the basic direction of development of stochastic quasigradient methods which allow one to solve optimization problems without calculating the precise values of objective and constraints function (all the more of their derivatives). For deterministic nonlinear optimization problems these methods can be regarded as methods of random search. For the stochastic programming problems, SQG methods generalize the well-known stochastic approximation method for unconstrained optimization of the expectation of random functions to problems involving general constraints.

302 citations


Book ChapterDOI
01 Jan 1983
TL;DR: Solutions techniques for stochastic programs are reviewed and particular emphasis is placed on those methods that allow us to proceed by approximation.
Abstract: Solutions techniques for stochastic programs are reviewed. Particular emphasis is placed on those methods that allow us to proceed by approximation. We consider both stochastic programs with recourse and stochastic programs with chance-constraints.

214 citations


Journal ArticleDOI
TL;DR: The applications of stochastic processes to studying social mobility and flows of personnel within organizations receive much more extended treatment here than in other introductory treatments of applied stochastics processes.
Abstract: of the models analyzed include the spectral representation of solution vectors, limiting states, the covariance matrix of the elements of the state composition vector, the means and variances of sojourn times, and expanding and contracting systems, rather than methods of statistical estimation. In the discussion of discrete time models, the illustrations are drawn primarily from the study of social and occupational mobility, and for continuous time models, they are drawn from the field of educational and manpower planning. The remaining five chapters treat control theory for Markov models, models for duration and size, models for social systems with fixed class sizes, and simple and general epidemic models for the diffusion of news, rumors, and ideas. Simple epidemic models are birth process models that assume that infection is an irreversible state, so given either a constant individual rate of transmission or a single constant source of transmission, the entire population is eventually infected. General epidemic models allow for the duration of infection to be a random variable. The book ends with a full, up-to-date bibliography, an author index, and a subject index. In summary, Bartholomew gives an excellent introduction to many types of stochastic processes and a broad range of applications for modeling and planning social systems. The applications of stochastic processes to studying social mobility and flows of personnel within organizations receive much more extended treatment here than in other introductory treatments of applied stochastic processes. The "Complements" section at the end of each chapter is a useful overview of recent research investigations in many other areas of application that apply or extend the models presented in the chapter. Since no problems for solution are contained and the exposition is often informal, some teachers may wish to supplement the book with more traditional stochastic process textbooks, one good choice being Karlin and Taylor (1975). There seem to be few typographical errors.

187 citations


Journal ArticleDOI
TL;DR: An algorithm for solving stochastic programs with simpleourse generated by a linear programming problem with stochastics coefficients and a specific loss function is described.
Abstract: In this paper we describe an algorithm for solving stochastic programs with simplerecourse, i.e.,generated by a linear programming problem with stochastic coefficients and a specific loss function ...

111 citations



Book
01 Aug 1983
TL;DR: The XIth International Symposium on Mathematical Programming presents a review of recent developments in Algorithms and Software for Trust Region Methods, and discusses the Origins of Linear Programming, Semi-Infinite Programming and Applications.
Abstract: I. About the XIth International Symposium on Mathematical Programming.- Program and Organizing Committee.- Welcoming Addresses.- List of Sponsors.- The Fulkerson Prize and the Dantzig Prize 1982.- II. Mathematical Programming: The State of the Art - Bonn 1982.- Predictor-Corrector and Simplicial Methods for Approximating Fixed Points and Zero Points of Nonlinear Mappings.- Polyhedral Theory and Commutative Algebra.- Reminiscences About the Origins of Linear Programming.- Penalty Functions.- Applications of the FKG Inequality and its Relatives.- Semi-Infinite Programming and Applications.- Applications of Matroid Theory.- Recent Results in the Theory of Machine Scheduling.- Submodular Functions and Convexity.- Recent developments in Algorithms and Software for Trust Region Methods.- Variable Metric Methods for Constrained Optimization.- Polyhedral Combinatorics.- Generalized Equations.- Generalized Subgradients in Mathematical Programming.- Nondegeneracy Problems in Cooperative Game Theory.- Conic Methods for Unconstrained Minimization and Tensor Methods for Nonlinear Equations.- Min-Max Results in Combinatorial Optimization.- Generalized Gradient Methods of Non-Differentiable Optimization Employing Space Dilatation Operations.- The Problem of the Average Speed of the Simplex Method.- Solution of Large Linear Systems of Equations by Conjugate Gradient Type Methods.- Stochastic Programming: Solution Techniques and Approximation Schemes.- III. Scientific Program.- IV. List of Authors.

54 citations



Journal ArticleDOI
TL;DR: In this article, Monte Carlo and stochastic parameter simulations were compared in a simple model of algal competition, and the results showed that the ecological implications and empirical results of the two methods were significantly different.

50 citations


Journal ArticleDOI
TL;DR: In this article, two simple versions of this two-stage hierarchical scheduling problem are presented, and heuristic solution methods are described and their performance is asymptotically optimal both in expectation and in probability.
Abstract: Certain multistage decision problems that arise frequently in operations management planning and control allow a natural formulation as multistage stochastic programs. In job shop scheduling, for example, the first stage could correspond to the acquisition of resources subject to probabilistic information about the jobs to be processed, and the second stage to the actual allocation of the resources to the jobs given deterministic information about their processing requirements. For two simple versions of this two-stage hierarchical scheduling problem, we describe heuristic solution methods and show that their performance is asymptotically optimal both in expectation and in probability.

49 citations


Journal ArticleDOI
TL;DR: In this paper, the authors consider deterministic and stochastic versions of discrete time analogs of optimization problems of the Bolza type and obtain optimality conditions that are always sufficient and which are also necessary if the given problem satisfies a strict feasibility condition and a bounded recourse condition.
Abstract: In this paper we consider deterministic and stochastic versions of discrete time analogs of optimization problems of the Bolza type. The functionals are assumed to be convex, but we make no differentiability assumptions and allow for the explicit or implicit presence of constraints both on the state xt and the increments△x t. The deterministic theory serves to set the stage for the stochastic problem. We obtain optimality conditions that are always sufficient and which are also necessary if the given problem satisfies a strict feasibility condition and, in the stochastic case, a bounded recourse condition. This is a new condition that bypasses the uniform boundedness restrictions encountered in earlier work on related problems.

32 citations


Journal ArticleDOI
TL;DR: In this paper, an approximation approach to the solution of chance-constrained stochastic programming problems is proposed, which relies in a fundamental way on the theory of convergence of sequences.
Abstract: This paper proposes an approximation approach to the solution of chance-constrained stochastic programming problems. The results rely in a fundamental way on the theory of convergence of sequences ...

Book
03 Aug 1983
TL;DR: Information is provided on how to construct models for linear and nonlinear programming using the Simplex Method, as well as some of the techniques used in Integer Programming and Dynamic Programming.
Abstract: LINEAR PROGRAMMING. An Introduction to Linear Programming. The Simplex Method. Duality Theory and Sensitivity Analysis. The Transportation and Assignment Problems. Goal Programming. MATHEMATICAL PROGRAMMING. Network Models. PERT/CPM Models. Integer Programming. Nonlinear Programming. Dynamic Programming. Game Theory. PROBABLE PROBABILISTIC MODELS. Waiting Line Models. Markov Processes. Inventory Models. Simulation Models. Decision Analysis. SYNTHESIS. Implementation of Management Science. Appendices. Answers to Even Numbered Questions. Index.

Journal ArticleDOI
TL;DR: In this article, the authors deal with the problem of determining the optimal emission abatement policy in a region, which minimizes the overall emission cost under the constraint of meeting a given ambient standard.

Journal ArticleDOI
TL;DR: Based on the stationary co-content theorem in non-linear circuit theory and the penalty function approach inNon-linear programming theory, a canonical circuit for simulating general non- linear programming problems with equality and/or inequality constraints has been developed.
Abstract: Based on the stationary co-content theorem in non-linear circuit theory and the penalty function approach in non-linear programming theory, a canonical circuit for simulating general non-linear programming problems with equality and/or inequality constraints has been developed. the task of solving a non-linear optimization problem with constraints reduces to that of finding the solution of the associated canonical circuit using a circuit simulation program, such as SPICE. A catalogue of canonical circuits is given for each class of non-linear programming problem. Using this catalogue, an engineer can solve non-linear optimization problems by a cook-book approach without learning any theory on non-linear programming. Several examples are given which demonstrate how SPICE can be used, without modification, for solving linear programming problems, quadratic programming problems, and polynomial programming problems.

Journal ArticleDOI
01 Sep 1983
TL;DR: Several ways in which imprecision may be incorporated into the programs are discussed, including proximate programming, inexact programming and fuzzy programming.
Abstract: Conventional linear programming requires the deterministic specification of all the relevant data but generally this is only known imprecisely. Several ways in which imprecision may be incorporated into the programs are discussed. These include proximate programming, inexact programming and fuzzy programming. A simple illustrative example concerned with water quality is reworked using some of the described techniques. Fuzzy programming is a particularly useful model which can handle imprecision with respect to all the parameters and can also incorporate multiple goals.

Journal ArticleDOI
TL;DR: This survey covers the state of the art of large scale mathematical programming systems (MPS's) for solving problems which can be modeled using linear programming or its extensions, such as mixed integer and some types of nonlinear programming.

Journal ArticleDOI
TL;DR: The authors discuss basic problems in its applications to real planning and suggest a general idea of fuzzy dynamic programming, which can be applied to management.

Journal ArticleDOI
TL;DR: In this article, the Llano Basin white-tailed deer (Odocoileus virginianus) population was used to construct a 2-variable population dynamics model and the model provided the basis for estimating optimal harvesting strategies as a feedback function of the current values of the state variables (prefawning older deer and juveniles).

Book ChapterDOI
01 Jan 1983
TL;DR: In this paper, a variety of finite-stage sequential-decision models are discussed, illustrating the wide range of applications of stochastic dynamic programming, and the interchange argument in sequencing with examples.
Abstract: This chapter discusses a variety of finite-stage sequential-decision models, illustrating the wide range of applications of stochastic dynamic programming. The chapter discusses a situation where an individual is presented with n offers in sequential order. After looking at an offer, the individual must decide whether to accept it or to reject it. Once rejected, an offer is lost. If it is supposed that the only information the individual has at any time is the relative rank of the present offer compared with previous ones, the objective is to maximize the probability of selecting the best offer when all n ! orderings of the offers are assumed to be equally likely. In some problems, a policy consists of a sequence of decisions that is fixed at time zero. In such problems, a valuable technique is to consider an arbitrary sequence and then to see what happens when two adjacent decisions are interchanged. The chapter illustrates the interchange argument in sequencing with examples.

01 Jan 1983
TL;DR: The present paper gives a general formulation of such stochastic programs and provides a framework for the design and analysis of heuristics for their solution.
Abstract: As we have argued in previous papers, multi-level decision problems can often be modeled as multi-stage stochastic programs, and hierarchical planning systems designed for their solution, when viewed as stochastic programming heuristics, can be subjected to analytical performance evaluation. The present paper gives a general formulation of such stochastic programs and provides a framework for the design and analysis of heuristics for their solution. The various ways to measure the performance of such heuristics are reviewed, and some relations between these measures are derived. Our concepts are illustrated on a simple two-level planning problem of a general nature and on a more complicated two-level scheduling problem.


Journal ArticleDOI
TL;DR: In this paper, the problems of model building and identification of input-output complex systems, formulated as some special stochastic optimization problems, are considered from a unique optimization point of view.

Journal ArticleDOI
TL;DR: A model of watershed land-use planning is formulated that improves on existing models by recognizing that land- use decisions have uncertain outcomes and that land uses change over time.
Abstract: A model of watershed land-use planning is formulated that improves on existing models by recognizing that land-use decisions have uncertain outcomes and that land uses change over time. Implications of recognizing the distinction between land-use decisions and their uncertain outcomes are discussed. The land-use changes are modelled using a Markov process. Because of the computational difficulties in determining the return associated with the complete range of possible decision sets, a heuristic technique is required. A heuristic search procedure based on stochastic dynamic programming is described.

Journal ArticleDOI
TL;DR: On such method of analysis is discussed in this paper that requires that the system examine the model and make such determination as linear or nonlinear determination.

01 Jan 1983
TL;DR: In this paper, two simple versions of this two-stage hierarchical scheduling problem are presented, and heuristic solution methods are described and their performance is asymptotically optimal both in expectation and in probability.
Abstract: Certain multistage decision problems that arise frequently in operations management planning and control allow a natural formulation as multistage stochastic programs. In job shop scheduling, for example, the first stage could correspond to the acquisition of resources subject to probabilistic information about the jobs to be processed, and the second stage to the actual allocation of the resources to the jobs given deterministic information about their processing requirements. For two simple versions of this two-stage hierarchical scheduling problem, we describe heuristic solution methods and show that their performance is asymptotically optimal both in expectation and in probability.

Book ChapterDOI
TL;DR: The dynamic version of the mean-variance model of optimal portfolio investment has found very wide applications for the investor's decision problem (Lin and Boot 1982, Mao 1969, Sharpe 1970, Ziemba and Vickson 1975) as discussed by the authors.
Abstract: The static version of the mean-variance model of optimal portfolio investment has found very wide applications for the investor’s decision problem (Lin and Boot 1982, Mao 1969, Sharpe 1970, Ziemba and Vickson 1975). The dynamic version has not been so adequately analyzed in the standard literature, perhaps due to the specification problems of intertemporal variations in mean and variance of portfolio returns. Hillier (1963) attempted a nonlinear programming version of the intertemporal problem of risky interrelated investments with discounted cash flows that have random components over time. Dynamic stochastic programming models have also been considered for the consumer, who has to optimally decide between consumption and investment over his lifetime, when there are risky and also riskless assets (Ziemba and Vickson 1975). These models however, in their steady state, do not necessarily lead to a static mean-variance formulation of the standard portfolio model. Besides, they do not analyze specifically for the investor dealing inn risky assets such decision problems as risk-sensitivity, the length of the planning horizon.

Proceedings ArticleDOI
12 Dec 1983
TL;DR: Quasi-Monte Carlo integration, when applicable, has an order of magnitude smaller error bound than standard Monte Carlo, and analogs of variance reduction techniques for the latter are considered and their effectiveness is discussed.
Abstract: Quasi-Monte Carlo integration, when applicable, has an order of magnitude smaller error bound than standard Monte Carlo. For the former we consider analogs of variance reduction techniques for the latter and discuss their effectiveness. The results are applicable to stochastic programming and stochastic networks, for example.A May 1983 technical report by the same title is available from the author.

Book ChapterDOI
01 Jan 1983
TL;DR: Solving stochastic optimization problems with respect to a time interval the authors get often rather better results then solving the corresponding separated problems, caused by a Stochastic dependency of the random elements in problems repeated in a time.
Abstract: Solving stochastic optimization problems with respect to a time interval we get often rather better results then solving the corresponding separated problems. This is caused by a stochastic dependency of the random elements in problems repeated in a time.

Journal Article
TL;DR: In this article, a stochastic dynamic programming (SDP) model for underground coal slurry haulage networks is presented, which can be used to determine the equipment configuration and operating regimes that minimize the overall unit cost of coal haulage.
Abstract: This paper summarizes recent developments in modeling of underground coal slurry haulage networks for determination of optimum design and operating parameters. The model presented here is based on a stochastic dynamic programming formulation, applicable in any typical room-and-pillar and/or longwall mining configuration commonly practiced in the United States. The formulation and the structure of the model is general enough to handle design problems involving more than one face and mining method. Given the stochastic operating characteristics and a system layout, the model can be used to determine the equipment configuration and operating regimes that minimize the overall unit cost of coal haulage.

Journal ArticleDOI
TL;DR: In this paper, a tractable model for a dynamic economy with many sectors and many goods is presented, where rational agents with different preferences act upon self-fulfilling expectations.