Mathematical Decision Making: Predictive Models and Optimization

Overview

Handle complex decisions with ease and confidence using powerful mathematical concepts in this course taught by an award-winning mathematician. “Mathematical Decision Making: Predictive Models and Optimization” provides tools to navigate the world of data-driven choices across various fields.

Course Instructor

The course is led by Professor Scott Stevens of James Madison University, who explains advanced techniques in mathematical decision-making that can be applied in real-world scenarios.

Video Lessons

1. The Operations Research Superhighway
   • Duration: 33 min
   • Description: Introduction to operations research and predictive analytics, including historical context and major concepts.

2. Forecasting with Simple Linear Regression
   • Duration: 32 min
   • Description: Analyze relationships using linear regression, exemplified by predicting waiting times.

• Nonlinear Trends and Multiple Regression
  • Duration: 32 min
  • Description: Explore complexities like nonlinear functions and multiple inputs in regression analysis.

4. Time Series Forecasting
   • Duration: 32 min
   • Description: Delve into time series forecasting using U.S. housing starts as an example.

5. Data Mining-Exploration and Prediction
   • Duration: 32 min
   • Description: Investigate data mining techniques for classification and prediction using real-world examples.

6. Data Mining for Affinity and Clustering
   • Duration: 30 min
   • Description: Learn about affinity analysis and clustering methods, applied in recommendation systems.

7. Optimization-Goals, Decisions, and Constraints
   • Duration: 29 min
   • Description: Understand optimization principles and model problems in various fields.

8. Linear Programming and Optimal Network Flow
   • Duration: 32 min
   • Description: Discuss linear programming methods for optimal decision-making in logistics.

• Scheduling and Multiperiod Planning
  • Duration: 29 min
  • Description: Explore multiperiod planning while applying learned optimization techniques.

• Visualizing Solutions to Linear Programs
  • Duration: 31 min
  • Description: Learn to visualize solutions for optimization problems using graphs.

11. Solving Linear Programs in a Spreadsheet
    • Duration: 31 min
    • Description: Implement the simplex algorithm for solving linear programming using spreadsheets.

12. Sensitivity Analysis-Trust the Answer?
    • Duration: 31 min
    • Description: Investigate sensitivity analysis and its importance in understanding optimization results.

13. Integer Programming-All or Nothing
    • Duration: 31 min
    • Description: Study the challenges of integer programming and its applications in decision-making.

14. Where Is the Efficiency Frontier?
    • Duration: 32 min
    • Description: Analyze the efficiency of operations and how to compare productivity across sectors.

15. Programs with Multiple Goals
    • Duration: 30 min
    • Description: Evaluate solutions based on multiple objectives in the decision-making process.

16. Optimization in a Nonlinear Landscape
    • Duration: 31 min
    • Description: Explore nonlinear programming challenges and solutions outside linear assumptions.

17. Nonlinear Models-Best Location, Best Pricing
    • Duration: 33 min
    • Description: Solve optimization problems for selecting best locations and pricing strategies.

18. Randomness, Probability, and Expectation
    • Duration: 29 min
    • Description: Understand how probability theories guide decision-making under uncertainty.

19. Decision Trees-Which Scenario Is Best?
    • Duration: 31 min
    • Description: Utilize decision trees and probability analysis for optimal decision-making scenarios.

20. Bayesian Analysis of New Information
    • Duration: 31 min
    • Description: Study Bayesian statistics and how it adjusts predictions based on new data.

21. Markov Models-How a Random Walk Evolves
    • Duration: 31 min
    • Description: Learn about Markov analysis in predicting transitions in various contexts.

22. Queuing-Why Waiting Lines Work or Fail
    • Duration: 30 min
    • Description: Analyze queues and how changes in systems can improve efficiency.

• Monte Carlo Simulation for a Better Job Bid
  • Duration: 30 min
  • Description: Understand how simulations model complex variables to optimize decision-making.

24. Stochastic Optimization and Risk
    • Duration: 32 min
    • Description: Conclude by applying stochastic optimization to enhance risk management strategies.