Prof. Warren B. Powell published a new book “A Modern Approach to Teaching an Introduction to Optimization“. He states: “Optimization should be the science of making the best decisions we can… The vast majority of optimization problems are used to make decisions that arise over time, which means they are sequential decision problems that have to be solved as new information continues to arrive.“ While he concentrates on the question “We need to modernize how we introduce students to optimization“, many of his observations are valid for bringing the optimization approach and supporting tools to business analysts. Free PDF
Some observations:
- Optimization should be the science of making the best decisions we can.
- We should start with the simplest nontrivial decision problems that students are most familiar with. Examples include machine learning (a form of nonlinear optimization), and an array of sequential decision problems where the decisions may be binary (selling an asset, booking a flight, choosing a webpage design), discrete (choosing the best product to recommend, medical treatment, person to perform a task, …) or a continuous scalar (price, dosage, concentration, time, …).
- Most optimization courses in industrial engineering, operations research, MBA programs, … emphasize linear programs. Virtually no one without formal training has even heard of a linear program, and very few students who take a course in linear programming ever solve a linear program. Of course, there are many applications of linear programming (and integer programming), but these are more complex problems.
- Linear programs (along with integer and nonlinear programs) are almost always presented as static problems. However, the vast majority of optimization problems are used to make decisions that arise over time, which means they are sequential decision problems that have to be solved as new information continues to arrive.
Many people with formal training will recognize a sequential decision problem as a dynamic program, which normally leads to sophisticated material based on Bellman’s equation. The only time I use Bellman’s equation is to solve a simple deterministic shortest path problem. Please keep in mind that while the academic community likes to bring a high level of sophistication to optimization problems that involve uncertainty, people deal with uncertainty all the time, and there are methods for solving these problems that are quite simple.