Showing papers on "Stochastic programming published in 1984"
TL;DR: The authors developed a stochastic dynamic programming model which employs the best forecast of the current period's inflow to define a reservoir release policy and to calculate the expected benefits from future operations.
Abstract: Most applications of stochastic dynamic programming have derived stationary policies which use the previous period's inflow as a hydrologic state variable. This paper develops a stochastic dynamic programming model which employs the best forecast of the current period's inflow to define a reservoir release policy and to calculate the expected benefits from future operations. Use of the best inflow forecast as a hydrologic state variable, instead of the preceding period's inflow, resulted in substantial improvements in simulated reservoir operations with derived stationary reservoir operating policies. While these results are for a dam at Aswan in the Nile River Basin, operators of other reservoir systems also have available to them information other than the preceding period's inflow which can be used to develop improved inflow forecasts.
358 citations
TL;DR: This paper investigates the computation of optimal policies in constrained discrete stochastic dynamic programming with the average reward as utility function, and an algorithm to compute such an optimal policy is presented.
Abstract: In this paper we investigate the computation of optimal policies in constrained discrete stochastic dynamic programming with the average reward as utility function. The state-space and action-sets are assumed to be finite. Constraints which are linear functions of the state-action frequencies are allowed. In the general multichain case, an optimal policy will be a randomized nonstationary policy. An algorithm to compute such an optimal policy is presented. Furthermore, sufficient conditions for optimal policies to be stationary are derived.
There are many applications for constrained undiscounted stochastic dynamic programming, e.g., in multiple objective Markovian decision models.
109 citations
Book•
01 Jan 1984
TL;DR: This book discusses linear programming, Probabilistic models: simulation decision theory and decision trees project management - PERT and CPM inventory models with probabilistic demand queuing models forecasting and introduction to non-linear programming.
Abstract: (NOTE: At the End of Each Chapter is a Video Case.) 1. Introduction: Models and Modeling. I: DETERMINISTIC MODELS. 2. Linear Programming: Formal and Spreadsheet Models. 3. Linear Programming: Geometric Representations and Graphical Solutions. 4. Analysis of LP Models: The Graphical Approach. 5. Linear Programs: Computer Analysis, Interpreting Sensitivity Output, and the Dual Problem. 6. Linear Programming: The Simplex Method. 7. Linear Programming: Special Applications. 8. Integer and Quadratic Programming. 9. Network Models. 10. Inventory Control with Known Demand. 11. Heuristics, Multiple Objectives, and Goal Programming. 12. Calculus-Based Optimization and an Introduction to Nonlinear Programming. II: PROBABILISTIC MODELS. 13. Simulation. 14. Decision Theory and Decision Trees. 15. Project Management: PERT and CPM. 16. Inventory Models with Probabilistic Demand. 17. Queuing Models. 18. Forecasting. Answers to Odd-Numbered Problems. Appendix A: Basic Concepts in Probability. Using LINDO. Index.
83 citations
TL;DR: In this paper, the authors give an overview of stochastic optimal control theory and its applications to operational research, and their actual and potential impact on OR is discussed from a methodological point of view.
53 citations
TL;DR: In this article, an expansion planning method was developed which considered the complex, uncertain and dynamic nature of the electric utility decision environment, and a stochastic dynamic programming model was formkilated and applied in case studies.
Abstract: An expansion planning method is developed which considers the complex, uncertain and dynamic nature of the electric utility decision environment. A stochastic dynamic programming model is formkilated and applied in case studies. Uncertainty in demarid, the commercialization date of new technologies, and the possible loss of service of existing nuclear capacity is considered. Uncertainty affects the current expansion decision. Because of these uncertainties, no single expansion plan is optimal. Contingency plans are established which consider how uncertainty is resolved over time. The conditions which must exist for the new technology to be chosen are identified.
45 citations
TL;DR: Stability of the optimal solution of stochastic programs with recourse with recourse under assumption of strict complementarity known from the theory of nonlinear programming is studied.
Abstract: In this paper, stability of the optimal solution of stochastic programs with recourse with respect to parameters of the given distribution of random coefficients is studied Provided that the set of admissible solutions is defined by equality constraints only, asymptotical normality of the optimal solution follows by standard methods If nonnegativity constraints are taken into account the problem is solved under assumption of strict complementarity known from the theory of nonlinear programming (Theorem 1) The general results are applied to the simple recourse problem with random right-hand sides under various assumptions on the underlying distribution (Theorems 2–4)
45 citations
TL;DR: General convergence characteristics of stochastic optimization methods are investigated, when convex and/or differentiable structure of the optimization problems to be solved is not assumed.
Abstract: General convergence characteristics of stochastic optimization methods are investigated, when convex and/or differentiable structure of the optimization problems to be solved is not assumed, First, some basic stochastic optimization schemes are introduced and their convergence properties are analysed, then the obtained results are extended for the case of stochastically combined (hybrid) procedures. Finally, some experimental results with hybrid optimization methods are summarized.
43 citations
TL;DR: For several versions of this difficult optimization problem, it is shown that simple heuristics have strong properties of asymptotically optimal behavior.
Abstract: Hierarchical vehicle routing problems, in which the decision to acquire a number of vehicles has to be based on imperfect (probabilistic) information about the location of future customers, allow a natural formulation as two-stage stochastic programming problems, where the objective is to minimize the sum of the acquisition cost and the length of the longest route assigned to any vehicle. For several versions of this difficult optimization problem, we show that simple heuristics have strong properties of asymptotically optimal behavior.
29 citations
TL;DR: In this article, a general formulation of multi-stage stochastic programs and a framework for the design and analysis of heuristics for their solution are presented. But these methods are not suitable for multi-level decision problems.
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.
TL;DR: This work characterize optimal solutions for the dynamic lot-sizing problem when demand quantities are known, but their timing is uncertain and outlines a dynamic program for the solution of these problems.
Abstract: We characterize optimal solutions for the dynamic lot-sizing problem when demand quantities are known, but their timing is uncertain. The characterization states that for some possible history of demands following a period of production, there is a period with zero inventory before another period with production. Using this characterization, we outline a dynamic program for the solution of these problems. Some results from sample problems illustrate the variety of optimal solutions that can occur.
TL;DR: Quadratic programming has several reliable and efficient algorithms for its solution which require more computation than does linear programming, but owing to the reduced number of iterations in optimization, the total work involved in SQP is in general less than that of SLP.
Abstract: On the basis of previous works, here we propose an approach to the optimal design of engineering structures for member sizing and shape optimization. This approach is based on the transformation of a non-linear programming problem (NLP) into a sequence of quadratic programming problems (SQP). Compared with the commonly used sequential linear programming (SLP), SQP is more suited to the highly non-linear problems of structural optimization. Different modes of SQP may be used. Four types ofSQP presented in this paper have been demonstrated to be stable and rapid in their convergence according to our experiences. Quadratic programming (QP) has several reliable and efficient algorithms for its solution which require more computation than does linear programming, but owing to the reduced number of iterations in optimization, the total work involved in SQP is in general less than that of SLP. Further developments of SQP will be very helpful for structural optimization.
Book•
01 Jan 1984
01 Jan 1984
TL;DR: The methodology and models developed to solve the operations scheduling problem for the Brazilian system, ranging from hourly transmission-constrained dispatch to multi-year reservoir optimization, include stochastic dynamic programming, Dantzig-Wolfe decomposition, network flows and multistage Stochastic Benders decomposition.
Abstract: This paper presents the methodology and models developed to solve the operations scheduling problem for the Brazilian system. A chain of four individual programs ranging from hourly transmission-constrained dispatch to multi-year reservoir optimization has been used. The output of the programs at higher levels impose targets or constraints on the lower level programs. In addition, feedback links from lower level to higher level programs help ensure a global optimization of the scheduling process. The techniques employed to solve the scheduling problems at each level include stochastic dynamic programming, Dantzig-Wolfe decomposition, network flows and multistage stochastic Benders decomposition.
01 Dec 1984
TL;DR: In this paper, a general dynamic programming algorithm for the solution of optimal stochastic control problems concerning a class of discrete event systems is presented, and the algorithm is shown to be optimal in the presence of discrete events.
Abstract: This paper presents a general dynamic programming algorithm for the solution of optimal stochastic control problems concerning a class of discrete event systems.
TL;DR: The combination of simulation and optimization for probabilistic models with continuous decision variables is discussed and the stochastic quasigradient method which is a well known technique in Stochastic optimization may also successfully applied for simulation-optimization problems.
Abstract: A major part of all simulation models contains a number of decision variables. For such models the problem of optimal decision arises in a natural way. The combination of simulation and optimization for probabilistic models with continuous decision variables is discussed in this paper. Several important techniques for solving the combined problem are presented. In particular the stochastic quasigradient method which is a well known technique in stochastic optimization may also successfully applied for simulation-optimization problems.
TL;DR: In this paper, the problem of minimizing the total cost of a pump-pipe system in series is considered and a general mathematical model is formulated and dynamic programming is used to find an optimal solution.
Abstract: In this paper the problem of minimizing the total cost of a pump-pipe system in series is considered. The route of the pipeline and the number of pumping stations are known. The optimization will then consist in determining the control variables, diameter and thickness of the pipe and the size of the pumps. A general mathematical model is formulated and Dynamic Programming is used to find an optimal solution. Practical reasons, derived from the techniques engineers generally use to cope with such problems, and special characteristics of the mathematical structure of the model justified the consideration of particular cases of the system. This analysis, based on Dynamic Programming, enabled us to elaborate a simple heuristic method, condensing those techniques, and supplied sufficient conditions for the heuristic to operate as an optimal procedure. The solution of a realistic example confirms the viability of the conditions developed and tests the formulation (also presented) of the optimization problem by...
TL;DR: The sequential linear programming method is shown to be particularly efficient for application to structural design problems and some comments on the development of computer software for structural optimization are also given.
Abstract: The use of three non‐linear mathematical programming techniques for the optimization of structural design problems is discussed. The methods — sequential linear programming, the feasible direction method and the sequential unconstrained minimization technique — are applied to a portal frame problem to enable a study of their convergence efficiency to be studied. These methods are used for both the sizing of the structural members and determining the optimum roof pitch. The sequential linear programming method is shown to be particularly efficient for application to structural design problems. Some comments on the development of computer software for structural optimization are also given.
TL;DR: Exact solution by stochastic dynamic programming is possible only for a one-reservoir model, and this result is compared to the deterministic and linear feedback solutions.
Abstract: Seasonal reservoir scheduling for multireservoir hydrothermal power systems is a practical, nonlinear, stochastic problem of high dimension. Extension of an existing deterministic algorithm to handle stochastic aspects is desirable. A linear feedback rule, but with chance constraints on lower limits only, gives some promising results. Exact solution by stochastic dynamic programming is possible only for a one-reservoir model. This result is compared to the deterministic and linear feedback solutions.
TL;DR: An adaptive dual control guidance algorithm is presented for intercepting a moving target in the presence of an interfering target (decoy) in a stochastic environment and approximate prior probability densities are obtained and used to describe the future learning and control.
01 Jan 1984
TL;DR: This note reviews and completes the approximation results for stochastic programs with recourse and addresses the question of how to easily find a (starting) solution.
Abstract: We review and complete the approximation results for stochastic programs with recourse Since this note is to serve as a preamble to the development of software for stochastic programming problems, we also address the question of how to easily find a (starting) solution
TL;DR: In this article, the optimal harvest strategies for a vegetation-ungulate system were estimated using stochastic dynamic programming (SDP) for a randomly fluctuating mortality rate and alternative assumptions about vegetation production are considered in the estimation.
TL;DR: Some modeling alternatives for handling risk in decision-making processes for unconstrained stochastic optimization problems are reviewed and solution strategies are discussed and compared.
Abstract: We review some modeling alternatives for handling risk in decision-making processes for unconstrained stochastic optimization problems. Solution strategies are discussed and compared.
01 Jan 1984
TL;DR: An enlarged linear network problem is obtained and solved, producing a very efficient solution method based on separable programming techniques for the stochastic transportation problem.
Abstract: This paper describes a solution method based on separable programming techniques for the stochastic transportation problem. An enlarged linear network problem is obtained and solved, producing a very efficient solution method. The difficulty of accuracy estimation is discussed, and a procedure using the dual variables to solve the lagrangian relaxation of the problem is described. The solution method is compared to some other methods for the STP. (Author/TRRL)
TL;DR: In this paper, it is shown that for a certain class of dynamic programming problems, the optimal control policy is independent of the future, and further applications in the theories of economic growth and corporate finance are discussed.
01 May 1984
TL;DR: This paper reports on the application of stochastic programming with recourse models to strategic planning problems typical of those faced by an electric utility using Benders' decomposition method.
Abstract: This paper reports on the application of stochastic programming with recourse models to strategic planning problems typical of those faced by an electric utility. A prototype model was constructed using realistic data, and optimized using Benders' decomposition method. The decomposition treats simultaneously stochastic programming and mixed integer programming structures arising naturally in strategic planning models.
TL;DR: In this article, the authors consider open-loop solutions of linear stochastic optimal control problems with constraints on control variables and probabilistic constraints on state variables and show that this problem reduces to an equivalent linear deterministic optimal control problem with similar constraints and with a new criterion to minimize.
Abstract: We consider open-loop solutions of linear stochastic optimal control problems with constraints on control variables and probabilistic constraints on state variables. It is shown that this problem reduces to an equivalent linear deterministic optimal control problem with similar constraints and with a new criterion to minimize. Concavity or convexity is preserved. Hence, the machinery available for solving deterministic optimal control problems can be used to get an open-loop solution of the stochastic problem. The convex case is investigated and a bound on the difference between closed-loop and open-loop optimal costs is given.