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Showing papers on "Stochastic programming published in 1985"


Journal ArticleDOI
TL;DR: Dec decomposition and partitioning methods for solvingMultistage stochastic linear programs model problems in financial planning, dynamic traffic assignment, economic policy analysis, and many other applications.
Abstract: Multistage stochastic linear programs model problems in financial planning, dynamic traffic assignment, economic policy analysis, and many other applications. Equivalent representations of such problems as deterministic linear programs are, however, excessively large. This paper develops decomposition and partitioning methods for solving these problems and reports on computational results on a set of practical test problems.

608 citations


Journal ArticleDOI
TL;DR: A comprehensive study of various mathematical programming methods for structural optimization is presented in this article, where the authors discuss the applicability of modern optimization techniques to structural design problems, and present mathematical programming method from a unified and design engineers' viewpoint.
Abstract: A comprehensive study of various mathematical programming methods for structural optimization is presented. In recent years, many modern optimization techniques and convergence results have been developed in the field of mathematical programming. The aim of this paper is twofold: (a) to discuss the applicability of modern optimization techniques to structural design problems, and (b) to present mathematical programming methods from a unified and design engineers' viewpoint. Theoretical aspects are considered here, while numerical results of test problems are discussed in a companion paper. Special features possessed by structural optimization problems, together with recent developments in mathematical programming (recursive quadratic programming methods, global convergence theory), have formed a basis for conducting the study. Some improvements of existing methods are noted and areas for future investigation are discussed.

482 citations


Book
28 Feb 1985
TL;DR: A slide comprising a pair of telescopically related track members, ball bearings supporting the track members for relative longitudinal movement, a cage or retainer for the ball bearings longitudinally movable relative to the trackMembers, and a device for locking the retainer against movement from a predetermined locking position relative to one of the track Members when the other of theTrack members is moved longitudally out of engagement with the said one track member.
Abstract: A slide comprising a pair of telescopically related track members, ball bearings supporting the track members for relative longitudinal movement, a cage or retainer for the ball bearings longitudinally movable relative to the track members, and a device for locking the retainer against movement from a predetermined locking position relative to one of the track members when the other of the track members is moved longitudinally out of engagement with the said one track member. The locking device includes a locking member carried on the retainer and a cooperating locking member carried on the said one track member, the locking members being engageable when the retainer is in its said locking position and the said other track member is disengaged from the said one track member.

193 citations


Journal ArticleDOI
TL;DR: An optimization model with an ability to reflect uncertainties present in water quality problems and the technique employed is chance constrained programming wherein probabilistic constraints in a water quality optimization problem are replaced with their deterministic equivalents.
Abstract: An optimization model with an ability to reflect uncertainties present in water quality problems is described. The technique employed is chance constrained programming wherein probabilistic constraints in a water quality optimization problem are replaced with their deterministic equivalents. The uncertainty inherent in the random elements of the problem is characterized using first-order uncertainty analysis for the case study described.

111 citations


Journal ArticleDOI
TL;DR: In this paper, error bounds on the value of the optimal solution of the original problem are obtained from the Solution of the aggregated problem, and these bounds apply for aggregation of both random variables and time periods.
Abstract: Stochastic linear programs become extremely large and complex as additional uncertainties and possible future outcomes are included in their formulation. Row and column aggregation can significantly reduce this complexity, but the solutions of the aggregated problem only provide an approximation of the true solution. In this paper, error bounds on the value of the optimal solution of the original problem are obtained from the solution of the aggregated problem. These bounds apply for aggregation of both random variables and time periods.

91 citations


Journal ArticleDOI
TL;DR: Numerical procedures that avoid the difficulties associated with solving the “inner” problem with respect to probability measures are proposed for stochastic extremal problems in which the distribution function is only partially known.
Abstract: The main purpose of this paper is to discuss numerical optimization procedures, based on duality theory, for stochastic extremal problems in which the distribution function is only partially known. We formulate such problems as minimax problems in which the “inner” problem involves optimization with respect to probability measures. The latter problem is solved using generalized linear programming techniques. Then we state the dual problem to the initial stochastic optimization problem. Numerical procedures that avoid the difficulties associated with solving the “inner” problem are proposed.

75 citations


Journal ArticleDOI
TL;DR: In this paper, a family of eight models ranging from a single-period, aggregate and deterministic model to a multiperiod, disaggregate and probabilistic model is introduced.
Abstract: This paper examines issues in building decision support models for budgeting nursing workforce requirements in a hospital. We determine regular-time, overtime, and agency workforce levels for various skill classes in a budget cycle. We introduce a family of eight models ranging from a single-period, aggregate and deterministic model to a multiperiod, disaggregate and probabilistic model. In a single-period model, we ignore the time-varying nature of demand for nursing hours. Aggregation is done over the nurse skill class mix. For probabilistic models, we consider demand uncertainty. Using empirical data, we evaluate the effects of level of sophistication in model building and in information requirements on their relative performances. The results suggest that ignoring the time-varying nature of demand does not induce gross errors in budget estimates. However, ignoring demand uncertainty produces underestimates about five to six percent of budget needs-a consequence of a Madansky Madansky, A. 1960. Inequalities for stochastic linear programming problem. Management Sci.6 197-204. inequality. It also induces added costs to the system due to implementing nonoptimal regular-time workforce levels. Finally, we find that a simple formula using a single-period demand estimate gives excellent approximations to the budget estimates obtainable from the more precise models.

65 citations


Journal ArticleDOI
TL;DR: In this article, the problem of planning the long-term operation of a multireservoir hydrothermal electric power generation system is solved by a stochastic dynamic programming (SDP) algorithm using successive approximations.
Abstract: The problem of planning the long-term (multiyear) operation of a multireservoir hydrothermal electric power generation system is solved by a sto- chastic dynamic programming (SDP) algorithm using successive approximations. The hydro system model consists of a set of disjoint hydro chains each modeled by an equivalent reservoir and hydroplant. The inflow to the equivalent reservoir in each hydro chain is modeled as an independent log-normal random variable with a time correlation of lag one. The remaining river inflows in the system are modeled as a function of the equivalent reservoir inflows. Thermal unit and load curtailment cost curves are modeled as piecewise linear and convex. The successive approximations algorithm involves the solution of a 2-state stochastic dynamic programming problem for each hydro chain which has as its objective the minimization of the expected discounted production cost, plus the terminal hydro cost, subject to satisfying a number of constraints on the hydro and thermal system and the monthly demand which is represented by a load duration curve. A production-grade computer program has been developed and tested with data for a real system. Numerical results are reported for two study cases with up to eight reservoirs.

64 citations


Journal ArticleDOI
TL;DR: It is shown that use of the dynamic program results based on a small number of storage states results in unrealistically skewed storage probability distributions that are attributed to trapping states at the low end of the storage range.
Abstract: A stochastic dynamic programming model is applied to a small hydroelectric system. The variation in number of stage iterations and the computer time required to reach steady state conditions with changes in the number of storage states is investigated. The increase in computer time required to develop the storage probability distributions with increase in the number of storage states is reviewed. It it found that for an average of seven inflow states, the largest number of storage states for which it is computationally feasible to develop the storage probability distributions is nine. It is shown that use of the dynamic program results based on a small number of storage states results in unrealistically skewed storage probability distributions. These skewed distributions are attributed to trapping states at the low end of the storage range.

53 citations


Journal ArticleDOI
TL;DR: It is shown that PE has properties which make it suitable to treat stochastic programs, and the dual problem of DP is equivalent to Expected Utility Maximization of the classical Lagrangian dual function of SP, with the utility being of the constant-risk-aversion type.
Abstract: A penalty-type decision-theoretic approach to Nonlinear Programming Problems with stochastic constraints is introduced. The Stochastic Program SP is replaced by a Deterministic Program DP by adding a term to the objective function to penalize solutions which are not “feasible in the mean.” The special feature of our approach is the choice of the penalty function PE, which is given in terms of the relative entropy functional, and is accordingly called entropic penalty. It is shown that PE has properties which make it suitable to treat stochastic programs. Some of these properties are derived via a dual representation of the entropic penalty which also enable one to compute PE more easily, in particular if the constraints in SP are stochastically independent. The dual representation is also used to express the Deterministic Problem DP as a saddle function problem. For problems in which the randomness occurs in the rhs of the constraints, it is shown that the dual problem of DP is equivalent to Expected Utility Maximization of the classical Lagrangian dual function of SP, with the utility being of the constant-risk-aversion type. Finally, mean-variance approximations of PE and the induced Approximating Deterministic Program are considered.

43 citations


Journal ArticleDOI
TL;DR: A dynamic model for repetitive decision‐making in the cost–loss ratio situation is described and some theoretical and numerical results related to the optimal use and economic value of weather forecasts within the framework of the model are presented.
Abstract: The purposes of this paper are to describe a dynamic model for repetitive decision‐making in the cost–loss ratio situation and to present some theoretical and numerical results related to the optimal use and economic value of weather forecasts within the framework of the model. This model involves the same actions and events as the standard (i.e., static) cost–loss ratio situation, but the former (unlike the latter) is dynamic in the sense that it possesses characteristics (e.g., decisions, events) that are related over time. We assume that the decision maker wants to choose the sequence of actions over an n‐occasion time period that minimizes the total expected expense. A computational technique known as stochastic dynamic programming is employed to determine this optimal policy and the total expected expense. Three types of weather information are considered in studying the value of forecasts in this context: 1) climatological information; 2) perfect information; and 3) imperfect forecasts. Cli...

Journal ArticleDOI
TL;DR: In this paper, the authors employ stochastic dynamic programming to analyze two hedging problems which arise frequently, especially in international finance, and show that a risk-averse agent will hedge a fraction of his maximum potential exposure to reduce risk.
Abstract: This paper employs stochastic dynamic programming to analyze two hedging problems which arise frequently, especially in international finance One is the hedging of an uncertain exposure when the arrival of new information is anticipated It is shown that a risk-averse agent will hedge a fraction of his maximum potential exposure to reduce risk The second problem concerns hedging an exposure which extends beyond the delivery date of the available forward contract The solution yields a rule by which successive contracts can be linked to form an optimal hedging strategy A short empirical study illustrates this rule

Journal ArticleDOI
TL;DR: For a two-stage stochastic programming with recourse model the deterministic equivalent model is found using a Bayesian approach and similar results are obtained for chance constrained programming models.
Abstract: In probabilistic linear programming models the decision maker is typically assumed to know the probability distribution of the random parameters. Here it is assumed that the distribution functions of the parameters have a specified functional form F(t, θ), where θ is an unknown (real) vector parameter. We suppose that the decision maker has the opportunity of observing a random sample drawn from F(t, θ). For a two-stage stochastic programming with recourse model the deterministic equivalent model is found using a Bayesian approach. Properties are presented for the deterministic equivalents in general and in the special case of the simple recourse model. Expressions for Expected Value of Sample Information (EVSI) and Expected Net Gain from Sampling (ENGS) are also derived. In the final section similar results are obtained for chance constrained programming models.

Journal ArticleDOI
TL;DR: In this paper, a new application of the Aggregation-Decomposition approach (AD) to the optimal scheduling of large hydrothermal generation systems with multiple reservoirs is presented, where the problem (with N reservoirs) is decomposed into N subproblems with two state variables.
Abstract: A new application of the Aggregation-Decomposition approach (AD) to the optimal scheduling of large hydrothermal generation systems with multiple reservoirs is presented. The problem (with N reservoirs) is decomposed into N subproblems with two state variables. Each subproblem finds the optimal operating policy for one of the reservoir as a function of the energy content of that reservoir and the aggregate energy content of the remaining reservoirs. The subproblems are solved by stochastic dynamic programming taking into account the detailed models of the hydro chains as well as the stochasticity and correlation of the hydro inflows. The method has been successfully implemented on a 10 reservoir hydrothermal power system.

Book
01 Nov 1985
TL;DR: This volume contains selected papers presented at the IIASA Workshop on nondifferentiable optimization in September 1984 and is divided into four sections dealing with the following topics: Concepts in Nonsmooth Analysis; Multicriteria Optimization and Control Theory; Algorithms and Optimization Methods; and Stochastic Programming and Applications.
Abstract: IIASA has been involved in research on nondifferentiable optimization since 1976. The Institute's research in this field has been very productive, leading to many important theoretical, algorithmic and applied results. Nondifferentiable optimization has now become a recognized and rapidly developing branch of mathematical programming. To continue this tradition and to review developments in this field IIASA held this Workshop in Sopron (Hungary) in September 1984. This volume contains selected papers presented at the Workshop. It is divided into four sections dealing with the following topics: (I) Concepts in Nonsmooth Analysis; (II) Multicriteria Optimization and Control Theory; (III) Algorithms and Optimization Methods; (IV) Stochastic Programming and Applications.

Journal ArticleDOI
TL;DR: In this paper, G-convergence theory of elliptic operators is exploited in order to define and characterize generalized optimal solutions for nonsmooth optimization problems, and necessary and sufficient optimality conditions are derived.
Abstract: The paper is devoted to analysis of optimization problems in coefficients of fourth order elliptic boundary value problems. Similar problems were investigated in the framework of shape optimal design of thin plates. Since in general such problems have no optimal solution, G-convergence theory of elliptic operators is exploited in order to define and to characterize generalized optimal solutions. Necessary optimality conditions for nonsmooth optimization problems are derived. Results of computations for two examples are presented.

Journal ArticleDOI
TL;DR: The stability of solutions to stochastic programming problems with complete recourse is studied and the Lipschitz continuity of optimal solutions as well as the associated Lagrange multipliers with respect to the parameters of the distribution function are shown.
Abstract: In this paper we study the stability of solutions to stochastic programming problems with complete recourse and show the Lipschitz continuity of optimal solutions as well as the associated Lagrange multipliers with respect to the parameters of the distribution function.

Journal ArticleDOI
TL;DR: It is shown that the Hakimi theorem still holds in this model when the firm is risk-neutral, and in the case of a risk-averse firm, it ceases to be true in that all the points of the network must be considered to obtain an optimal location.

Journal ArticleDOI
TL;DR: In this article, the effects of uncertain − r t r o average implied by the USLE mean values on the probability of soil loss in farm planning models were analyzed. But the impact of probabilistic soil loss constraints on farm level bilistic losses constraints was not examined.
Abstract: probability of meeting conservation goals in the short run, rather than rely on long-run This paper analyzes the effects of uncertain . r t r o averages implied by the USLE mean values. soil loss in farm planning models. A disag- averages implied by the USLE mean values gregated approach was ued because of an A stochastic, farm level programming model gregated approach was used because of an interest in examining the impact of proba- was used to analyze the impacts of probabilistic soil loss constraints on farm level bilistic soil loss constraints. The objective of decisionmaking. A stochastic programming this paper is to determine how net returns model was used to consider different levels and the combinations of production activities of probability of soil loss. Traditional meth- are affected when levels of probability of soil ods of analysis are shown to consistently ov- loss are varied for a representative farm in erestimate net returns. South-Central Virginia.

Journal ArticleDOI
TL;DR: In this article, a stochastic dynamic programing algorithm with nested reliability constraints is proposed to minimize the expected thermal generating costs subject to prbabilistic constraints on the failure to supply the energy load.
Abstract: This work presents a new approach to tlhee problem of finding opcperating strategies for a hydthermalro power generating system. The objective is to minimize the expected thermal generating costs subject to prbabilistic constraints on the failure to supply the energy load. The problem is solved by a stochastic dynamic programing algorithm with nested reliability constraints fromcn each stage to the end of the planning period. A decomacposition approach is used to extend the methodology to the operation of two interconnmected systems. Case studies with the South and Southeast Brazilian generating systems are presented and discussed.

Journal ArticleDOI
TL;DR: In this paper, a stochastic dynamic programming model was formulated to derive a schedule of seasonal optimal reservoir releases and their respective probabilities of occurrence, and an operating policy was postu-lated, based on the same set of legal decisions that prescribed the active storage volume, and target reservoir releases were assumed.
Abstract: Designing a surface reservoir involves the concept of re- servoir yield. This concept embodies three basic information items: hydrologic regime, active storage volume, and reservoir release policy. In the actual case presented below, the magnitude of the active storage was prescribed by a legal procedure, so that the planning issue became that of determining the reservoir yield given the hydrological informa- tion. A stochastic dynamic programming model was formulated to de- rive a schedule of seasonal optimal reservoir releases and their respective probabilities of occurrence. This schedule is the reservoir yield. The yearly cycle was divided into three seasons representing the actual climatic conditions, and conditional probabilities linking streamflows in consecutive seasons were estimated. An operating policy was postu- lated, based on the same set of legal decisions that prescribed the active storage volume, and target reservoir releases were assumed. Similarly, target storages at the end of each season were set up. The optimizing/ minimizing criterion in the dynamic programming formulation was the sum of squares of deviations of actual releases and final storage volumes from their respective targets. (KEY TERMS: dynamic programming; reservoir yields; surface stor- age.)

Journal ArticleDOI
TL;DR: In this paper, the authors give strong duality results in multistage stochastic programming without assuming compactness and without applying induction arguments, and show that the duality result holds even in the case of multi-stage stochastically distributed programming.
Abstract: The paper gives strong duality results in multistage stochastic programming without assuming compactness and without applying induction arguments.

Journal ArticleDOI
TL;DR: In this paper, the authors present new reliability optimization models which can be formulated as parametric nonlinear integer programming problems, and the solution methods are illustrated with examples and flow charts.
Abstract: In practical reliability optimization models, finding an optimal solution to the model is not the only requirement. One may also be interested in solutions that are close to optimum, or one may want to know what happens if a change is made in the model. This paper presents new reliability optimization models which can be formulated as parametric nonlinear integer programming problems. Solution methods are illustrated with examples and flow charts.

Book
01 Jan 1985
TL;DR: In this paper, a minimax policy for optimal portfolio choice and a two-period stochastic inventory model are presented for portfolio investment in a dynamic horizon with uncertain entry of new players.
Abstract: I. Introductory problems.- 1. Stochastic optimization: examples and applications.- 2. Stochastic optimization in linear economic models.- A. Stochastic linear programming.- B. Linear stochastic control.- II. Linear quadratic models.- 3. Informetric analysis of dynamic decision rules in applied economic models..- 4. Optimal output-inventory decisions in stochastic markets.- 5. A minimax policy for optimal portfolio choice.- 6. A two-period stochastic inventory model.- 7. Risk in supply response: an econometric application.- 8. Optimal portfolio investment in a dynamic horizon.- 9. Short-term industry - output behavior: an economic analysis.- III. Game theory in economics.- 10. Optimal control in limit pricing under uncertain entry.- 11. Game theory models applied to economic systems: their information structure and stability.- 12. Stochastic models in dynamic economics: problems of time inconsistency, causality and estimation.- IV. Efficiency analysis and risk aversion in economic models.- 13. Multivariate risk aversion with applications.- V. Economic planning and stochastic optimization.- 14. Uncertainty and economic planning, selective survey and appraisal.- 15. Risk aversion in decision models.- 16. Risk aversion, robustness and adaptive information in decision models.- VI. Index.

Journal ArticleDOI
TL;DR: In this article, a quantitative evaluation of the effect of using the stochastic representation of the inflows as compared with deterministic approaches in the generation scheduling of the Brazilian systems is carried out.

Journal ArticleDOI
TL;DR: In this paper, an approach based on multiple objective linear programming is presented, which allows the decision maker to be more involved in the tolerance selection process, but does not demand a priori decisions on appropriate tolerances.

Journal ArticleDOI
TL;DR: In this paper, the authors use stochastic integer programming (SILP) to model hierarchical decision situations with combinatorial features and find optimal solutions to bin packing and multiknapsack problems.
Abstract: Stochastic integer programming is a suitable tool for modeling hierarchical decision situations with combinatorial features. In continuation of our work on the design and analysis of heuristics for such problems, we now try to find optimal solutions. Dynamic programming techniques can be used to exploit the structure of two–stage scheduling, bin packing and multiknapsack problems. Numerical results for small instances of these problems are presented.

Journal ArticleDOI
TL;DR: In this article, a stochastic optimization-simulation method is presented for delineating least-cost treatment sequences for a centralized liquid industrial waste treatment facility, where a dynamic programming model performs the optimization.
Abstract: A stochastic optimization‐simulation method is presented for delineating least‐cost treatment sequences for a centralized liquid industrial waste treatment facility. A dynamic programming model performs the optimization. The function of the model is to delineate least‐cost treatment sequences that will produce an acceptable effluent stream qualify given a probabilistically‐generated influent waste regime. The model is structured to permit the following user‐determined options: waste types and respective volumes in the waste inventory; specific contaminants within each waste type; contaminant‐specific probability density functions for waste strength; unit treatment processes including performance efficiencies and related costs; and individual contaminant effluent standards. The stochastic dynamic programming model served as a screening device, identifying unit treatment processes and sequences of processes with favorable cost‐effectiveness attributes. The treatment paths thus identified were further analyz...

Journal ArticleDOI
TL;DR: In this article, a stochastic programming model for the minimization of the total capital invested in safety stocks under prescribed probability constraints subject to the continuous supply of each stage of production is presented.

Journal ArticleDOI
TL;DR: In this paper, sampling dynamic programming is applied to define the daily operating policy of a reservoir taking into account the inflow stochasticity, which allows the evaluation of mean costs of operation in each stage of the operating period.