The challenge of using computers requires bridging complex problems and mathematical modeling. When these problems involve making decisions over time (which covers a vast range of applications), the research literature has fragmented into over a dozen different communities, each with their own notation, modeling styles, and algorithms illustrated using carefully chosen examples.
Traditional approaches for optimizing systems are limited to narrow classes of (typically complex) applications. Combining decisions and uncertainty invariably leads to sophisticated tools with arcane mathematics, as evidenced by the almost universal lack of general purpose software packages.
We pursue these problems using the principle of "model first, then solve" which is guided by the overarching philosophy:
If you want to run a better {anything} you have to make better decisions.
Our approach focuses on making the best decisions, but not just the decisions that fit some optimization model… this website spans any decision. We start in English (not math), and begin by defining decisions, then we identify 10 types of decisions. We use a universal modeling framework for evaluating any method for making decisions (called “policies”), from simple rules to large-scale deterministic integer programs. We also identify 12 categories of uncertainty that may come in a range of styles and time scales.
Motivated by decades of working on complex, real-world problems, we start in English with a process of framing problems by posing three questions:
- What are the performance metrics?
- What types of decisions are being made (and who makes them)?
- What are the sources of uncertainty?
Be sure to check out our new tool for framing decision problems.
These questions help to clarify thinking about problems, which is all that is needed for most decisions. For applications that warrant more careful analysis, the questions lay the foundation for the Universal Modeling Framework which can represent any sequential decision problem as a mathematical model.
A good way to start is to follow the instructions in A guided tour which starts with material on problem framing that requires no math. Most of the presentation is free of math, while a few pages have some math. If you are interested in more depth, try using Ask Professor Powell which will use as much math as you want (just ask). The chatbot has been trained with all my books, 1,000 pages of LinkedIn posts on decision analytics, and the contents of this website.
The thoughts on this website are based on a lifetime of research using computers to make decisions. I hope you find it useful. Please share!
Warren Powell
Professor (emeritus), Princeton University
Chief Innovation Officer, Optimal Dynamics