Mathematical Decision Making: Predictive Models and Optimization

Handle complex decisions with ease and confidence using powerful mathematical concept in this course taught by an award-winning mathematician.
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Researchers have perfected mathematical techniques for predicting the best possible outcomes when faced with conflicting options. Now, all you need is a computer and spreadsheet program to harness the power of these methods for solving practical problems. Discover the endless ways in which applying quantitative methods helps problem solvers like you make better decisions in business, research, government, and beyond.


Scott P. Stevens
Scott P. Stevens

If you keep your eyes and mind open, you're going to find a lot of other places that our ideas apply.


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 abilities in the classroom, Professor Stevens has been a recipient of the Carl Harter Award, his university's highest teaching award; been named the outstanding graduate teacher in JMU's M.B.A. program; and has on five occasions been selected by students as the outstanding teacher in JMU's undergraduate business program, the first teacher to be so honored. A frequent consultant in the business arena, Professor Stevens has been published in a broad variety of academic and professional journals, writing or collaborating on subjects as varied as neural network prediction of survival in blunt-injured trauma patients; the effect of private school competition on public schools; standards of ethical computer usage in different countries; automatic data collection in business; and optimization of the purchase, transportation, and deliverability of natural gas from the Gulf of Mexico.

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The Operations Research Superhighway

01: 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.

33 min
Forecasting with Simple Linear Regression

02: 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....

32 min
Nonlinear Trends and Multiple Regression

03: 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....

32 min
Time Series Forecasting

04: 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....

32 min
Data Mining-Exploration and Prediction

05: 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....

32 min
Data Mining for Affinity and Clustering

06: 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....

30 min
Optimization-Goals, Decisions, and Constraints

07: 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. ...

29 min
Linear Programming and Optimal Network Flow

08: 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....

32 min
Scheduling and Multiperiod Planning

09: 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....

29 min
Visualizing Solutions to Linear Programs

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....

31 min
Solving Linear Programs in a Spreadsheet

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!...

31 min
Sensitivity Analysis-Trust the Answer?

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....

31 min
Integer Programming-All or Nothing

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....

31 min
Where Is the Efficiency Frontier?

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....

32 min
Programs with Multiple Goals

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....

30 min
Optimization in a Nonlinear Landscape

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....

31 min
Nonlinear Models-Best Location, Best Pricing

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....

33 min
Randomness, Probability, and Expectation

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."...

32 min
Decision Trees-Which Scenario Is Best?

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....

31 min
Bayesian Analysis of New Information

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 itthis simple but powerful idea serves as a corrective to bad decision making in many spheres....

31 min
Markov Models-How a Random Walk Evolves

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....

31 min
Queuing-Why Waiting Lines Work or Fail

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....

30 min
Monte Carlo Simulation for a Better Job Bid

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....

30 min
Stochastic Optimization and Risk

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....

32 min