This book provides an elementary and self-contained introduction to the basic concepts involved in making decisions in an optimization-based environment. The mathematical level of the text is directed to the post-secondary reader, or university students in the initial years.
The large and complex challenges the world is facing, the growing prevalence of huge data sets, and the new and developing ways for addressing them (artificial intelligence, data science, machine learning, etc.), means it is increasingly vital that academics and professionals from across disciplines have a basic understanding of the mathematical underpinnings of effective, optimized decision-making. Without it, decision makers risk being overtaken by those who better understand the models and methods, that can best inform strategic and tactical decisions.
Introduction to Optimization-Based Decision-Making
provides an elementary and self-contained introduction to the basic concepts involved in making decisions in an optimization-based environment. The mathematical level of the text is directed to the post-secondary reader, or university students in the initial years. The prerequisites are therefore minimal, and necessary mathematical tools are provided as needed. This lean approach is complemented with a problem-based orientation and a methodology of generalization/reduction. In this way, the book can be useful for students from STEM fields, economics and enterprise sciences, social sciences and humanities, as well as for the general reader interested in multi/trans-disciplinary approaches.
Features
Collects and discusses the ideas underpinning decision-making through optimization tools in a simple and straightforward manner Suitable for an undergraduate course in optimization-based decision-making, or as a supplementary resource for courses in operations research and management science Self-contained coverage of traditional and more modern optimization models, while not requiring a previous background in decision theory
1. First Notes on Optimization for Decision Support. 1.1. Introduction.
1.2. First Steps. 1.3. Introducing Proportionality. 1.4. A Non-Proportional
Instance. 1.5. An Enlarged and Non-Proportional Instance. 1.6. Concluding
Remarks.
2. Linear Algebra. 2.1. Introduction. 2.2. Gauss Elimination on the
Linear System. 2.3. Gauss Elimination with the Augmented Matrix. 2.4.
Gauss-Jordan and the Inverse Matrix. 2.5. Cramers Rule and Determinants.
2.6. Concluding Remarks.
3. Linear Programming Basics. 3.1. Introduction.
3.2. Graphical Approach. 3.3. Algebraic Form. 3.4. Tableau Form. 3.5. Matrix
Form. 3.6. Updating the Inverse Matrix. 3.7. Concluding Remarks.
4. Duality.
4.1. Introduction. 4.2. Primal-Dual Transformations. 4.3. Dual Simplex
Method. 4.4. Duality Properties. 4.5. Duality and Economic Interpretation.
4.6. A First Approach to Optimality Analysis. 4.7. Concluding Remarks.
5.
Calculus Optimization. 5.1. Introduction. 5.2. Constrained Optimization with
Lagrange Multipliers. 5.3. Generalization of the Constrained Optimization
Case. 5.4. Lagrange Multipliers for the Furniture Factory Problem. 5.5.
Concluding Remarks.
6. Optimality Analysis. 6.1. Introduction. 6.2. Revising
LP Simplex. 6.3. Sensitivity Analysis. 6.4. Parametric Analysis. 6.5.
Concluding Remarks.
7. Integer Linear Programming. 7.1. Introduction. 7.2.
Solving Integer Linear Programming Problems. 7.3. Modeling with Binary
Variables. 7.4. Solving Binary Integer Programming Problems. 7.5. Concluding
Remarks.
8. Game Theory. 8.1. Introduction. 8.2. Constant-Sum Game. 8.3.
Zero-Sum Game. 8.4. Mixed Strategies - LP Approach. 8.5. Dominant Strategies.
8.6. Concluding Remarks.
9. Decision Making Under Uncertainty. 9.1.
Introduction. 9.2. Multiple Criteria and Decision Maker Values. 9.3. Capacity
Expansion for the Furniture Factory. 9.4. A Comparison Analysis. 9.5.
Concluding Remarks.
10. Robust Optimization. 10.1. Introduction. 10.2. Notes
on Stochastic Programming. 10.3. Robustness Promotion on Models and
Solutions. 10.4. Models Generalization onto Robust Optimization. 10.5.
Concluding Remarks. Selected References
Joćo Luķs de Miranda is Professor at ESTG-Escola Superior de Tecnologia e Gestćo (IPPortalegre) and Researcher in Optimization methods and Process Systems Engineering (PSE) at CERENA-Centro de Recursos Naturais e Ambiente (IST/ULisboa). He has been teaching for more than twenty years in the field of Mathematics (e.g., Calculus, Operations Research-OR, Management Science-MS, Numerical Methods, Quantitative Methods, Statistics) and has authored/edited several publications in Optimization, PSE, and Education subjects in Engineering and OR/MS contexts. Joćo Luķs de Miranda is addressing the research subjects through international cooperation in multidisciplinary frameworks, and is serving on several boards/committees at national and European level.
