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Showing papers on "Stochastic programming published in 1980"


Journal ArticleDOI
TL;DR: A network investment application is given which includes as a special case a coal transportation problem which is exploited to solve two stage linear programs under uncertainty where the first stage variables are 0–1.
Abstract: Stochastic programs with continuous variables are often solved using a cutting plane method similar to Benders' partitioning algorithm. However, mixed 0–1 integer programs are also solved using a similar procedure along with enumeration. This similarity is exploited in this paper to solve two stage linear programs under uncertainty where the first stage variables are 0–1. Such problems often arise in capital investment. A network investment application is given which includes as a special case a coal transportation problem.

91 citations


Journal ArticleDOI
TL;DR: This note is concerned with the problem of resource allocation under uncertainty in a research and development laboratory andulations are introduced that allow both types of interrelationships to be formally included in a resource allocation optimization model.
Abstract: This note is concerned with the problem of resource allocation under uncertainty in a research and development laboratory. A distinction is defined between project interrelationships that are specific (or internal) to certain projects and interrelationships resulting from external environmental factors. Formulations are introduced that allow both types of interrelationships to be formally included in a resource allocation optimization model. In the case of external environmental factors, an example is presented and analyzed.

67 citations


Journal ArticleDOI
TL;DR: Having reviewed a number of modeling approaches, the authors are able to draw certain conclusions as to their applicability for solving various practical problems.
Abstract: To manage its manpower, the organization must be informed about its internal dynamics and about the dynamics of its environment. This involves the monitoring of internal personnel movements and the analysis of external supplies. The internal situation can largely be controlled through hirings, promotions, internal transfers, redundancies and retirement planning. The problem is precisely to plan and control these interrelated activities in order to achieve a stable organization capable of meeting its objectives. The influence of the environment, through the economic situation, legislation, competition and other factors complicates the problem further. To assist in the planning and control of these activities, the organization can have recourse to models that are either descriptive (Markov chains, renewal models) or normative (linear and goal programming, network methods, stochastic programming). Having reviewed a number of modeling approaches the authors are able to draw certain conclusions as to their applicability for solving various practical problems.

56 citations


Journal ArticleDOI
TL;DR: A unified approach to stochastic feasible direction methods is developed and an abstract point-to-set map description of the algorithm is used and a general convergence theorem is proved.
Abstract: A unified approach to stochastic feasible direction methods is developed. An abstract point-to-set map description of the algorithm is used and a general convergence theorem is proved. The theory is used to develop stochastic analogs of classical feasible direction algorithms.

55 citations


Journal ArticleDOI
TL;DR: In this article, a stochastic dynamic programming model was proposed to determine the optimal selling time and feeding levels until sale for culling cows. But the model was not applied to cattle marketing.
Abstract: Feeding and marketing strategies for cull beef cows were analyzed by formulating a stochastic dynamic programming model which allowed simultaneous determination of optimal selling time and feeding levels until sale. The state variables were cow weight and monthly price; the latter was estimated statistically as a first-order autoregressive process with parameters changing monthly. Results for Montana cow prices at Billings suggested substantial gains to feeding healthy cows through the winter instead of immediate sale after fall culling.

29 citations


Journal ArticleDOI
TL;DR: A stochastic dynamic programming model was developed to estimate optimal strategies for U.S. wheat reserves policy using the results of an econometric model which reflects the complex dynamics of supply response.
Abstract: A stochastic dynamic programming model was developed to estimate optimal strategies for U.S. wheat reserves policy using the results of an econometric model which reflects the complex dynamics of supply response. Empirical results indicated that U.S. producers are the beneficiaries of a wheat storage program, while domestic and foreign consumers are relatively small and large losers, respectively. Another result is that wheat storage capacity in excess of 2 billion bushels is difficult to justify economically.

27 citations


Book
01 Jan 1980
TL;DR: These methods are based on the large-scale programming techniques of decomposition, partitioning, and basic factorization and show conditions under which the stochastic program need not be solved.
Abstract: : Linear programs have been formulated for many practical situations that require decisions made periodically through time. These dynamic linear programs often involve uncertainties. Deterministic solutions of these problems may lead to costly incorrect decisions, and, when a stochastic solution is attempted the problem may become too large. In this report, we present methods for reducing the computational cost of these stochastic programs, and we show conditions under which the stochastic program need not be solved. Our methods are based on the large-scale programming techniques of decomposition, partitioning, and basic factorization. (Author)

21 citations


Journal ArticleDOI
TL;DR: In this article, two general classes of methods for taking into account the inflow availability are presented, namely two-stage linear programming under uncertainty and chanced constrained programming, and the computational feasibility of both methods is illustrated by solution of a sample problem.

18 citations


Journal ArticleDOI
TL;DR: The algorithm for solving stochastic linear programs with simple recourse may be particularly interesting since Wets shows in that paper how the problem can be reduced to an equivalent deterministic linear program of the same dimensionality.
Abstract: Presented here is an introduction to stochastic linear programs with recourse. The paper is by no means a comprehensive survey of the field; that would be an encyclopedic task at best. This paper discusses formulation, interpretation, and computational aspects of stochastic linear programs with simple and fixed recourse. The paper is pedagogical in nature and is aimed to whet the interest of the decision scientist that has little or no background in stochastic programming. Moreover, the papers in this field have appeared in diverse journals not always readily available to the typical management scientist or practitioner and quite often at a very sophisticated mathematical level. For the practitioner, Wets's algorithm for solving stochastic linear programs with simple recourse may be particularly interesting since Wets shows in that paper how the problem can be reduced to an equivalent deterministic linear program of the same dimensionality.

16 citations


BookDOI
01 Jan 1980

15 citations


Journal ArticleDOI
TL;DR: In this paper, a general model for (nonsequential) statistical decision theory, which extends Wald's classical model, is presented, and a general theorem on the existence of admissible nonrandomized Bayes rules is derived.

ReportDOI
TL;DR: In this article, the authors considered the implications of the rational expectations -New Classical Macroeconomics revolution for the "rules versus discretion" debate and established the robustness of the proposition that contingent (closed-loop or feedback) rules dominate fixed (open-loop) rules.
Abstract: The paper considers the implications of the rational expectations - New Classical Macroeconomics revolution for the "rules versus discretion" debate. The following issues are covered 1) The ineffectiveness of anticipated stabilization policy, 2) Non-causal models and rational expectations, 3) optimal control in non-causal models -the inconsistency of optimal plans. I established the robustness of the proposition that contingent (closed-loop or feedback) rules dominate fixed (open-loop) rules. The optimal contingent rule in non-causal models - the innovation or disturbance-contingent feedback rule - is quite different from the state-contingent feedback rule derived by dynamic stochastic programming

Book ChapterDOI
01 Jan 1980
TL;DR: In this article, types of linear models that are used to represent stochastic processes are discussed. And the purpose is to generate likely future sequences of data for design and planning.
Abstract: This chapter concerns types of linear models that are used to represent stochastic processes. The purpose is to generate likely future sequences of data for design and planning. In general, the models are formulated so that the current value of a variable is the weighted sum of past values and random numbers which represent unknown effects.

Book ChapterDOI
01 Jan 1980
TL;DR: The problem of water resources management and planning is complex mainly due to the multipurpose character and to the stochastic nature of flows entering the reservoirs and this features should be taken into account when formulating the model.
Abstract: The problem of water resources management and planning is complex mainly due to the multipurpose character and to the stochastic nature of flows entering the reservoirs. This features should be taken into account when formulating the model. One possibility is to apply stochastic programming methods.

Journal ArticleDOI
TL;DR: It is shown that under suitable simplifying assumptions, stochastic linear programming methods could provide good approximations to the more general nonlinear programming models.

Journal ArticleDOI
TL;DR: In this article, the authors discuss the limitations of a model presented by Muhlemann, Lockett, and Gear for the portfolio selection problem in multiple-criteria situations under uncertainty.
Abstract: Harrington and Fischer [2] discuss some of the limitations of a model presented by Muhlemann, Lockett, and Gear [8] for the portfolio selection problem in multiple-criteria situations under uncertainty. They go on to propose integer goal programming and simulation as an alternative solution procedure. The purpose of this note is to critically examine their proposal and to contrast the two approaches. It is shown that the problem is being viewed from different decision-making standpoints.

Posted Content
TL;DR: In this article, the authors considered the implications of the rational expectations -New Classical Macroeconomics revolution for the "rules versus discretion" debate and established the robustness of the proposition that contingent (closed-loop or feedback) rules dominate fixed (open-loop) rules.
Abstract: The paper considers the implications of the rational expectations - New Classical Macroeconomics revolution for the "rules versus discretion" debate. The following issues are covered 1) The ineffectiveness of anticipated stabilization policy, 2) Non-causal models and rational expectations, 3) optimal control in non-causal models -the inconsistency of optimal plans. I established the robustness of the proposition that contingent (closed-loop or feedback) rules dominate fixed (open-loop) rules. The optimal contingent rule in non-causal models - the innovation or disturbance-contingent feedback rule - is quite different from the state-contingent feedback rule derived by dynamic stochastic programming

Book ChapterDOI
01 Jan 1980
TL;DR: The applicability of known stochastic programming models and methods for the solution of problems in classical statistics and probability is shown by a number of examples as discussed by the authors, such as testing of hypotheses, constructing of tolerance regions, planning of optimal sampling and the Moran model for the dam.
Abstract: The applicability of known stochastic programming models and methods for the solution of problems in classical statistics and probability is shown by a number of examples. These concern testing of hypotheses, constructing of tolerance regions, planning of optimal sampling and the Moran model for the dam.

Journal ArticleDOI
TL;DR: In usual stochastic programming problems involving randomly distributed "resources" and chance constraints, decision variables are taken as deterministic, and it is shown that minimum expected values could be made smaller by treating the decision variable as random.
Abstract: In usual stochastic programming problems involving randomly distributed "resources" and chance constraints, decision variables are taken as deterministic. With the help of simple illustrations involving a single decision variable, Vajda and Greenberg showed that minimum expected values could be made smaller by treating the decision variable as random. This idea has been extended here to the case of two decision variables. The difficulty of finding an optimal mixed strategy in the case of an infinite-range distribution of the decision variable(s) has also been shown.

Book ChapterDOI
01 Jan 1980
TL;DR: The results of the numerical comparative experiment with the simplex method are presented in this paper, and the method for solving the typical linear optimal control problem is grounded, while the adaptive method for linear programming problems is described.
Abstract: The results of the authors and their colleagues on investigation of linear programming problems and their application are given in the report. The adaptive method for solving the general linear programming problem is described. The results of the numerical comparative experiment with the simplex method are presented. New methods for solving the large linear programming problems are given. The method for solving the typical linear optimal control problem is grounded.



Journal ArticleDOI
TL;DR: The recommended QP procedure offers both technical relief from the computational difficulties posed by the probabilistic constraints and a desired flexibility in generating and presenting the relevant information for decisions under uncertainty.
Abstract: This paper applies mathematical programming to cost-volume-profit (CVP) analysis under contribution margin uncertainty. Three CVP probabilistic chance-constraint models based on various safety-first criteria for decisions under uncertainty are presented and compared. It is shown that a break-even segment of the mean-standard deviation frontier is a set of optimal solutions for the proposed models. An operational parametric quadratic programming (QP) model is constructed, and the efficiency frontier is generated. The procedures for locating an optimal solution on the efficiency frontier are then presented. The recommended QP procedure offers both technical relief from the computational difficulties posed by the probabilistic constraints and a desired flexibility in generating and presenting the relevant information for decisions under uncertainty.

Journal ArticleDOI
TL;DR: In this paper, the equivalence of optimality over plans and optimality of a two-stage procedure related to dynamic programming was shown for completely convex stochastic programming problems.

Journal ArticleDOI
TL;DR: Three methods are discussed here for selecting an optimal decision vector in a linear programming framework, where some stochastic components are present, and the complexity of the problem of characterizing the so-called best optimal solution is focused.
Abstract: Three methods are discussed here for selecting an optimal decision vector in a linear programming framework, where some stochastic components are present. The methods deal with problems of efficient estimation, problems of selecting the bent population and the game-theoretic solutions. The complexity of the problem of characterizing the so-called best optimal solution is focused here.


Book ChapterDOI
TL;DR: Based on a measurable selection theorem, an elementary derivation of sufficient conditions to assure that the optimal value operator behaves well is given that is illustrated with a general N-stage inventory control model.
Abstract: In this chapter we deal with the dynamic programming algorithm DPA for the finite-horizon stochastic dynamic programming problem SDP introduced in Section 4.6. Roughly speaking, the following decision process is described by SDP. There is a discrete time stochastic system, and the state of the system evoluates in a Markovian way. At each stage of time the current state is observed, and using this information the decision maker has to select an action. Any action will influence the immediate cost of the corresponding stage as well as the probability distribution of the next state. The purpose is to minimize the expected costs, summed over all stages. For details on the SDP problem we refer the reader to Section 4.6. There we gave also a formal definition of a “policy”; a policy may be seen as a complete specification of all particular choices which possibly are made by the decision maker at any stage and at any state.

Journal ArticleDOI
TL;DR: It is shown that nonserial problems can be solved by the use of dynamic programming incorporating algorithms based on heuristics, and two such algorithms are developed using artificial intelligence concepts of estimating the likelihood of future results on present decisions.
Abstract: Dynamic programming is an extremely powerful optimization approach used for the solution of problems which can be formulated to exhibit a serial stage-state structure. However, many design problems are not serial but have highly connected interdependent structures. Existing methods, for the solution of nonserial problems require the problem to possess a certain structure or limit the size of the problem due to storage and computational time requirements. The aim of this paper is to show that nonserial problems can be solved by the use of dynamic programming incorporating algorithms based on heuristics. Two such algorithms are developed using artificial intelligence concepts of estimating the likelihood of future results on present decisions. The algorithms are explained in detail, A small problem is solved and the results of testing them on large scale problems are given. The method is then used to solve a problem drawn from the literature.


Journal ArticleDOI
TL;DR: In this paper, a two-stage stochastic programming approach is used to yield an optimal "quasi" flow solution, which minimizes flow costs and expected costs for compensating nonconformity with the actual realizations of the demand/supply.
Abstract: If the demand/supply values at the nodes of a given graph are assumed to be random variables standard flow theory is no longer meaningful. A two stage stochastic programming approach can be used to yield an optimal “quasi”-flow Solution which minimizes “quasi”-flow costs and expected costs for compensating nonconformity with the actual realizations of the demand/supply. A special case of this formulation is shown to be the well-known stochastic transportation problem. An example is included for illustration.