Stochastic linear programming : models, theory, and computation /

Stochastic linear programming : models, theory, and computation /

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Bibliographic Details
Main Author: Kall, Peter
Other Authors: Mayer, János
Format: Book
Language:English
Published: New York : Springer, c2011
New York, NY : c2011
Edition:2nd ed
Series:International series in operations research & management science ; 156
Subjects:
Linear programming
Stochastic processes
Table of Contents:
  • 1 Basics
  • 1.1. Introduction
  • Exercises
  • 1.2. Linear Programming Prerequisites
  • 1.2.1. Algebraic concepts and properties
  • 1.2.2. Geometric interpretation
  • 1.2.3. Duality statements
  • 1.2.4. Simplex method
  • 1.2.5. dual Simplex method
  • Exercises
  • 1.2.6. Dual decomposition method
  • 1.2.7. Nested decomposition
  • 1.2.8. Regularized decomposition
  • 1.2.9. Interior Point Methods
  • Exercises
  • 1.3. Nonlinear Programming Prerequisites
  • 1.3.1. Optimality Conditions
  • 1.3.2. Solution methods
  • Cutting Planes: Outer Linearization (Kelley)
  • Cutting Planes: Outer Linearization (Veinott)
  • Cutting Planes: Outer Linearization (Zoutendijk)
  • Central Cutting Plane Method (Elzinga-Moore)
  • Exercises
  • 2. Single-stage SLP models
  • 2.1. Introduction
  • Exercises
  • 2.2. Models involving probability functions
  • 2.2.1. Basic properties
  • 2.2.2. Finite discrete distribution
  • 2.2.3. Separate probability functions
  • Only the right-hand-side is stochastic
  • Multivariate normal distribution
  • Stable distributions
  • distribution-free approach
  • 2.2.4. independent case
  • 2.2.5. Joint constraints: random right-hand-side
  • Generalized-concave probability measures
  • Generalized-concave distribution functions
  • Maximizing joint probability functions
  • 2.2.6. Joint constraints: random technology matrix
  • 2.2.7. Summary on the convex programming subclasses
  • Exercises
  • 2.3. Quantile functions, Value at Risk
  • 2.4. Models based on expectation
  • 2.4.1. Integrated chance constraints
  • Separate integrated probability functions
  • Joint integrated probability functions
  • 2.4.2. model involving conditional expectation
  • 2.4.3. Conditional Value at Risk
  • Exercises
  • 2.5. Models built with deviation measures
  • 2.5.1. Quadratic deviation
  • 2.5.2. Absolute deviation
  • 2.5.3. Quadratic semi-deviation
  • 2.5.4. Absolute semi-deviation
  • Exercises
  • 2.6. Modeling risk and opportunity
  • 2.7. Risk measures
  • 2.7.1. Risk measures in finance
  • 2.7.2. Properties of risk measures
  • 2.7.3. Portfolio optimization models
  • 2.7.4. Optimizing performance
  • Exercises
  • 3. SLP models with recourse
  • 3.1. general multi-stage SLP
  • 3.2. two-stage SLP: Properties and solution appraoches
  • 3.2.1. complete fixed recourse problem (CFR)
  • 3.2.1.1. CFR: Direct bounds for the expected recourse 2(x)
  • 3.2.1.2. CFR: Moment problems and bounds for 2(x)
  • 3.2.1.3. CFR: Approximation by successive discretization
  • DAPPROX: Approximating CFR solutions
  • Exercises
  • 3.2.2. simple recourse case
  • 3.2.2.1. standard simple recourse problem (SSR)
  • 3.2.2.2. SSR: Approximation by successive discretization
  • SRAPPROX: Approximating SSR solutions
  • 3.2.2.3. multiple simple recourse problem
  • 3.2.2.4. generalized simple recourse problem (GSR)
  • GSR-CUT: Solving GSR by successive cuts
  • Exercises
  • 3.2.3. CVaR and recourse problems
  • 3.2.4. Some characteristic values for two-stage SLP's
  • 3.3. multi-stage SLP
  • 3.3.1. MSLP with finite discrete distributions
  • 3.3.2. MSLP with non-discrete distributions
  • 4. Algorithms
  • 4.1. Introduction
  • 4.2. Single-stage models with separate probability functions
  • 4.2.1. guide to available software
  • 4.3. Single-stage models with joint probability functions
  • 4.3.1. Numerical considerations
  • 4.3.2. Cutting plane methods
  • 4.3.3. Other algorithms
  • 4.3.4. Bounds for the probability distribution function
  • 4.3.5. Computing probability distribution functions
  • Monte-Carlo approach with antithetic variates
  • Monte-Carlo approach based on probability bounds
  • 4.3.6. Finite discrete distributions
  • 4.3.7. guide to available software
  • SLP problems with logconcave distribution functions
  • Evaluating probability distribution functions
  • SLP problems with finite discrete distributions
  • Exercises
  • 4.4. Single-stage models based on expectation
  • 4.4.1. Solving equivalent LP's
  • 4.4.2. Dual decomposition revisited
  • 4.4.3. Models with separate integrated probability functions
  • 4.4.4. Models involving CVaR
  • 4.4.5. Models with joint integrated probability functions
  • 4.4.6. guide to available software
  • Models with separate integrated probability functions
  • Models with joint integrated probability functions
  • Models involving CVaR
  • Exercises
  • 4.5. Single-stage models involving VaR
  • 4.6. Single-stage models with deviation measures
  • 4.6.1. guide to available software
  • 4.7. Two-stage recourse models
  • 4.7.1. Decomposition methods
  • 4.7.2. Successive discrete approximation methods
  • Computing the Jensen lower bound
  • Computing the E-M upper bound for an interval
  • Computing the bounds for a partition
  • successive discrete approximation method
  • Implementation
  • Simple recourse
  • Other successive discrete approximation algorithms
  • 4.7.3. Stochastic algorithms
  • Sample average approximation (SAA)
  • Stochastic decomposition
  • Other stochastic algorithms
  • 4.7.4. Simple recourse models
  • 4.7.5. guide to available software
  • Exercises
  • 4.8. Multistage recourse models
  • 4.8.1. Finite discrete distribution
  • 4.8.2. Scenario generation
  • Bundle-based sampling
  • moment-matching heuristics
  • 4.8.3. guide to available software
  • 4.9. Modeling systems for SLP
  • 4.9.1. Modeling systems for SLP
  • 4.9.2. SLP-IOR
  • General issues
  • Analyze tools and workbench facilities
  • Transformations
  • Scenario generation
  • solver interface
  • System requirements and availability.

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