Decision Analytics

Mathematical Models and Algorithms for Sequential Decision-Making
1. Auflage 2027
ISBN: 978-1-394-34578-6
Verlag: Wiley

Buch, Englisch, 256 Seiten

Mathematical models and algorithms for sequential decisions under uncertainty

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

Designed for undergraduate and graduate students in industrial engineering, operations research, and related STEM disciplines with introductory knowledge of mathematics, probability, and statistics, this book also serves researchers and professionals who require unified treatment of sequential decision-making methods.

Autoren/Hrsg.

Denton, Brian T.

Fachgebiete

• Technische Wissenschaften Maschinenbau | Werkstoffkunde Maschinenbau Konstruktionslehre, Bauelemente, CAD
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Optimierung
• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
• Technische Wissenschaften Bauingenieurwesen Mathematische Methoden, Computeranwendungen (Bauingenieurwesen)

Inhaltsverzeichnis

Table of Contents

About the author

Acknowledgement

1 Introduction

1.1 Introduction

1.2 Mathematical Models for Decision Making

1.3 Examples of Practical Applications

1.4 Python and Computational Examples

1.5 Summary of Future Chapters

1.6 Concluding Remarks

1.7 Practice Exercises

2 Decision Trees

2.1 Decision Trees

2.2 Basic Probability Concepts

2.3 Quantifying Decisions: Payoffs and Decision-Maker Perspectives

2.3.1 Quality Adjusted Life Years

2.3.2 Probability of an Event

2.3.3 Utility

2.3.4 Time Value of Rewards

2.3.5 Regret

2.4 Multi-stage Decision Trees

2.5 Expected Value of Perfect Information

2.6 Concluding Remarks

2.7 Practice Exercises

3 Deterministic Dynamic Programs

3.1 Introduction

3.2 Mathematical Formulation of Dynamic Programs

3.3 Shortest Path Problems on Directed Acyclic Networks

3.4 Production Lot-sizing

3.5 Resource Allocation

3.6 Pattern Recognition

3.7 Generalization of Shortest Path Problems to Include Cycles

3.8 Counter Example: When DP Does Not Work

3.9 Concluding Remarks

3.10 Practice Exercises

4 Markov Decision Processes

4.1 Introduction

4.2 Markov Chains

4.3 Markov Decision Processes (MDPs)

4.3.1 Estimating Computational Complexity of Policy Evaluation

4.3.2 Finding Optimal Policies Efficiently

4.3.3 Analysis of the Backward Induction Algorithm

4.3.4 Shortest Path Problem Revisited

4.4 Optimal Stopping Time Problems

4.5 Production Planning with Uncertain Demand

4.6 MDP Parameter Estimation

4.7 Infinite-Horizon MDPs

4.7.1 Policy Evaluation Over an Infinite Horizon

4.7.2 Optimality Equations for Infinite-Horizon MDPs

4.7.3 Solving the Optimality Equations for Infinite-Horizon MDPs

Value Iteration

The Reasons Value Iteration W

Über Autor(innen)

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.