Mathematical Decision Making: Predictive Models and Optimization

Course Description:
Master the tools of predictive analytics and optimization to solve real-world problems with confidence. This course, taught by an award-winning mathematician, guides you through regression, time series forecasting, data mining, optimization models, decision trees, Bayesian analysis, simulation, and more. Gain the mathematical insight to improve decision making in business, finance, technology, and everyday life.

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Course Outline

01: The Operations Research Superhighway
Survey the history and applications of operations research and predictive analytics, from WWII to the modern computer era.
33 min

02: Forecasting with Simple Linear Regression
Use linear regression to predict outcomes, such as geyser eruptions, by analyzing historical patterns.
32 min

03: Nonlinear Trends and Multiple Regression
Tackle complex regression problems with transformations and multiple inputs using graphical and spreadsheet methods.
32 min

04: Time Series Forecasting
Forecast future values by analyzing historical data trends and seasonal cycles, such as U.S. housing starts.
32 min

05: Data Mining—Exploration and Prediction
Apply classification trees and predictive models to massive datasets, with examples like spam filtering.
32 min

06: Data Mining for Affinity and Clustering
Discover association rules and clustering techniques for pattern recognition, as used by Pandora Radio.
30 min

07: Optimization—Goals, Decisions, and Constraints
Model optimization problems by defining objectives, variables, and constraints, with examples from airlines.
29 min

08: Linear Programming and Optimal Network Flow
Explore how linear programming solves large-scale logistical problems, such as railroad car distribution.
32 min

09: Scheduling and Multiperiod Planning
Plan inventory, activities, and investments across multiple time periods using optimization tools.
29 min

10: Visualizing Solutions to Linear Programs
See how graphical methods reveal optimal solutions, illustrated with personal finance and investments.
31 min

11: Solving Linear Programs in a Spreadsheet
Use the simplex algorithm in Excel or Calc to solve linear programs efficiently.
31 min

12: Sensitivity Analysis—Trust the Answer?
Evaluate how robust optimal solutions are by testing parameter changes and tipping points.
31 min

13: Integer Programming—All or Nothing
Handle problems where variables must be integers, from production units to facility counts.
31 min

14: Where Is the Efficiency Frontier?
Measure productivity and efficiency with data envelopment analysis in nonprofits and government.
32 min

15: Programs with Multiple Goals
Balance competing objectives using weighted averages, penalties, and prioritization strategies.
30 min

16: Optimization in a Nonlinear Landscape
Transition from linear to nonlinear optimization with intuitive problem-solving techniques.
31 min

17: Nonlinear Models—Best Location, Best Pricing
Solve practical nonlinear problems like hub location and optimal retail pricing.
33 min

18: Randomness, Probability, and Expectation
Apply probability to decision making in uncertain environments, from investments to waiting lines.
32 min

19: Decision Trees—Which Scenario Is Best?
Use decision trees to map uncertain outcomes and guide corporate strategy.
31 min

20: Bayesian Analysis of New Information
Update probabilities with new data using Bayes’s theorem, applied to real-world searches.
31 min

21: Markov Models—How a Random Walk Evolves
Predict future states of random systems using Markov analysis, applied to business survival.
31 min

22: Queuing—Why Waiting Lines Work or Fail
Study random arrivals and how small adjustments reduce waiting times in service systems.
30 min

23: Monte Carlo Simulation for a Better Job Bid
Model competitive situations with simulation to optimize strategies, such as project bids.
30 min

24: Stochastic Optimization and Risk
Combine analytics and optimization to evaluate risk and outperform competitors.
32 min