Decision Analytics: Mathematical Models and Algori thms for Sequential Decision-Making
Autor Brian T. Dentonen Limba Engleză Hardback – 22 oct 2026
Sequential decisions under uncertainty arise in many fields including energy, healthcare, finance, transportation, and logistics, yet accessible treatments linking foundational theory to computational practice remain scarce. Decision Analytics: Mathematical Models and Algorithms for Sequential Decision-Making, written by Brian T. Denton, a past President of INFORMS, presents a structured progression from core concepts through advanced methods, pairing rigorous mathematics with implementable Python code.
Across ten chapters, Decision Analytics covers decision trees, Monte Carlo simulation, Markov chains, Markov decision processes, partially observable Markov decision processes, and constrained optimization models, including stochastic programs. Dedicated chapters on reinforcement learning and multi-agent learning introduce model-free approaches for finding optimal or near-optimal solutions. The final chapter covers approximate dynamic programming for decision-making at scale. Real-world examples, exercises, and an instructor's solution manual support classroom adoption.
Readers will also find:
- Coverage of artificial intelligence techniques applied to sequential decision-making problems
- Monte Carlo simulation methods used to analyse decision trees, Markov decision processes, and stochastic programming formulations
- Python code examples throughout the text enabling direct implementation and experimentation with each model and algorithm presented
- Practice exercises with solutions and an instructor's manual designed to support both self-study and classroom-based teaching
- A concept-first pedagogical approach that explains foundational principles before demonstrating how they solve applied problems
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Specificații
ISBN-13: 9781394345786
ISBN-10: 139434578X
Pagini: 240
Greutate: 0.85 kg
Editura: John Wiley & Sons, Inc.
ISBN-10: 139434578X
Pagini: 240
Greutate: 0.85 kg
Editura: John Wiley & Sons, Inc.
Notă biografică
Brian T. Denton, PhD, is the Stephen M. Pollock Collegiate Professor of Industrial and Operations Engineering at the University of Michigan. A past President of INFORMS, his research focuses on data-driven sequential decision making and optimization under uncertainty. His work has earned the National Science Foundation Career Award, INFORMS Daniel H. Wagner Prize, and the George E. Kimball medal. He is a Fellow of INFORMS and the Institute of Industrial and Systems Engineers.
Cuprins
About the Author xi
Acknowledgments xiii
About the Companion Website xv
1 Introduction to Decision Analytics 1
1.1 Introduction 1
1.2 Mathematical Models for Decision-making 1
1.3 Examples of Practical Applications 3
1.4 Python and Computational Examples 5
1.5 Summary of Future Chapters 6
1.6 Concluding Remarks 7
1.7 Practice Exercises 7
2 Decision Trees 11
2.1 Introduction 11
2.2 Basic Probability Concepts 12
2.3 Quantifying Decisions: Payoffs and Decision-maker Perspectives 14
2.4 Multi-stage Decision Trees 17
2.5 Expected Value of Perfect Information 19
2.6 Concluding Remarks 21
2.7 Practice Exercises 21
3 Deterministic Dynamic Programs 25
3.1 Introduction 25
3.2 Mathematical Formulation of Dynamic Programs 25
3.3 Shortest Path Problems on Directed Acyclic Networks 26
3.4 Production Lot-sizing 28
3.5 Resource Allocation 31
3.6 Pattern Recognition 34
3.7 Generalization of Shortest Path Problems to Include Cycles 36
3.8 Counter Example: When DP Does Not Work 41
3.9 Concluding Remarks 42
3.10 Practice Exercises 42
4 Markov Decision Processes 47
4.1 Introduction 47
4.2 Markov Chains 47
4.3 Markov Decision Processes 49
4.4 Optimal Stopping Time Problems 56
4.5 Production Planning with Uncertain Demand 60
4.6 MDP Parameter Estimation 64
4.7 Infinite-horizon MDPs 65
4.8 Concluding Remarks 78
4.9 Practice Exercises 79
5 Constrained Optimization Models 83
5.1 Introduction 83
5.2 A Visual Introduction to Linear Programming Models 85
5.3 The Shortest Path Problem Revisited 87
5.4 Relationship Between Dynamic Programs and Linear Programs 90
5.5 Two-stage Stochastic Linear Programs 92
5.6 Expected Value of Perfect Information (EVPI) 102
5.7 Concluding Remarks 106
5.8 Practice Exercises 106
6 Monte Carlo Simulation 109
6.1 Introduction 109
6.2 Curse of Dimensionality 109
6.3 Monte Carlo Sampling 110
6.4 Using Monte Carlo Simulation to Estimate Expectations 112
6.5 Sampling a Markov Chain 114
6.6 Approximating Stochastic Programs with Monte Carlo Simulation 120
6.7 Monte Carlo Sampling for MDPs 123
6.8 Concluding Remarks 124
6.9 Practice Exercises 125
7 Partially Observable Markov Decision Processes 127
7.1 Introduction 127
7.2 Hidden Markov Models 127
7.3 HMM Parameter Estimation 129
7.4 POMDP Model Formulation 130
7.5 Solution Methods for POMDPs 131
7.6 Approximation Methods for POMDPs 135
7.7 Concluding Remarks 141
7.8 Practice Exercises 142
8 Reinforcement Learning 145
8.1 Introduction 145
8.2 Contexts and Types of Learning 146
8.3 Greedy Monte Carlo Policy Iteration 148
8.4 Monte Carlo Policy Iteration 153
8.5 Q-learning 157
8.6 Concluding Remarks 162
8.7 Practice Exercises 163
9 Multi-agent Markov Decision Processes 165
9.1 Introduction 165
9.2 A Two-agent Model: Decision-maker vs. an Adversary 165
9.3 Cooperative Multi-agent Markov Decision Processes (MAMDPs) 170
9.4 Concluding Remarks 187
9.5 Practice Exercises 187
10 Approximation Methods for Large-scale Models 191
10.1 Introduction 191
10.2 Value Function Approximations 192
10.3 Policy Iteration-based Approximation 204
10.3.1 Policy Approximation Methods 210
10.4 Concluding Remarks 212
10.5 Practice Exercises 213
References 213
Appendix 215
Index 221
Acknowledgments xiii
About the Companion Website xv
1 Introduction to Decision Analytics 1
1.1 Introduction 1
1.2 Mathematical Models for Decision-making 1
1.3 Examples of Practical Applications 3
1.4 Python and Computational Examples 5
1.5 Summary of Future Chapters 6
1.6 Concluding Remarks 7
1.7 Practice Exercises 7
2 Decision Trees 11
2.1 Introduction 11
2.2 Basic Probability Concepts 12
2.3 Quantifying Decisions: Payoffs and Decision-maker Perspectives 14
2.4 Multi-stage Decision Trees 17
2.5 Expected Value of Perfect Information 19
2.6 Concluding Remarks 21
2.7 Practice Exercises 21
3 Deterministic Dynamic Programs 25
3.1 Introduction 25
3.2 Mathematical Formulation of Dynamic Programs 25
3.3 Shortest Path Problems on Directed Acyclic Networks 26
3.4 Production Lot-sizing 28
3.5 Resource Allocation 31
3.6 Pattern Recognition 34
3.7 Generalization of Shortest Path Problems to Include Cycles 36
3.8 Counter Example: When DP Does Not Work 41
3.9 Concluding Remarks 42
3.10 Practice Exercises 42
4 Markov Decision Processes 47
4.1 Introduction 47
4.2 Markov Chains 47
4.3 Markov Decision Processes 49
4.4 Optimal Stopping Time Problems 56
4.5 Production Planning with Uncertain Demand 60
4.6 MDP Parameter Estimation 64
4.7 Infinite-horizon MDPs 65
4.8 Concluding Remarks 78
4.9 Practice Exercises 79
5 Constrained Optimization Models 83
5.1 Introduction 83
5.2 A Visual Introduction to Linear Programming Models 85
5.3 The Shortest Path Problem Revisited 87
5.4 Relationship Between Dynamic Programs and Linear Programs 90
5.5 Two-stage Stochastic Linear Programs 92
5.6 Expected Value of Perfect Information (EVPI) 102
5.7 Concluding Remarks 106
5.8 Practice Exercises 106
6 Monte Carlo Simulation 109
6.1 Introduction 109
6.2 Curse of Dimensionality 109
6.3 Monte Carlo Sampling 110
6.4 Using Monte Carlo Simulation to Estimate Expectations 112
6.5 Sampling a Markov Chain 114
6.6 Approximating Stochastic Programs with Monte Carlo Simulation 120
6.7 Monte Carlo Sampling for MDPs 123
6.8 Concluding Remarks 124
6.9 Practice Exercises 125
7 Partially Observable Markov Decision Processes 127
7.1 Introduction 127
7.2 Hidden Markov Models 127
7.3 HMM Parameter Estimation 129
7.4 POMDP Model Formulation 130
7.5 Solution Methods for POMDPs 131
7.6 Approximation Methods for POMDPs 135
7.7 Concluding Remarks 141
7.8 Practice Exercises 142
8 Reinforcement Learning 145
8.1 Introduction 145
8.2 Contexts and Types of Learning 146
8.3 Greedy Monte Carlo Policy Iteration 148
8.4 Monte Carlo Policy Iteration 153
8.5 Q-learning 157
8.6 Concluding Remarks 162
8.7 Practice Exercises 163
9 Multi-agent Markov Decision Processes 165
9.1 Introduction 165
9.2 A Two-agent Model: Decision-maker vs. an Adversary 165
9.3 Cooperative Multi-agent Markov Decision Processes (MAMDPs) 170
9.4 Concluding Remarks 187
9.5 Practice Exercises 187
10 Approximation Methods for Large-scale Models 191
10.1 Introduction 191
10.2 Value Function Approximations 192
10.3 Policy Iteration-based Approximation 204
10.3.1 Policy Approximation Methods 210
10.4 Concluding Remarks 212
10.5 Practice Exercises 213
References 213
Appendix 215
Index 221