Introduction to Stochastic ProgrammingSpringer Science & Business Media, 6 kwi 2006 - 421 The aim of stochastic programming is to find optimal decisions in problems which involve uncertain data. This field is currently developing rapidly with contributions from many disciplines including operations research, mathematics, and probability. Conversely, it is being applied in a wide variety of subjects ranging from agriculture to financial planning and from industrial engineering to computer networks. This textbook provides a first course in stochastic programming suitable for students with a basic knowledge of linear programming, elementary analysis, and probability. The authors aim to present a broad overview of the main themes and methods of the subject. Its prime goal is to help students develop an intuition on how to model uncertainty into mathematical problems, what uncertainty changes bring to the decision process, and what techniques help to manage uncertainty in solving the problems. The first chapters introduce some worked examples of stochastic programming and demonstrate how a stochastic model is formally built. Subsequent chapters develop the properties of stochastic programs and the basic solution techniques used to solve them. Three chapters cover approximation and sampling techniques and the final chapter presents a case study in depth. A wide range of students from operations research, industrial engineering, and related disciplines will find this a well-paced and wide-ranging introduction to this subject. |
Spis treści
| 3 | |
Uncertainty and Modeling Issues | 49 |
Basic Properties | 83 |
The Value of Information and the Stochastic Solution | 122 |
TwoStage Linear Recourse Problems | 155 |
Nonlinear Programming Approaches to TwoStage Recourse | 198 |
Multistage Stochastic Programs | 233 |
Stochastic Integer Programs | 253 |
Monte Carlo Methods | 331 |
Multistage Approximations | 353 |
Capacity Expansion | 375 |
A Sample Distribution Functions | 385 |
| 392 | |
| 401 | |
Author Index | 411 |
Approximation and Sampling Methods | 283 |
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algorithm approach assume basic Birge and Wets capacity Chapter complete recourse components computation consider convergence convex function convex hull corresponding costs defined demand deterministic equivalent dual Ermoliev EVPI example Exercise expected value extreme point feasibility cut feasible solution given go to Step importance sampling inequality integer interior point methods iterations J.R. Birge L-shaped method lower bound matrix nonanticipativity nonlinear programming normally distributed objective value obtain Operations Research optimal solution optimal value optimality cuts period piecewise linear possible probability measure procedures Proof random variables random vector realizations recourse function recourse problem region regularized decomposition right-hand side scenario second-stage Section simple recourse solve stage stochastic linear program Stochastic Optimization stochastic programming subgradient subproblem Suppose Theorem tion two-stage upper bound variance yields ξξ