Showing papers on "Stochastic programming published in 2002"
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01 Jan 2002TL;DR: This thesis proposes and studies actor-critic algorithms which combine the above two approaches with simulation to find the best policy among a parameterized class of policies, and proves convergence of the algorithms for problems with general state and decision spaces.
Abstract: Many complex decision making problems like scheduling in manufacturing systems, portfolio management in finance, admission control in communication networks etc., with clear and precise objectives, can be formulated as stochastic dynamic programming problems in which the objective of decision making is to maximize a single “overall” reward. In these formulations, finding an optimal decision policy involves computing a certain “value function” which assigns to each state the optimal reward one would obtain if the system was started from that state. This function then naturally prescribes the optimal policy, which is to take decisions that drive the system to states with maximum value.
For many practical problems, the computation of the exact value function is intractable, analytically and numerically, due to the enormous size of the state space. Therefore one has to resort to one of the following approximation methods to find a good sub-optimal policy: (1) Approximate the value function. (2) Restrict the search for a good policy to a smaller family of policies.
In this thesis, we propose and study actor-critic algorithms which combine the above two approaches with simulation to find the best policy among a parameterized class of policies. Actor-critic algorithms have two learning units: an actor and a critic. An actor is a decision maker with a tunable parameter. A critic is a function approximator. The critic tries to approximate the value function of the policy used by the actor, and the actor in turn tries to improve its policy based on the current approximation provided by the critic. Furthermore, the critic evolves on a faster time-scale than the actor.
We propose several variants of actor-critic algorithms. In all the variants, the critic uses Temporal Difference (TD) learning with linear function approximation. Some of the variants are inspired by a new geometric interpretation of the formula for the gradient of the overall reward with respect to the actor parameters. This interpretation suggests a natural set of basis functions for the critic, determined by the family of policies parameterized by the actor's parameters. We concentrate on the average expected reward criterion but we also show how the algorithms can be modified for other objective criteria. We prove convergence of the algorithms for problems with general (finite, countable, or continuous) state and decision spaces.
To compute the rate of convergence (ROC) of our algorithms, we develop a general theory of the ROC of two-time-scale algorithms and we apply it to study our algorithms. In the process, we study the ROC of TD learning and compare it with related methods such as Least Squares TD (LSTD). We study the effect of the basis functions used for linear function approximation on the ROC of TD. We also show that the ROC of actor-critic algorithms does not depend on the actual basis functions used in the critic but depends only on the subspace spanned by them and study this dependence.
Finally, we compare the performance of our algorithms with other algorithms that optimize over a parameterized family of policies. We show that when only the “natural” basis functions are used for the critic, the rate of convergence of the actor critic algorithms is the same as that of certain stochastic gradient descent algorithms. However, with appropriate additional basis functions for the critic, we show that our algorithms outperform the existing ones in terms of ROC. (Copies available exclusively from MIT Libraries, Rm. 14-0551, Cambridge, MA 02139-4307. Ph. 617-253-5668; Fax 617-253-1690.)
1,766 citations
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TL;DR: A Monte Carlo simulation--based approach to stochastic discrete optimization problems, where a random sample is generated and the expected value function is approximated by the corresponding sample average function.
Abstract: In this paper we study a Monte Carlo simulation--based approach to stochastic discrete optimization problems. The basic idea of such methods is that a random sample is generated and the expected value function is approximated by the corresponding sample average function. The obtained sample average optimization problem is solved, and the procedure is repeated several times until a stopping criterion is satisfied. We discuss convergence rates, stopping rules, and computational complexity of this procedure and present a numerical example for the stochastic knapsack problem.
1,728 citations
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01 Jan 2002
TL;DR: Pardalos and Resende as mentioned in this paper proposed a method to solve the problem of finding the minimum-cost single-Commodity Flow (MCSF) in a network.
Abstract: PrefacePanos M. Pardalos and Mauricio G. C. Resende: IntroductionPanos M. Pardalos and Mauricio G. C. Resende: Part One: Algorithms 1: Linear Programming 1.1: Tamas Terlaky: Introduction 1.2: Tamas Terlaky: Simplex-Type Algorithms 1.3: Kees Roos: Interior-Point Methods for Linear Optimization 2: Henry Wolkowicz: Semidefinite Programming 3: Combinatorial Optimization 3.1: Panos M. Pardalos and Mauricio G. C. Resende: Introduction 3.2: Eva K. Lee: Branch-and-Bound Methods 3.3: John E. Mitchell: Branch-and-Cut Algorithms for Combinatorial Optimization Problems 3.4: Augustine O. Esogbue: Dynamic Programming Approaches 3.5: Mutsunori Yagiura and Toshihide Ibaraki: Local Search 3.6: Metaheuristics 3.6.1: Bruce L. Golden and Edward A. Wasil: Introduction 3.6.2: Eric D. Taillard: Ant Systems 3.6.3: John E. Beasley: Population Heuristics 3.6.4: Pablo Moscato: Memetic Algorithms 3.6.5: Leonidas S. Pitsoulis and Mauricio G. C. Resende: Greedy Randomized Adaptive Search Procedures 3.6.6: Manuel Laguna: Scatter Search 3.6.7: Fred Glover and Manuel Laguna: Tabu Search 3.6.8: E. H. L. Aarts and H. M. M. Ten Eikelder: Simulated Annealing 3.6.9: Pierre Hansen and Nenad Mladenovi'c: Variable Neighborhood Search 4: Yinyu Ye: Quadratic Programming 5: Nonlinear Programming 5.1: Gianni Di Pillo and Laura Palagi: Introduction 5.2: Gianni Di Pillo and Laura Palagi: Unconstrained Nonlinear Programming 5.3: Constrained Nonlinear Programming }a Gianni Di Pillo and Laura Palagi 5.4: Manlio Gaudioso: Nonsmooth Optimization 6: Christodoulos A. Floudas: Deterministic Global Optimizatio and Its Applications 7: Philippe Mahey: Decomposition Methods for Mathematical Programming 8: Network Optimization 8.1: Ravindra K. Ahuja, Thomas L. Magnanti, and James B. Orlin: Introduction 8.2: Ravindra K. Ahuja, Thomas L. Magnanti, and James B. Orlin: Maximum Flow Problem 8.3: Edith Cohen: Shortest-Path Algorithms 8.4: S. Thomas McCormick: Minimum-Cost Single-Commodity Flow 8.5: Pierre Chardaire and Abdel Lisser: Minimum-Cost Multicommodity Flow 8.6: Ravindra K. Ahuja, Thomas L. Magnanti, and James B. Orlin: Minimum Spanning Tree Problem 9: Integer Programming 9.1: Nelson Maculan: Introduction 9.2: Nelson Maculan: Linear 0-1 Programming 9.3: Yves Crama and peter L. Hammer: Psedo-Boolean Optimization 9.4: Christodoulos A. Floudas: Mixed-Integer Nonlinear Optimization 9.5: Monique Guignard: Lagrangian Relaxation 9.6: Arne Lookketangen: Heuristics for 0-1 Mixed-Integer Programming 10: Theodore B. Trafalis and Suat Kasap: Artificial Neural Networks in Optimization and Applications 11: John R. Birge: Stochastic Programming 12: Hoang Tuy: Hierarchical Optimization 13: Michael C. Ferris and Christian Kanzow: Complementarity and Related Problems 14: Jose H. Dula: Data Envelopment Analysis 15: Yair Censor and Stavros A. Zenios: Parallel Algorithms in Optimization 16: Sanguthevar Rajasekaran: Randomization in Discrete Optimization: Annealing Algorithms Part Two: Applications 17: Problem Types 17.1: Chung-Yee Lee and Michael Pinedo: Optimization and Heuristics of Scheduling 17.2: John E. Beasley, Abilio Lucena, and Marcus Poggi de Aragao: The Vehicle Routing Problem 17.3: Ding-Zhu Du: Network Designs: Approximations for Steiner Minimum Trees 17.4: Edward G. Coffman, Jr., Janos Csirik, and Gerhard J. Woeginger: Approximate Solutions to Bin Packing Problems 17.5: Rainer E. Burkard: The Traveling Salesmand Problem 17.6: Dukwon Kim and Boghos D. Sivazlian: Inventory Management 17.7: Zvi Drezner: Location 17.8: Jun Gu, Paul W. Purdom, John Franco, and Benjamin W. Wah: Algorithms for the Satisfiability (SAT) Problem 17.9: Eranda Cela: Assignment Problems 18: Application Areas 18.1: Warren B. Powell: Transportation and Logistics 18.2: Gang Yu and Benjamin G. Thengvall: Airline Optimization 18.3: Alexandra M. Newman, Linda K. Nozick, and Candace Arai Yano: Optimization in the Rail Industry 18.4: Andres Weintraub Pohorille and John Hof: Forstry Industry 18.5: Stephen C. Graves: Manufacturing Planning and Control 18.6: Robert C. Leachman: Semiconductor Production Planning 18.7: Matthew E. Berge, John T. Betts, Sharon K. Filipowski, William P. Huffman, and David P. Young: Optimization in the Aerospace Industry 18.8: Energy 18.8.1: Gerson Couto de Oliveira, Sergio Granville, and Mario Pereira: Optimization in Electrical Power Systems 18.8.2: Roland N. Horne: Optimization Applications in Oil and Gas Recovery 18.8.3: Roger Z. Rios-Mercado: Natural Gas Pipeline Optimization 18.9: G. Anandalingam: Opimization of Telecommunications Networks 18.10: Stanislav Uryasev: Optimization of Test Intervals in Nuclear Engineering 18.11: Hussein A. Y. Etawil and Anthony Vannelli: Optimization in VLSI Design: Target Distance Models for Cell Placement 18.12: Michael Florian and Donald W. Hearn: Optimization Models in Transportation Planning 18.13: Guoliang Xue: Optimization in computation Molecular Biology 18.14: Anna Nagurney: Optimization in the Financial Services Industry 18.15: J. B. Rosen, John H. Glick, and E. Michael Gertz: Applied Large-Scale Nonlinear Optimization for Optimal Control of Partial Differential Equations and Differential Algebraic Equations 18.16: Kumaraswamy Ponnambalam: Optimization in Water Reservoir Systems 18.17: Ivan Dimov and Zahari Zlatev: Optimization Problems in Air-Pollution Modeling 18.18: Charles B. Moss: Applied Optimization in Agriculture 18.19: Petra Mutzel: Optimization in Graph Drawing 18.20: G. E. Stavroulakis: Optimization for Modeling of Nonlinear Interactions in Mechanics Part Three: Software 19: Emmanuel Fragniere and Jacek Gondzio: Optimization Modeling Languages 20: Stephen J. Wright: Optimization Software Packages 21: Andreas Fink, Stefan VoB, and David L. Woodruff: Optimization Software Libraries 22: John E. Beasley: Optimization Test Problem Libraries 23: Simone de L. Martins, Celso C. Ribeiro, and Noemi Rodriguez: Parallel Computing Environment 24: Catherine C. McGeoch: Experimental Analysis of Optimization Algorithms 25: Andreas Fink, Stefan VoB, and David L. Woodruff: Object-Oriented Programming 26: Michael A. Trick: Optimization and the Internet Directory of Contributors Index
631 citations
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TL;DR: By exploiting duality relations of convex analysis, the quantile model of stochastic dominance for general distributions is developed and it is shown that several models using quantiles and tail characteristics of the distribution are in harmony with the stoChastic dominance relation.
Abstract: We consider the problem of constructing mean-risk models which are consistent with the second degree stochastic dominance relation. By exploiting duality relations of convex analysis we develop the quantile model of stochastic dominance for general distributions. This allows us to show that several models using quantiles and tail characteristics of the distribution are in harmony with the stochastic dominance relation. We also provide stochastic linear programming formulations of these models.
510 citations
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TL;DR: The author considers a hidden Markov model where a single Markov chain is observed by a number of noisy sensors and designs algorithms for choosing dynamically at each time instant which sensor to select to provide the next measurement.
Abstract: The author considers a hidden Markov model (HMM) where a single Markov chain is observed by a number of noisy sensors. Due to computational or communication constraints, at each time instant, one can select only one of the noisy sensors. The sensor scheduling problem involves designing algorithms for choosing dynamically at each time instant which sensor to select to provide the next measurement. Each measurement has an associated measurement cost. The problem is to select an optimal measurement scheduling policy to minimize a cost function of estimation errors and measurement costs. The optimal measurement policy is solved via stochastic dynamic programming. Sensor management issues and suboptimal scheduling algorithms are also presented. A numerical example that deals with the aircraft identification problem is presented.
285 citations
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TL;DR: It is shown that, under mild regularity conditions, such a min-max problem generates a probability distribution on the set of permissible distributions with the min- max problem being equivalent to the expected value problem with respect to the corresponding weighted distribution.
Abstract: In practical applications of stochastic programming the involved probability distributions are never known exactly. One can try to hedge against the worst expected value resulting from a considered set of permissible distributions. This leads to a min-max formulation of the corresponding stochastic programming problem. We show that, under mild regularity conditions, such a min-max problem generates a probability distribution on the set of permissible distributions with the min-max problem being equivalent to the expected value problem with respect to the corresponding weighted distribution. We consider examples of the news vendor problem, the problem of moments and problems involving unimodal distributions. Finally, we discuss the Monte Carlo sample average approach to solving such min-max problems.
258 citations
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21 Jul 2002TL;DR: In this paper, the authors introduce stochastic constraint programming (SCP) to model combinatorial decision problems involving uncertainty and probability, and propose a number of complete algorithms and approximation procedures.
Abstract: To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables (which follow a probability distribution). They combine together the best features of traditional constraint satisfaction, stochastic integer programming, and stochastic satisfiability. We give a semantics for stochastic constraint programs, and propose a number of complete algorithms and approximation procedures. Finally, we discuss a number of extensions of stochastic constraint programming to relax various assumptions like the independence between stochastic variables, and compare with other approaches for decision making under uncertainty.
183 citations
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01 Jan 2002TL;DR: The MARKAL family of models has been contributing to energy/environmental planning since the early J980’s and was enlarged by members to model material flows, to employ stochastic programming (SP) to address future uncertainties, and to model endogenous technology learning using mixed integer programming (MIP) techniques.
Abstract: This article presents an overview and a flavour of almost two decades of MARKAL model developments and selected applications. The MARKAL family of models has been contributing to energy/environmental planning since the early J980’s. Under the auspices of the International Energy Agency’s (IEA) Energy Technology Systems Analysis Programme (ETSAP) the model started as a linear programming (LP) application focused strictly on the integrated assessment of energy systems. It was followed by a non-linear programming (NLP) formulation which combines the ‘bottom-up’ technology model with a ‘top-down’ simplified macro-economic model. In recent years, the family was enlarged by members to model material flows, to employ stochastic programming (SP) to address future uncertainties, to model endogenous technology learning using mixed integer programming (MIP) techniques, and to model multiple regions (NLP/LP).
170 citations
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TL;DR: New valid inequalities for these mixed integer programming problems with probabilistic constraints involving random variables with discrete distributions are developed using specific properties of stochastic programming problems and bounds on the probability of the union of events.
Abstract: We consider stochastic programming problems with probabilistic constraints involving random variables with discrete distributions. They can be reformulated as large scale mixed integer programming problems with knapsack constraints. Using specific properties of stochastic programming problems and bounds on the probability of the union of events we develop new valid inequalities for these mixed integer programming problems. We also develop methods for lifting these inequalities. These procedures are used in a general iterative algorithm for solving probabilistically constrained problems. The results are illustrated with a numerical example.
168 citations
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TL;DR: In this article, a review of structural and acoustic analysis techniques using numerical methods like the finite-and/or the boundary-element method is presented, followed by a survey of techniques for structural-acoustic coupling.
Abstract: Low noise constructions receive more and more attention in highly industrialized countries. Consequently, decrease of noise radiation challenges a growing community of engineers. One of the most efficient techniques for finding quiet structures consists in numerical optimization. Herein, we consider structural-acoustic optimization understood as an (iterative) minimum search of a specified objective (or cost) function by modifying certain design variables. Obviously, a coupled problem must be solved to evaluate the objective function. In this paper, we will start with a review of structural and acoustic analysis techniques using numerical methods like the finite- and/or the boundary-element method. This is followed by a survey of techniques for structural-acoustic coupling. We will then discuss objective functions. Often, the average sound pressure at one or a few points in a frequency interval accounts for the objective function for interior problems, wheareas the average sound power is mostly used for external problems. The analysis part will be completed by review of sensitivity analysis and special techniques. We will then discuss applications of structural-acoustic optimization. Starting with a review of related work in pure structural optimization and in pure acoustic optimization, we will categorize the problems of optimization in structural acoustics. A suitable distinction consists in academic and more applied examples. Academic examples iclude simple structures like beams, rectangular or circular plates and boxes; real industrial applications consider problems like that of a fuselage, bells, loudspeaker diaphragms and components of vehicle structures. Various different types of variables are used as design parameters. Quite often, locally defined plate or shell thickness or discrete point masses are chosen. Furthermore, all kinds of structural material parameters, beam cross sections, spring characteristics and shell geometry account for suitable design modifications. This is followed by a listing of constraints that have been applied. After that, we will discuss strategies of optimization. Starting with a formulation of the optimization problem we review aspects of multiobjective optimization, approximation concepts and optimization methods in general. In a final chapter, results are categorized and discussed. Very often, quite large decreases of noise radiation have been reported. However, even small gains should be highly appreciated in some cases of certain support conditions, complexity of simulation, model and large frequency ranges. Optimization outcomes are categorized with respect to objective functions, optimization methods, variables and groups of problems, the latter with particular focus on industrial applications. More specifically, a close-up look at vehicle panel shell geometry optimization is presented. Review of results is completed with a section on experimental validation of optimization gains. The conclusions bring together a number of open problems in the field.
152 citations
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08 May 2002TL;DR: In this paper, an approach based on stochastic dynamic programming is proposed to develop optimal operating policies for automotive powertrain systems, aiming to minimize fuel consumption and tailpipe emissions.
Abstract: An approach based on stochastic dynamic programming is proposed to develop optimal operating policies for automotive powertrain systems. The goal is to minimize fuel consumption and tailpipe emissions. Unlike in the conventional approach, the minimization is performed not for a predetermined drive cycle, but in a stochastic "average" sense over a class of trajectories from an underlying Markov chain drive cycle generator. The objective of this paper is to introduce the approach and illustrate its applications. with several examples.
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TL;DR: In this article, a unified framework for optimizing energy and reserve bidding strategies under a deregulated market is presented, where the hourly MCPs and reserve prices are modeled as discrete random variables, whose probability mass functions are predicted with a classification based neural network approach.
Abstract: In the deregulated power industry, a generation company (GenCo) sells energy and ancillary services primarily through bidding at a daily market. Developing effective strategies to optimize hourly bid curves for a hydrothermal power system to maximize profits becomes one of the most important tasks of a GenCo. This paper presents a unified framework for optimizing energy and reserve bidding strategies under a deregulated market. In view of high volatilities of market clearing prices (MCP), the hourly MCPs and reserve prices are modeled as discrete random variables, whose probability mass functions are predicted with a classification based neural network approach. The mean-variance method is applied to manage bidding risks, where a risk penalty term related to MCP and reserve price variances is added to the objective function. To avoid buying too much power from the market at high prices, a GenCo may also require covering at least a certain percentage of its own customer load. This self-scheduling requirement is modeled similar to the system demand in traditional unit commitment problems. The formulation is a stochastic mixed-integer optimization with a separable structure. An optimization based algorithm combining Lagrangian relaxation and stochastic dynamic programming is presented to optimize bids for both energy and reserve markets. Numerical testing based on an 11-unit system in New England market shows that the method can significantly reduce profit variances and thus reduce bidding risks. Near-optimal energy and reserve bid curves are obtained in 4-5 minutes on a 600 Hz Pentium III PC, efficient for daily use.
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TL;DR: In this article, a new approach is proposed to solve a kind of nonlinear optimization problem under uncertainty, in which some dependent variables are to be constrained with a predefined probability.
Abstract: Optimization under uncertainty is considered necessary for robust process design and operation. In this work, a new approach is proposed to solve a kind of nonlinear optimization problem under uncertainty, in which some dependent variables are to be constrained with a predefined probability. Such problems are called optimization under chance constraints. By employment of the monotony of these variables to one of the uncertain variables, the output feasible region will be mapped to a region of the uncertain input variables. Thus, the probability of holding the output constraints can be simply achieved by integration of the probability density function of the multivariate uncertain variables. Collocation on finite elements is used for the numerical integration, through which sensitivities of the chance constraints can be computed as well. The proposed approach is applied to the optimization of two process engineering problems under various uncertainties.
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TL;DR: In this paper, a method based on stochastic programming that explicitly incorporates uncertainty into the RTO problem is presented, which is limited to situations where uncertain parameters enter the constraints nonlinearly and uncertain economics enter the objective function linearly.
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TL;DR: A model for portfolio selection based on the semiabsolute deviation measure of risk, which can be transformed to a linear interval programming model studied in the paper, is proposed.
Abstract: This paper discusses a class of linear programming problems with interval coefficients in both the objective functions and constraints. The noninferior solutions to such problems are defined based on two order relations between intervals, and can be found by solving a parametric linear programming problem. Considering the uncertain returns of assets in capital markets as intervals, we propose a model for portfolio selection based on the semiabsolute deviation measure of risk, which can be transformed to a linear interval programming model studied in the paper. The method is illustrated by solving a simplified portfolio selection problem.
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01 Jan 2002TL;DR: In this paper, a stochastic programming model for the coordination of physical generation resources with hedging through the forward and option market is presented for a five-stage, 256 scenario model that has a two year horizon.
Abstract: Electricity producers participating in the Nordic wholesale-level market face significant uncertainty in inflow to reservoirs and prices in the spot and contract markets. Taking the view of a single risk-averse producer, we propose a stochastic programming model for the coordination of physical generation resources with hedging through the forward and option market. Numerical results are presented for a five-stage, 256 scenario model that has a two year horizon.
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TL;DR: The approximate method, proposed, minimize the cost functions of the resulting nonlinear programming problems include complex averaging operations, and is considered as an extension to the Ritz method, for which fixed basis functions are used.
Abstract: Functional optimization problems can be solved analytically only if special assumptions are verified; otherwise, approximations are needed. The approximate method that we propose is based on two steps. First, the decision functions are constrained to take on the structure of linear combinations of basis functions containing free parameters to be optimized (hence, this step can be considered as an extension to the Ritz method, for which fixed basis functions are used). Then, the functional optimization problem can be approximated by nonlinear programming problems. Linear combinations of basis functions are called approximating networks when they benefit from suitable density properties. We term such networks nonlinear (linear) approximating networks if their basis functions contain (do not contain) free parameters. For certain classes of d-variable functions to be approximated, nonlinear approximating networks may require a number of parameters increasing moderately with d, whereas linear approximating networks may be ruled out by the curse of dimensionality. Since the cost functions of the resulting nonlinear programming problems include complex averaging operations, we minimize such functions by stochastic approximation algorithms. As important special cases, we consider stochastic optimal control and estimation problems. Numerical examples show the effectiveness of the method in solving optimization problems stated in high-dimensional setting, involving for instance several tens of state variables.
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TL;DR: This study carefully examines the trade-off between computation time and the aggregation level of demand uncertainty with examples of a multi-leg flight and a single-hub network.
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TL;DR: A scenario-based approach for capturing the evolution of demand and a stochastic programming model for determining technology choices and capacity plans are developed, which is likely to be large and may not be easy to solve with standard software packages.
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TL;DR: An efficient algorithm for the numerical solution of the stochastic differential equation is developed and interesting properties of the algorithm enable the treatment of problems with a large number of variables.
Abstract: We propose a new stochastic algorithm for the solution of unconstrained vector optimization problems, which is based on a special class of stochastic differential equations. An efficient algorithm for the numerical solution of the stochastic differential equation is developed. Interesting properties of the algorithm enable the treatment of problems with a large number of variables. Numerical results are given.
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IBM1
TL;DR: It is found that arbitrage pricing in incomplete markets fails to model incentives to buy or sell options, and an extension of the model to incorporate pre-existing liabilities and endowments reveals the reasons why buyers and sellers trade in options.
Abstract: The hedging of contingent claims in the discrete time, discrete state case is analyzed from the perspective of modeling the hedging problem as a stochastic program. Application of conjugate duality leads to the arbitrage pricing theorems of financial mathematics, namely the equivalence of absence of arbitrage and the existence of a probability measure that makes the price process into a martingale. The model easily extends to the analysis of options pricing when modeling risk management concerns and the impact of spreads and margin requirements for writers of contingent claims. However, we find that arbitrage pricing in incomplete markets fails to model incentives to buy or sell options. An extension of the model to incorporate pre-existing liabilities and endowments reveals the reasons why buyers and sellers trade in options. The model also indicates the importance of financial equilibrium analysis for the understanding of options prices in incomplete markets.
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TL;DR: A method is developed to model new product development as a series of continuation/abandonment options, deciding at each stage in pharmaceutical R&D whether to proceed further or stop development, and a proposed framework provides a road map for future decisions.
Abstract: This paper presents a stochastic optimization model (OptFolio) of pharmaceutical research and development (R&D) portfolio management using a real options approach for making optimal project selection decisions. A method is developed to model new product development as a series of continuation/abandonment options, deciding at each stage in pharmaceutical R&D whether to proceed further or stop development. Multistage stochastic programming is utilized to model the flexibility afforded by the abandonment option. The resulting mixed-integer linear programming formulation is applied to a case study involving the selection of the optimal product portfolio from a set of 20 candidate drugs at different stages in the developmental pipeline over a planning horizon of 6 years. This proposed framework provides a road map for future decisions by tracking the decision of abandonment over time and calculating the minimum market value above which development is continued under changing resource constraints and estimated ...
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TL;DR: In this paper, the problem of determining the optimal operating schedule that minimizes the operating cost in an energy-intensive air separation plant is addressed by developing an efficient two-stage stochastic programming approach.
Abstract: This work addresses the problem of determining the optimal operating schedule that minimizes the operating cost in an energy-intensive air separation plant. The difficulty arises from the fact that the rate at which the utility company supplies electricity to the plant is subject to high fluctuations. This creates a potential opportunity to reduce average operating costs by changing the operating mode and production rates depending on the power costs. However, constraints occur due to product distribution requirements and plant capabilities. The scheduling optimization problem is made more challenging because the power prices are only known for a portion of the desired optimization horizon. These challenges were addressed by developing an efficient two-stage stochastic programming approach. Extensive analysis was done which resulted in a MILP problem formulation that uses an ARIMA model to generate the necessary scenarios for future power prices. The proposed problem was solved by utilizing commercial sof...
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TL;DR: In this article, a two-stage stochastic programming model for the short- or mid-term cost-optimal electric power production planning is developed, where the power generation in a hydro-thermal generation system under uncertainty in demand (or load) and prices for fuel and delivery contracts is considered.
Abstract: A two-stage stochastic programming model for the short- or mid-term cost-optimal electric power production planning is developed. We consider the power generation in a hydro-thermal generation system under uncertainty in demand (or load) and prices for fuel and delivery contracts. The model involves a large number of mixed-integer (stochastic) decision variables and constraints linking time periods and operating power units. A stochastic Lagrangian relaxation scheme is designed by assigning (stochastic) multipliers to all constraints that couple power units. It is assumed that the stochastic load and price processes are given (or approximated) by a finite number of realizations (scenarios). Solving the dual by a bundle subgradient method leads to a successive decomposition into stochastic single unit subproblems. The stochastic thermal and hydro subproblems are solved by a stochastic dynamic programming technique and by a specific descent algorithm, respectively. A Lagrangian heuristics that provides approximate solutions for the primal problem is developed. Numerical results are presented for realistic data from a German power utility and for numbers of scenarios ranging from 5 to 100 and a time horizon of 168 hours. The sizes of the corresponding optimization problems go up to 400.000 binary and 650.000 continuous variables, and more than 1.300.000 constraints.
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TL;DR: This paper finds that due to the ability of the stochastic programming model to adapt to the information in the scenario tree, it dominates the fixed mix approach to asset liability management.
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01 Jan 2002TL;DR: A dynamic multistage stochastic programming model for the cost-optimal generation of electric power in a hydro-thermal system under uncertainty in load, inflow to reservoirs and prices for fuel and delivery contracts is presented.
Abstract: We present a dynamic multistage stochastic programming model for the cost-optimal generation of electric power in a hydro-thermal system under uncertainty in load, inflow to reservoirs and prices for fuel and delivery contracts. The stochastic load process is approximated by a scenario tree obtained by adapting a SARIMA model to historical data, using empirical means and variances of simulated scenarios to construct an initial tree, and reducing it by a scenario deletion procedure based on a suitable probability distance. Our model involves many mixed-integer variables and individual power unit constraints, but relatively few coupling constraints. Hence we employ stochastic Lagrangian relaxation that assigns stochastic multipliers to the coupling constraints. Solving the Lagrangian dual by a proximal bundle method leads to successive decomposition into single thermal and hydro unit subproblems that are solved by dynamic programming and a specialized descent algorithm, respectively. The optimal stochastic multipliers are used in Lagrangian heuristics to construct approximately optimal first stage decisions. Numerical results are presented for realistic data from a German power utility, with a time horizon of one week and scenario numbers ranging from 5 to 100. The corresponding optimization problems have up to 200,000 binary and 350,000 continuous variables, and more than 500,000 constraints.
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TL;DR: A stochastic programming model is presented to describe farmers' sequential decisions in reaction to rainfall and illustrates how operations research techniques can be usefully applied to study grass root problems in developing countries.
Abstract: Farmers on the Central Plateau of Burkina Faso in West Africa cultivate under precarious conditions. Rainfall variability is extremely high in this area and accounts for much of the uncertainty surrounding the farmers' decision-making process. Strategies to cope with these risks are typically dynamic. Sequential decision making is one of the most important ways to cope with risk due to uncertain rainfall. In this paper, a stochastic programming model is presented to describe farmers' sequential decisions in reaction to rainfall. The model describes farmers' strategies of production, consumption, selling, purchasing, and storage from the start of the growing season until one year after the harvest period. This dynamic model better describes farmers' strategies than do static models that are usually applied. This study draws important policy conclusions regarding reorientation of research programs and illustrates how operations research techniques can be usefully applied to study grass root problems in developing countries.
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TL;DR: Modeling issues concerning applications of multistage stochastic programs with recourse (the choice of the horizon, stages, methods for generating scenario trees, etc.) will be discussed.
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TL;DR: In this article, the authors explored how the form of the recruitment and survival functions in a general population model for ducks affected the patterns in the optimal harvest strategy, using a combination of analytical, numerical, and simulation techniques.
Abstract: Optimal control theory is finding increased application in both theoretical and applied ecology, and it is a central element of adaptive resource management. One of the steps in an adaptive management process is to develop alternative models of system dynamics, models that are all reasonable in light of available data, but that differ substan- tially in their implications for optimal control of the resource. We explored how the form of the recruitment and survival functions in a general population model for ducks affected the patterns in the optimal harvest strategy, using a combination of analytical, numerical, and simulation techniques. We compared three relationships between recruitment and pop- ulation density (linear, exponential, and hyperbolic) and three relationships between survival during the nonharvest season and population density (constant, logistic, and one related to the compensatory harvest mortality hypothesis). We found that the form of the component functions had a dramatic influence on the optimal harvest strategy and the ultimate equi- librium state of the system. For instance, while it is commonly assumed that a compensatory hypothesis leads to higher optimal harvest rates than an additive hypothesis, we found this to depend on the form of the recruitment function, in part because of differences in the optimal steady-state population density. This work has strong direct consequences for those developing alternative models to describe harvested systems, but it is relevant to a larger class of problems applying optimal control at the population level. Often, different func- tional forms will not be statistically distinguishable in the range of the data. Nevertheless, differences between the functions outside the range of the data can have an important impact on the optimal harvest strategy. Thus, development of alternative models by iden- tifying a single functional form, then choosing different parameter combinations from extremes on the likelihood profile may end up producing alternatives that do not differ as importantly as if different functional forms had been used. We recommend that biological knowledge be used to bracket a range of possible functional forms, and robustness of conclusions be checked over this range.
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TL;DR: Using theory of Large Deviations it is shown that the sample size needed to calculate the optimal solution of stochastic programming problems where the objective function is given as an expected value of a convex piecewise linear random function is approximately proportional to the condition number.
Abstract: In this paper we consider stochastic programming problems where the objective function is given as an expected value of a convex piecewise linear random function. With an optimal solution of such a problem we associate a condition number which characterizes well or ill conditioning of the problem. Using theory of Large Deviations we show that the sample size needed to calculate the optimal solution of such problem with a given probability is approximately proportional to the condition number.