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Modeling with Stochastic Programming 2013 ed. [Hardback]

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Keywords:
This book bridges theory and application of stochastic programming in operations research. It describes various methods of formulating stochastic optimization problems, and illustrates their advantages and disadvantages with examples and case studies.

While there are several texts on how to solve and analyze stochastic programs, this is the first text to address basic questions about how to model uncertainty, and how to reformulate a deterministic model so that it can be analyzed in a stochastic setting. This text would be suitable as a stand-alone or supplement for a second course in OR/MS or in optimization-oriented engineering disciplines where the instructor wants to explain where models come from and what the fundamental issues are. The book is easy-to-read, highly illustrated with lots of examples and discussions. It will be suitable for graduate students and researchers working in operations research, mathematics, engineering and related departments where there is interest in learning how to model uncertainty. Alan King is a Research Staff Member at IBM's Thomas J. Watson Research Center in New York. Stein W. Wallace is a Professor of Operational Research at Lancaster University Management School in England.

Reviews

From the reviews:

It is the first book that systematically tries to answer the questions about modeling under uncertainty . The book is written in a very readable style . An experienced researcher who is already familiar with optimization under uncertainty will benefit from reading this book . (Laura Galli, Interfaces, Vol. 43 (5), September-October, 2013)

The book is intended as a textbook for graduate students and researchers interested in decision making under uncertainty. It is expected that the book will also be suitable for teaching some operations research courses for undergraduates. this textbook can indeed be very useful for mathematics students as a methodological guide to the applications of stochastic programming methods. The structure of the textbook is well adapted to teaching purposes. (A. H. ilinskas, Mathematical Reviews, January, 2013)

1 Uncertainty in Optimization
1(32)
1.1 Sensitivity Analysis, Scenarios, What-ifs and Stress Tests
2(2)
1.2 The News Mix Example
4(6)
1.2.1 Sensitivity Analysis
5(1)
1.2.2 Information Stages and Event Trees
6(2)
1.2.3 A Two-stage Formulation
8(1)
1.2.4 Thinking About Stages
9(1)
1.3 Appropriate Use of What-if Analysis
10(2)
1.3.1 Deterministic Decision Making
11(1)
1.4 Robustness and Flexibility
12(3)
1.4.1 Robust or Flexible: A Modeling Choice
12(3)
1.5 Transient Versus Steady-state Modeling
15(3)
1.5.1 Inherently Two-stage (Invest-and-use) Models
16(1)
1.5.2 Inherently Multistage (Operational) Models
16(2)
1.6 Distributions: Do They Exist and Can We Find Them?
18(5)
1.6.1 Generating Scenarios
20(1)
1.6.2 Dependent Random Variables
21(2)
1.7 Characterizing Some Examples
23(1)
1.8 Alternative Approaches
24(9)
1.8.1 Real Options Theory
24(3)
1.8.2 Chance-constrained Models
27(1)
1.8.3 Robust Optimization
28(3)
1.8.4 Stochastic Dynamic Programming
31(2)
2 Modeling Feasibility and Dynamics
33(28)
2.1 The Knapsack Problem
33(6)
2.1.1 Feasibility in the Inherently Two-Stage Knapsack Problem
34(2)
2.1.2 Two-Stage Models
36(1)
2.1.3 Chance-Constrained Models
37(1)
2.1.4 Stochastic Robust Formulations
38(1)
2.1.5 Two Different Multistage Formulations
39(1)
2.2 Overhaul Project Example
39(10)
2.2.1 Analysis
41(2)
2.2.2 A Two-Stage Version
43(2)
2.2.3 A Different Inherently Two-Stage Formulation
45(1)
2.2.4 Worst-Case Analysis
46(1)
2.2.5 A Comparison
47(1)
2.2.6 Dependent Random Variables
47(2)
2.2.7 Using Sensitivity Analysis Correctly
49(1)
2.3 An Inventory Problem
49(10)
2.3.1 Information Structure
50(3)
2.3.2 Analysis
53(1)
2.3.3 Chance-Constrained Formulation
54(1)
2.3.4 Horizon Effects
55(1)
2.3.5 Discounting
55(1)
2.3.6 Dual Equilibrium: Technical Discussion
56(3)
2.4 Summing Up Feasibility
59(2)
3 Modeling the Objective Function
61(16)
3.1 Distribution of Outcomes
61(1)
3.2 The Knapsack Problem, Continued
62(1)
3.3 Using Expected Values
63(3)
3.3.1 You Observe the Expected Value
63(1)
3.3.2 The Company Has Shareholders
64(1)
3.3.3 The Project Is Small Relative to the Total Wealth of a Company or Person
65(1)
3.4 Penalties, Targets, Shortfall, Options, and Recourse
66(3)
3.4.1 Penalty Functions
66(1)
3.4.2 Targets and Shortfall
66(2)
3.4.3 Options
68(1)
3.4.4 Recourse
68(1)
3.4.5 Multiple Outcomes
69(1)
3.5 Expected Utility
69(4)
3.5.1 Markowitz Mean-Variance Efficient Frontier
70(3)
3.6 Extreme Events
73(3)
3.7 Learning and Luck
76(1)
4 Scenario-Tree Generation: With Michal Kaut
77(26)
4.1 Creating Scenario Trees
79(4)
4.1.1 Plain Sampling
79(2)
4.1.2 Empirical Distribution
81(1)
4.1.3 What Is a Good Discretization?
81(2)
4.2 Stability Testing
83(5)
4.2.1 In-sample Stability
84(1)
4.2.2 Out-of-Sample Stability
85(1)
4.2.3 Bias
86(1)
4.2.4 Example: A Network Design Problem
86(1)
4.2.5 The Relationship Between In- and Out-of-Sample Stability
87(1)
4.2.6 Out-of-Sample Stability for Multiperiod Trees
87(1)
4.2.7 Other Approaches to Stability
88(1)
4.3 Statistical Approaches to Solution Quality
88(4)
4.3.1 Testing the Quality of a Solution
88(2)
4.3.2 Solution Techniques Based on the Optimality Gap Estimators
90(1)
4.3.3 Relation to the Stability Tests
91(1)
4.4 Property Matching Methods
92(10)
4.4.1 Regression Models
94(1)
4.4.2 The Transformation Model
95(5)
4.4.3 Independent and Uncorrelated Random Variables
100(1)
4.4.4 Other Construction Approaches
101(1)
4.5 Choosing an Approach
102(1)
5 Service Network Design: With Arnt-Gunnar Lium and Teodor Gabriel Crainic
103(20)
5.1 Cost Structure
103(1)
5.2 Warehouses and Consolidation
104(1)
5.3 Demand and Rejections
104(2)
5.4 How We Started Out
106(1)
5.5 The Stage Structure
107(1)
5.6 A Simple Service Network Design Case
107(4)
5.7 Correlations: Do They Matter?
111(5)
5.7.1 Analyzing the Results
111(4)
5.7.2 Relation to Options Theory
115(1)
5.7.3 Bidding for a Job
116(1)
5.8 The Implicit Options
116(6)
5.8.1 Reducing Risk Using Consolidation
117(2)
5.8.2 Obtaining Flexibility by Sharing Paths
119(2)
5.8.3 How Correlations Can Affect Schedules
121(1)
5.9 Conclusion
122(1)
6 A Multidimensional Newsboy Problem with Substitution: With Hajnalka Vaagen
123(16)
6.1 The Newsboy Problem
123(2)
6.2 Introduction to the Actual Problem
125(1)
6.3 Model Formulation and Parameter Estimation
126(2)
6.3.1 Demand Distributions
126(1)
6.3.2 Estimating Correlation and Substitution
127(1)
6.4 Stochastic Programming Formulation
128(2)
6.5 Test Case and Model Implementation
130(7)
6.5.1 Test Results
131(6)
6.6 Conclusion
137(2)
7 Stochastic Discount Factors
139(14)
7.1 Financial Market Information
139(9)
7.1.1 A Simple Options Pricing Example
140(4)
7.1.2 Stochastic Discount Factors
144(1)
7.1.3 Generalizing the Options Pricing Model
144(2)
7.1.4 Calibration of a Stochastic Discount Factor
146(2)
7.2 Application to the Classical NewsVendor Problem
148(2)
7.2.1 Calibration of Real Options Models
150(1)
7.3 Summary Discussion
150(3)
8 Long Lead Time Production: With Aliza Heching
153(12)
8.1 Supplier-Managed Inventory
153(1)
8.2 Supplier-Managed Inventory: Time Stages
154(2)
8.2.1 Modeling Time Stages
154(2)
8.3 Modeling the SMI Problem
156(2)
8.3.1 First- and Last-Stage Model
156(1)
8.3.2 Demand Forecasts and Supply Commitments
157(1)
8.3.3 Production and Inventory
157(1)
8.4 Capacity Model
158(3)
8.4.1 Orders and Review Periods
158(1)
8.4.2 The Model
159(1)
8.4.3 Objectives
159(2)
8.5 Uncertainty
161(4)
8.5.1 Uncertain Orders
161(1)
8.5.2 Inaccurate Reporting
162(1)
8.5.3 A Stochastic Programming Model
162(1)
8.5.4 Real Options Modeling
163(2)
References 165(6)
Index 171