Introduction to Data Analysis and Decision Making

1. Introduction to Data Analysis and Decision Making The book combines topics from (1) statistics and (2) management science. Statistics is the study of data analysis, whereas management science is the study of model building, optimization, and decision making. We don’t distinguish between ‘statistics’ and ‘management science’, instead, we examine a collection of useful quantitative methods that can be used to analyze data and help make business decisions. Three themes run through the book: (1) data analysis, (2) decision making, and (3) dealing with uncertainty.The book combines topics from (1) statistics and (2) management science. Statistics is the study of data analysis, whereas management science is the study of model building, optimization, and decision making. We don’t distinguish between ‘statistics’ and ‘management science’, instead, we examine a collection of useful quantitative methods that can be used to analyze data and help make business decisions. Three themes run through the book: (1) data analysis, (2) decision making, and (3) dealing with uncertainty.

2. Data Analysis Describing data and datasets Making inferences from data and datasets Searching for relationships in data and datasets

3. Decision Making Optimization Decision analysis with uncertainty Sensitivity Analysis

4. Uncertainty Measuring uncertainty Modeling and simulation

5. What is Management Science? Logical, systematic approach to decision making using quantitative methods. Science ?Scientific methods used to solve business related problems. Goal for this class: logically approach and solve many different problems.

6. Management Science Approach to Problem Solving Observation Definition of the Problem Constructing the Model Solving the Model/problem Implementation of Solution (process is never really complete)

7. Observation Identify the problem Problem does not imply that there is something wrong with the process “Problem” could imply need for improvement

8. Definition of the Problem Clearly define problem Prevents incorrect/inappropriate solution Listing goals could be helpful

9. Constructing the Model Represents the problem in abstract form Schematic, scale, mathematical relationship between variables (equation) Ex: Income = Hours Worked * Pay

10. Components of the Model Variable/Decision Variables Independent Dependent Objective Function Parameter Constraints

11. Model Solution Same as solving the problem: Ex: Z = $20X – 5X subject to 4X = 100 Solution: X=25 ?Z = $375

12. Implementation of Solution Solution aids us in making a decision but does not constitute the actual decision making.

13. Example Blue Ridge Hot Tubs manufactures and sell hot tubs. The company needs to decide how many hot tubs to produce during the next production cycle. The company buys prefabricated fiberglass hot tub shells from a local supplier and adds pump and tubing to the shells to create his hot tubs. The company has 200 pumps available. Each hot tub requires 9 hours of labor. The company expects to have 1,566 production labor hours during the next production cycle. A profit of $350 will be earned on each hot tub sold. The company is confident that all of the hot tubs will sell. The question is, how many should be produced if the company wants to maximize profits during the next production cycle?

14. Msci Approach to Problem Solving Problem: Determine # of hot tubs to produce Definition: Maximize profit within the constraints of the labor hours and materials available Model: Max Z = $350X subject to 9X ? 1,566 labor hours Solution: X = 174; Z = 350(174) = $60,900 Implementation: Recommend making 174 hot tubs

15. A Generic Mathematical Model