Scott P. Stevens – Mathematical Decision Making: Predictive Models and Optimization

Executives used to make decisions based on experience, intuition, and luck when faced with complex problems. There is a better way now. When faced with conflicting options, mathematics and computer science have developed techniques for predicting the best outcome. The purpose of this field is simple: to apply quantitative methods to help business managers, public servants, investors, scientific researchers, and problem solvers of all kinds make better decisions.

Consider the applications of this set of tools.

• Pricing : Costco rose to become one of the top-ranked retailers in the world by combining membership fees with the economy of selling in bulk. A mathematical technique—called genetic algorithms—shows the advantages of this strategy as well as the optimum prices to charge.
• Scheduling : Using nonlinear programming, many airlines employ scheduling software that can find the most favorable solution to unexpected disruptions—from weather to mechanical problems to crew availability—saving millions of dollars in operating costs.
• Bidding : Simulation models can take a lot of guesswork out of competitive bidding for a project. By running repeated simulations against competitors, a bidder can come up with a proposal that has a good chance of winning the job, while still making a profit.
• Queuing : Any process that reflects the behavior of waiting lines is known as queuing. Markov analysis shows how a small increase in input to a system can have a major impact on waiting times. The method also reveals surprising solutions for making long waits vanish.

Retirement planning, stock portfolio analysis, budget forecasting, health care allocation, public relations, marketing and advertising, and many other tasks can be done with the same techniques. The applications are endless.

During World War II, the Allies used top-secret operations research to protect convoys, improve the aim of anti-aircraft fire, and locate the weak points on Allied bombers. Private industry adopted operations research after the war, but it was expensive, slow, and only specialized experts could take advantage of the new methods. Nowadays anyone with a home computer and a spreadsheet program can use these methods to solve practical problems. The trick is knowing how to do it.

There are mathematical decision making models. You will learn the major mathematical techniques, applications, and spreadsheet procedures in 24 half-hour lectures. Scott Stevens is a professor at James Madison University.

Professor Stevens will be engaging in his presentation.

• managers eager to make better decisions—whether in business, technical, or non-profit endeavors;
• professionals aspiring to advance in their careers by mastering a proven approach to problem solving;
• those who work with or review spreadsheet and graphical presentations, and need to be able to separate good data from bad;
• students in business, mathematics, finance, marketing, health care, engineering, urban planning, and a host of other fields;
• math lovers curious to see a field that is often the opposite of calculus: simple functions and complex boundary conditions, instead of complex functions with simple boundary conditions; and
• lifelong learners who want to hone their critical thinking skills with important analytical techniques, made accessible and intellectually exciting as never before.

Discover the art of making a decision.

The wide choice of procedures you have at your fingertips makes the challenge of analyzing not the math, but the wide choice of procedures. Professor Stevens shows you how to pick the most effective one to apply to your problem. A willingness to use simple equations is all that is needed. Modern spreadsheets make setting up and visualization of problems simple and straightforward, and they take the drudgery out of finding solutions.

There is a mathematical decision making. graphs, charts, diagrams, and computer animations help to understand the material. Professor Stevens shows how to cultivate your visual intuition. The effects of synergy and interaction can have a strong impact on the bottom line when you move from linear programming to nonlinear programming. He shows how you can see the world as a landscape and then use your intuition to figure out how to approach the problem. You can see how the fight for dominance in the high-definition video market can be seen as a hyperbolic paraboloid, with all of the possible outcomes of the competition mapped onto its surface.

The course guide includes additional questions, problems, and answers for each lecture, along with recommended resources to help you dig deeper into any topic where you want to know more.

A wealth of cases can be analyzed.

The course features case after case of real-life examples. You will explore many of them.

• Public relations : The makers of Gerber baby food had experienced a public relations problem earlier in their history. See how they used decision tree analysis during a second budding crisis a dozen years later to map their options and reach a successful decision.
• Keeping clients happy : NBC schedulers once had to match advertisers to television time slots by hand, juggling a bewildering number of competing demands. You’ll learn how computer algorithms and the concept of “hard” and “soft” constraints revolutionized their job.
• Finding a missing plane : No one knew why Air France flight 447 crashed into the ocean in 2009—until Bayesian analysis led searchers to the wreck site and the black box. Bayes’s theorem tells how to compute new probabilities as new information becomes available.
• Evaluating efficiency : Non-profit organizations and government programs are notoriously hard to evaluate for efficiency. Using hospitals as a test case, you’ll discover how data envelopment analysis shows which facilities are performing effectively, as well as how to improve the ones that aren’t.

Professor Stevens is an acclaimed instructor who practices what he teaches. Neural network prediction of survival in trauma patients is one of the problems addressed by his research.

He loves mathematics and the wonders it can do. He marvels at the beauty of math. When I can get someone else to see a piece of it, I am happy. It is lovely, structured, consistent and reliable. It is a great world. With. There is a mathematical decision making. It is possible to see how mathematics can make the everyday world much better.

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