Preface
Related Literature
Audience
Required Background
Technical Difficulty
The Chapters
Acknowledgments
Contents
1 Uncertainty in Optimization
1.1 Sensitivity Analysis, Scenarios, What-If's and Stress Tests
1.2 The NewsMix Example
1.2.1 Sensitivity Analysis
1.2.2 Information Stages and Event Trees
1.2.3 A Two-Stage Formulation
1.2.4 Thinking About Stages
1.3 Deterministic Models and Options
1.4 Appropriate Use of What-If Analysis
1.5 Bad But Useful
1.6 Robustness and Flexibility
1.6.1 Robust or Flexible—A Modeling Choice
1.7 Transient Versus Steady State Modeling
1.7.1 Inherently Two-Stage (Invest-and-Use) Models
1.7.2 Inherently Multi-Stage (Operational) Models
1.8 Distributions—Do They Exist and Can We Find Them?
1.8.1 Generating Scenarios
1.8.2 Dependent Random Variables
1.8.2.1 Risk Management
1.9 Characterizing Some Examples
1.10 Alternative Approaches
1.10.1 Real Options Theory
1.10.1.1 Finding Recourse Options
1.10.2 Chance Constrained Models
1.10.3 Robust Optimization
1.10.3.1 Stochastic Robust Optimization
1.10.4 Distributionally Robust Optimization
1.10.5 Stochastic Dynamic Programming
1.10.6 Rolling Horizon
2 Information Structures and Feasibility
2.1 The Knapsack Problem
2.1.1 Feasibility in the Inherently Two-Stage Knapsack Problem
2.1.2 The Two-Stage Models
2.1.3 Chance Constrained Models
2.1.4 Stochastic Robust Formulations
2.1.5 The Two Different Multi-Stage Formulations
2.2 Overhaul Project Example
2.2.1 Analysis
2.2.2 A Two-Stage Version
2.2.3 A Different Inherently Two-Stage Formulation
2.2.4 Worst-Case Analysis
2.2.5 A Comparison
2.2.6 Dependent Random Variables
2.2.7 Using Sensitivity Analysis Correctly
2.3 Summing up about Feasibility
3 Modeling the Objective Function
3.1 The Knapsack Problem, Continued
3.2 Using Expected Values
3.3 Penalties, Targets, Shortfall, Options, and Recourse
3.3.1 Multiple Outcomes
3.4 Expected Utility
3.4.1 Markowitz Mean–Variance Efficient Frontier
3.5 Extreme Events
3.6 Options
3.6.1 A Simple Options Pricing Example
3.6.2 The Hidden Risk of Options
3.6.3 Financial Options in Stochastic Programming Models
3.7 Learning and Luck
4 Scenario Tree Generation
4.1 Creating Scenario Trees
4.1.1 Plain Sampling
4.1.2 Empirical Distribution
4.1.3 What Is a Good Discretization?
4.2 Stability Testing
4.2.1 In-Sample Stability
4.2.1.1 The Scenario Generation Procedure Is Deterministic
4.2.1.2 Why Measure the Objective Function Value?
4.2.2 Out-of-Sample Stability
4.2.3 Bias
4.2.4 Example: A Network Design Problem
4.2.5 The Relationship Between In- and Out-of-Sample Stability
4.2.6 Out-of-Sample Stability for Multi-period Trees
4.2.7 Other Approaches to Stability
4.3 Statistical Approaches to Solution Quality
4.3.1 Testing the Quality of a Solution
4.3.2 Solution Techniques Based on the Optimality Gap Estimators
4.3.3 Relation to the Stability Tests
4.4 Property-Matching Methods
4.4.1 Regression Models
4.4.2 The Transformation Model
4.4.2.1 Initialization
4.4.2.2 Correcting Correlations
4.4.2.3 Correcting Moments
4.4.2.4 Illustrative Example
4.4.2.5 Does It Always Work?
4.4.2.6 A Different Interpretation of the Model
4.4.2.7 Extensions of the Model
4.4.2.8 Alternative Approach Using Copula
4.4.3 Independent and Uncorrelated Random Variables
4.4.4 Other Construction Approaches
4.5 Problem-Driven Scenario Generation
4.5.1 Scenario Generation for Stochastic Programs with Tail Risk
4.5.2 Other Problem-Driven Approaches
4.6 What Approach to Pick?
5 High-Dimensional Dependent Randomness
5.1 The Stages
5.1.1 Stage 1
5.1.2 The Random Variables
5.1.3 Stage 2
5.2 Guessing a Correlation Matrix
5.3 The High-Dimension Hits Us
5.4 Problem Structure
5.4.1 So Why Does This Work?
6 Multistage Models
6.1 Capacity Planning Option Example
6.1.1 Capacity Model
6.1.2 Inventory Model
6.1.3 Objective
6.2 Mapping Dynamics into Stages
6.2.1 Timeline
6.2.2 Information State
6.2.3 Recipes
6.2.3.1 Recipes for Initial Stage
6.2.3.2 Recipes for Dynamic Stages
6.3 Modeling Multistage Uncertainty
6.4 Scenario Tree
6.4.1 Non-anticipativity, Implementability, and Nodes
6.5 How to Talk About Scenario Trees
6.5.1 What to Tell the Boss
6.5.2 [Technical] Conditional Expectation on Scenario Trees
6.5.3 Forecast and Surprise
6.5.4 Information State Using Forecast and Surprise Model
6.5.4.1 Demand
6.5.4.2 Prediction
6.6 Modeling the Horizon
6.6.1 Discounting
6.6.2 Dual Equilibrium
6.7 Formulation of the Full Capacity Option Model
6.8 [Technical] Decomposition by Inventory Subproblem
6.8.1 Inventory Subproblem
6.8.1.1 Horizon Stage
6.8.2 Capacity Option Decision Reformulation
6.8.2.1 Three Stages
6.8.2.2 Pre-exercise Prediction Model
6.8.2.3 Post-exercise Prediction Model
6.9 [Technical] Transient and Steady State Decomposition
6.9.1 Predictors for Steady State Solutions
6.9.2 Generators for Time Series
6.9.3 Counterfactuals
7 Service Network Design
7.1 Cost Structure
7.2 Warehouses and Consolidation
7.3 Demand and Rejections
7.4 How We Started Out
7.4.1 The Stage Structure
7.5 A Simple Service Network Design Case
7.6 Correlations: Do They Matter?
7.6.1 Analyzing the Results
7.6.2 Relation to Options Theory
7.6.3 Bidding for a Job
7.7 The Implicit Options
7.7.1 Reducing Risk Using Consolidation
7.7.2 Obtaining Flexibility by Sharing Paths
7.7.3 How Correlations Can Affect Schedules
7.8 Are Deterministic Models Useless?
7.9 Conclusion
8 A Multi-dimensional Newsboy Problem with Substitution
8.1 The Newsboy Problem
8.2 Introduction to the Actual Problem
8.3 Model Formulation and Parameter Estimation
8.3.1 Demand Distributions
8.3.2 Estimating Correlation and Substitution
8.4 Stochastic Programming Formulation
8.5 Test Case and Model Implementation
8.5.1 Test Results
8.6 Conclusion
References
Index