Mathematical Decision Making: Predictive Models and Optimization

Course No. 1342
Professor Scott P. Stevens, Ph.D.
James Madison University
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Course No. 1342
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What Will You Learn?

  • numbers Learn about time series forecasting and simple line regression.
  • numbers Use linear programs in spreadsheets, and learn how to visualize solutions.
  • numbers Tackle nonlinear landscapes and improve your mathematical intuition.
  • numbers Work with decision trees and see how famous theorems and models have impacted major decisions in history.

Course Overview

Not so long ago, executives faced with complex problems made decisions based on experience, intuition, and no small measure of luck. But now there’s a better way. In recent decades, mathematics and computer science have perfected formerly top-secret techniques for predicting the best possible outcomes when faced with conflicting options. This field goes by different names—analytics, operations research, linear and nonlinear programming, management science—but its purpose 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 following applications of this powerful 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.

These same techniques can be applied to retirement planning, stock portfolio analysis, budget forecasting, health care allocation, public relations, marketing and advertising, and many other tasks for enterprises large and small. The applications are truly endless!

Mathematical decision making got its first rigorous tests during World War II, when 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. After the war, private industry adopted operations research with enthusiasm, but these new methods were expensive, computing speed was slow, and only specialized experts could take advantage of the algorithms. That situation has changed dramatically, and today anyone with a home computer and a spreadsheet program can harness the power of these methods to solve practical problems. The trick is knowing what you can do and how to do it.

Mathematical Decision Making: Predictive Models and Optimization is your guide, teaching you the major mathematical techniques, applications, and spreadsheet procedures for basic analytics in 24 information-packed half-hour lectures. Your professor is award-winning educator Scott Stevens, Professor of Computer Information Systems and Business Analytics at James Madison University.

Those who will benefit from Professor Stevens’s engaging presentation include:

  • 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 Deciding

You’ll find that the challenge of analytics is not the math, which is often surprisingly easy, but the wide choice of procedures you have at your fingertips. The art is picking the most effective one to apply to your problem, and this is what Professor Stevens walks you through in fascinating detail. All that’s needed is a willingness to use simple equations. Moreover, you’ll see how modern spreadsheets take the drudgery out of finding solutions, and they make setting up and visualizing problems simple and straightforward.

Mathematical Decision Making is vividly illustrated with graphs, charts, diagrams, and computer animations, which greatly aid understanding the material. In addition, Professor Stevens demonstrates the importance of cultivating your visual intuition. This is particularly helpful when you move from linear programming to nonlinear programming, where effects of synergy and interaction can have strong impact on the bottom line. He shows how you can visualize this new world as a landscape, and then use your natural intuition to decide how best to approach the problem. As an illustration, you see how the fight between Blu-Ray and HD DVD for dominance in the high-definition video market can be pictured as a hyperbolic paraboloid—a saddle-shaped figure—with all of the possible outcomes of the competition mapped onto its surface.

Conveniently, the course guidebook includes additional thought-provoking 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.

Analyze a Wealth of Cases

The beauty of this course is that it features case after case of real-life examples. Among the many you’ll explore are these:

  • 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.

An acclaimed instructor who practices what he teaches, Professor Stevens has pushed the boundaries of mathematical decision making on many fronts. His research has addressed such problems as neural network prediction of survival in trauma patients and how to optimize the market for natural gas from the Gulf of Mexico.

Above all, he loves mathematics and the wonders it can perform. “Math is an absolutely beautiful thing,” he marvels. “I’m at my happiest when I can get someone else to see just a piece of that. It’s lovely, structured, consistent, reliable, surprising, enticing, exotic. It’s a great world!” With Mathematical Decision Making, see for yourself how mathematics can make the everyday world we all inhabit a more comprehensible and much better place.

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24 lectures
 |  Average 31 minutes each
  • 1
    The Operations Research Superhighway
    Survey the extraordinary range of applications for operations research and predictive analytics. Professor Stevens defines these fields, previews the mathematical techniques that underlie them, and charts their history, from World War II defense research to their rapid growth in the computer era. x
  • 2
    Forecasting with Simple Linear Regression
    Linear regression is a powerful method for describing connections between related quantities. Analyze several problems using linear regression. For example, predict the waiting time for an eruption of the Old Faithful geyser based on how long the previous eruption lasted. x
  • 3
    Nonlinear Trends and Multiple Regression
    Explore more complex linear regression problems, which involve nonlinear functions and/or multiple inputs. Many real-life situations require these approaches, called transformation of variables and multiple linear regression. Learn how to envision the data graphically, and witness the ease with which spreadsheets solve these problems. x
  • 4
    Time Series Forecasting
    Time series forecasting is a valuable tool when there's little data on what drives a process. Using the example of U.S. housing starts, learn how to glean information from historical figures, taking into account both long-term trends and seasonal fluctuations to create a forecast and assess its reliability. x
  • 5
    Data Mining: Exploration and Prediction
    Plunge into the fast-growing field of data mining, which exploits computational power and innovative algorithms to analyze the ever-increasing deluge of data. Focus on classification and prediction, seeing how classification trees can help solve the problem of building a filter that predicts spam email messages. x
  • 6
    Data Mining for Affinity and Clustering
    Delve deeper into data mining by exploring affinity analysis, or what goes with what." One approach uses association rules to discover relevant connections between variables, while another employs clustering. For example, Pandora Radio uses these tools to make music recommendations based on a listener's song preferences." x
  • 7
    Optimization: Goals, Decisions, and Constraints
    Get the big picture on optimization, which is the focus of the next section of the course. Optimization seeks the best possible answer to a given problem. Learn how to model an optimization problem by asking four key questions. Then trace the steps in an example from the airline industry. x
  • 8
    Linear Programming and Optimal Network Flow
    Continue your study of optimization problems by looking at solutions that use linear programming: an approach of exceptional power, speed, and simplicity. See how linear programming showed Union Pacific a cost-saving way to distribute railroad cars to locations throughout the country. x
  • 9
    Scheduling and Multiperiod Planning
    Investigate multiperiod planning problems. You will apply the tools from previous lectures to schedule activities and control inventory. You will also map out an investment plan that gives you the money you need, when you need it. x
  • 10
    Visualizing Solutions to Linear Programs
    Mathematical intuition can be a powerful tool for solving mathematical problems. See how the answer almost jumps out at you when you apply a graphical method to certain types of optimization problems. Professor Stevens walks you through a real-life example involving personal financial investments and spaghetti. x
  • 11
    Solving Linear Programs in a Spreadsheet
    Learn how to solve a linear program using the famous simplex algorithm, developed by George Dantzig. Follow this easy, step-by-step approach that will allow you to use a spreadsheet, such as Calc or Excel, to find the optimal solution to virtually any linear program that has one. Watch how fast you get results! x
  • 12
    Sensitivity Analysis: Trust the Answer?
    How much can you change a parameter in a problem before you affect the optimal solution? How do you forecast the tipping point at which dramatic changes occur? Sensitivity analysis will do the trick. Investigate the application of this valuable tool to linear programs. x
  • 13
    Integer Programming: All or Nothing
    Many problems contain variables that must be integers: for example, the number of units of a product or the number of production plants. Explore the special challenges presented by integer programs. Solve examples using the graphical method, then see how to find solutions with a spreadsheet. x
  • 14
    Where Is the Efficiency Frontier?
    Rating the efficiency of an operation is difficult if multiple inputs and outputs are involved. This often happens when trying to evaluate productivity among non-profits or government programs. Learn to use a popular technique that makes such comparisons simple, thanks to data envelopment analysis. x
  • 15
    Programs with Multiple Goals
    How do you evaluate the quality of a solution based on more than a single objective? Focus on three approaches: the weighted average, soft constraints combined with penalties, and prioritizing goals. Evaluate these in terms of NBC's difficulty in setting television advertising schedules, due to multiple objectives. x
  • 16
    Optimization in a Nonlinear Landscape
    Review the lessons of linear programming, which you have been studying since Lecture 8. Then venture into the world of nonlinear programming. Professor Stevens orients you to this fascinating realm by demonstrating techniques that build your mathematical intuition for solving nonlinear problems. x
  • 17
    Nonlinear Models: Best Location, Best Pricing
    Roll up your sleeves and tackle two practical problems in nonlinear programming: pick a location for a hub in an airline flight network, and price a retail product for maximum sales. In the latter case, you learn to model what makes Costco such a runaway success. x
  • 18
    Randomness, Probability, and Expectation
    Probability allows you to evaluate situations where only partial control is possible - such as investment opportunities, public relations problems, and waiting lines. Hone your skills in elementary probability with simple challenges, including a game called Cat or No Cat." x
  • 19
    Decision Trees: Which Scenario Is Best?
    See how decision trees and probability analysis can lead to optimal decisions in situations that seem bewilderingly uncertain. Professor Stevens focuses on a potential public relations disaster faced by executives at Gerber Products and how they used a decision tree to chart a successful strategy. x
  • 20
    Bayesian Analysis of New Information
    According to Bayes's theorem, the chance that something is true changes as new and better information becomes available. Trace the use of this principle in the search for wreckage from Air France flight 447, and learn how this simple but powerful idea serves as a corrective to bad decision making in many spheres. x
  • 21
    Markov Models: How a Random Walk Evolves
    Peer into the future with Markov analysis, which studies random systems to predict possible future outcomes. Apply this technique to the downed plane example from the previous lecture, and then see how Markov analysis helped a German direct-marketing firm avoid financial ruin. x
  • 22
    Queuing: Why Waiting Lines Work or Fail
    Extend your use of Markov analysis to waiting lines, or queues. Discover how a random arrival process is analogous to the sound of popcorn popping. Then probe the dramatic decrease in waiting times that can result from relatively minor adjustments in workforce or equipment. x
  • 23
    Monte Carlo Simulation for a Better Job Bid
    Graduate to one of the most versatile and widely used techniques in operations research: simulation, which models the intricate interplay of variables in complicated situations. Focus on a competitive bid for a building project and how simulation can come up with a winning strategy. x
  • 24
    Stochastic Optimization and Risk
    Bring your entire toolkit to bear on the case history from Lecture 23, using stochastic optimization to take the full measure of your competitors for the building project. With this closing problem, you'll see how combining predictive analytics and optimization can help you stay one step ahead of the competition. x

Lecture Titles

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  • Downloadable PDF of the course guidebook
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  • 24 lectures on 4 DVDs
  • 208-page printed course guidebook
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Course Guidebook Details:
  • 208-page printed course guidebook
  • Equations, tables & diagrams
  • Glossary

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Your professor

Scott P. Stevens

About Your Professor

Scott P. Stevens, Ph.D.
James Madison University
Dr. Scott P. Stevens is Professor of Computer Information Systems and Management Science at James Madison University in Harrisonburg, Virginia, where he has taught since 1984. Professor Stevens holds a Ph.D. in Mathematics from The Pennsylvania State University, where he received B.S. degrees in both Mathematics and Physics and graduated first in his class in the College of Science. Honored many times over for his remarkable...
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Mathematical Decision Making: Predictive Models and Optimization is rated 4.6 out of 5 by 60.
Rated 4 out of 5 by from Excellent content I am very happy with the purchase. the only criticism that I have is that the professor speaks too fast for me.
Date published: 2020-06-07
Rated 5 out of 5 by from The most practical and useful course I’ve loved the Great Courses for 10 years now. Some courses have been better than others. But this one, “Mathematical Decision Making” is the most practical and useful course I’ve taken from the Great Courses. I’m a manager and administrator, so I’m always looking for useful metrics and tools to help me evaluate my organization. (I’m a huge Lean Six Sigma fan). Well, this course is EXACTLY what I was looking for, adding more tools to my toolkit in managing my organization. Linear Programming and Linear/Multiple Regression Analysis are such examples. Moreover, the practical examples and application are FANTASTIC. Professor Stevens’ course is phenomenal and he’s a great professor. Though, I do wish the Great Courses would steer away a bit from a teleprompter kind of cadence and delivery, as it doesn’t suit Prof Stevens very well. Nevertheless, it doesn’t take away from the quality of the course. HIGHLY recommend for leaders and managers of organizations!
Date published: 2020-06-06
Rated 5 out of 5 by from Encompassing and relevant The combination of mathematics and programming/coding is the future. We need many more courese that teach this combination. Professor Stevens did an excellent job in trying to exaplain complex concepts in simple terms.
Date published: 2020-02-16
Rated 3 out of 5 by from Interesting but a bit dull. Lots of good information but I think that the material could have been presented more lively.
Date published: 2019-12-10
Rated 5 out of 5 by from Suprisingly Interesring If you have your own business, or want to start your own business, or manage a department of a large business, or you just want to evaluate possible investments, you will find this course remarkably helpful. Are you a math-phobic? Fear not! This course will show you how to get your spreadsheet to do the figuring for you, whether you use OpenOffice Calc or MS Office Excel. You can also get the spreadsheet to create graphs (yes, most of us humans process information visually more easily than in in raw numbers). If you're math-philic, be warned that this course is strongly business oriented, but it may give you ideas for a math-oriented business.
Date published: 2019-09-25
Rated 4 out of 5 by from Fairly accurate description. This course assumes a decent background in math, however, Prof. Stevens is an animated and lively speaker who has the knack of anticipating what you need to know in order to keep you on track with this content dense course. Most of the examples are geared toward business applications, but the processes can be applied to a lot of situations. I have to wonder about the comments stating that there's little math content in this course. There's plenty of math to be had including: alg. trig., statistics, logarithms (including "e"), probability theory and derivatives (calculus). Stevens thankfully spares us the tedious theoretical explanations and calculations and gets to the point. The graphics in this course are excellent and the course guide book is 255 pages long, very helpful with an excellent glossary. And who knew you could do so much with Excel. This course has a more focused objective so it's difficult to recommend it to my retired, mathophobic friends, but I, personally liked it and give it two thumbs up; it succeeds.
Date published: 2019-06-27
Rated 5 out of 5 by from Great teacher I am very happy I bought this course. It has been very valuable to me in gaining knowledge about mathematical decision making. The teacher is engaging and covered the topic in surprisingly enough depth. The instruction is clear, concise and easy to follow. I bought this course years back, but I keep watching this enjoyable course occasionally in order to refresh on the topics but more importantly to remind me about how to present a topic effectively.
Date published: 2019-04-20
Rated 3 out of 5 by from A bit disappointing I have watched the first 10 of 24 videos and was disappointed that a course billing itself as Mathematical Optimization so far contains no math.
Date published: 2018-12-24
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