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, motivated by decades of working on complex, real-world problems, starts 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?
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.
The framework spans any method for making decisions (called “policies”), from simple rules to large-scale deterministic integer programs, since these all fall in the four classes of policies. We also identify 12 categories of uncertainty that may come in a range of styles and time scales. The process of developing these tools has been dramatically streamlined in recent years with the emergence of large language models.
Start with Sequential decision problems in the menu on the left. I also suggest skimming Motivating applications since these were the problems that motivated the universal modeling framework. Then work through Modeling which starts with basic questions such as What is a decision. Click on Policies to learn about all four classes of policies, and finish with Teaching materials which describes courses and self-taught weekly seminars.
Be sure to try out the “Ask Professor Powell” chatbot at the top, which has been trained with all my books, 1,000 pages of LinkedIn posts and a number of webpages.
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