- 241 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
Introduction to Optimization-Based Decision-Making
About This Book
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
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- Collects and discusses the ideas underpinning decision-making through optimization tools in a simple and straightforward manner
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- Suitable for an undergraduate course in optimization-based decision-making, or as a supplementary resource for courses in operations research and management science
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- Self-contained coverage of traditional and more modern optimization models, while not requiring a previous background in decision theory
Frequently asked questions
Information
Chapter 1 First Notes on Optimization for Decision Support
1.1 Introduction
- First level: From 6 to 9 years old, up to 4 years of school.
- Second level: Between 10 and 11 years old, up to 6 years of school.
- Third level: From 12 to 14 years old, up to 9 years of school.
- It consists of either an open-ended scenario or the typical “What if?” analysis, where students with different knowledge levels (first, second, or higher levels) are challenged.
- Partial or complementary questions are properly ordered, allowing students to develop their own solution methods, which they perform autonomously.
- Using either teamwork (two or three students in each group) or individually, tutorial supervision promotes the goals at each level, ensuring that they are accomplished.
- The tutorial goals include self-contained strategies that young students can build on to solve the problem instances; for that, the instances are not defined or partitioned in a tight format.
1.2 First Steps
1.2.1 The Furniture Factory Problem: First Level
Noddy is trying to help Big Ears build some tables (each table is worth four chocolate cakes) and some chairs (each chair is worth three chocolate cakes) according to Figure 1.1a.However, there are only eight small-red and three big-blue pieces (Figure 1.1b).
How many tables and chairs does Noddy need to build to earn the most chocolate cakes?
- Optimal solution: Zero tables and three chairs; the value is 9 (0 × 4 + 3 × 3) and two small-red pieces are left.
- Second solution (sub-optimal): One table and one chair; the value is 7 (1 × 4 + 1 × 3), but four small-red pieces are left.
How do you know you have reached the end?
What if …
- There is one more big-blue piece?
It could build one more chair (gaining 3), obtaining a new maximum value of 12 (corresponding to 4 × 3).
- There is again one more big-blue piece?
It could build one more table (gaining 4) while undoing a chair (losing 3); therefore, the marginal value is 1 (4 – 3) and the total value is 13, corresponding to one table and three chairs (1 × 4 + 3 × 3).
- There is another big-blue piece to add?
Again, it could build one more table (gaining 4) while undoing a chair (losing 3); therefore, the marginal value remains 1 and the total value is 14 (2 × 4 + 2 × 3); this situation is repeated two more times, until the components of the two other chairs are made available to build two additional tables, obtaining a total of 16 (4 × 4 + 0 × 3) with a marginal value of 1 for each new big-blue piece.
- There is yet another big-blue piece to add?
No more additional tables can be produced, as there are no more chairs to undo; therefore, the marginal value is zero and the optimal solution is the previous solution.
1.3 Introducing Proportionality
1.3.1 The Furniture Factory Problem: Second ...
Table of contents
- Cover
- Half-Title
- Series
- Title
- Copyright
- Dedication
- Contents
- Foreword
- Preface
- Author
- CHAPTER 1 First Notes on Optimization for Decision Support
- CHAPTER 2 Linear Algebra
- CHAPTER 3 Linear Programming Basics
- CHAPTER 4 Duality
- CHAPTER 5 Calculus Optimization
- CHAPTER 6 Optimality Analysis
- CHAPTER 7 Integer Linear Programming
- CHAPTER 8 Game Theory
- CHAPTER 9 Decision-Making Under Uncertainty
- CHAPTER 10 Robust Optimization
- SELECTED REFERENCES
- INDEX