1.1 Your Instructor

linkedin

email: robert_b@payap.ac.th
Office: PC314 (Office hrs by appointment)

2.1 Key aspects of a good decision

• Accomplishes your goal
• Small footprint on others and the environment
• Decision based on careful consideration of the context
• Risks were minimized
• Effective, efficient execution of a plan

2.2 Consequences of a bad decision

• Goal not attained
• Loss of resources, time, even life
• Outcome adversely impacts others, careers

2.3 Steps to Good Decision making

• Step 1: Identify Goal
• Step 2: Weigh options
• Step 3: Review consequences
• Step 4: Choose the most appropriate option
• Step 5: Evaluate the Decision

2.4 So Where does math come in?

• Step 1: Identify Goal: popularity, safety, risks
• Step 2: Weigh options: costs, risks
• Step 3: Review consequences: probability of success/failure, expected cost/benefits
• Step 4: Choose the most appropriate option
• Step 5: Evaluate the Decision

3.1 Classify the problem.

• Is it generic?
• Is it exceptional and unique?
• Is it the first manifestation of a new genus and has no previous rules?

3.2 Define the problem.

• What are we dealing with?
• What are the context and parameters?

3.3 Explore potential solutions to the problem.

• What are the “boundary conditions”?

3.4 Evaluate options

• Decide on what is “right,” rather than what is acceptable
• Check that the boundary conditions are met
• Determine how to fully satisfy the specifications with minimal compromises, adaptations, and concessions

3.5 Build an action plan.

• What does the action commitment have to be?
• Who has to know about it?
• Who is involved with its execution?

3.6 Evaluate the outcome of the decision

• Test the validity and effectiveness of the decision against the actual course of events.
• How is the decision being carried out?
• Are the assumptions on which it is based appropriate or obsolete?

4.1 Additional information

4.2 Normalized data

5.1 Details

• Goal: develop a fire evacuation plan to rally in front of the school in minimal time

• 500 primary students in the school

5.2 Your task

• Assemble in your group
• Develop a model to understand the problem
• Work together to calculate the minimum time to get everyone out of the building and gathered at the rally point
• Calculate the numbers through each exit that is required to achieve this time
• Prepare a short report to explain your method and results

5.3 Group Presentations

5.4 Key Time Calculations: Based on Door assignments

\[t_{arrv} = t_{2exit} + t_{thruexit} + t_{walking}\]

5.5 Math model

\[\eqalign{ t_f &= 10 + \frac{60F}{60} +20 &= 30 + F\\ t_s &= 20 + \frac{60S}{20} +80 &= 100 + 3S\\ t_b &= 10 + \frac{60B}{30} +120 &= 130 + 2B\\ \\ t_f &= t_s = t_b\\ 500 &= F + S + B\\ }\]

5.6 Calculations: S

\[\eqalign{ 30 + F &= 100 + 3S\\ \color{red}{-100} + 30 + F &= 100 + 3S + \color{red}{-100}\\ \color{red}{\frac{1}{3}}\times(-70 + F) &= 3S\times\color{red}{\frac{1}{3}}\\ \frac{F - 70}{3} &= S\\ }\]

5.7 Calculation: B

\[\eqalign{ 30 + F &= 130 + 2B\\ \color{red}{-130} + 30 + F &= 130 + 2B+ \color{red}{-130}\\ \color{red}{-130} \times \left(-100 + F\right) &= 2B\times\color{red}{\frac{1}{2}}\\ \frac{F - 100}{2} &= B\\ }\]

5.8 Calculations

5.9 Calculations

\[\eqalign{ F &= 312.7\\ S &= \frac{T_f - 70}{3} &= \frac{312.7-70}{3} &= \frac{242.7}{3} &= 80.9\\ B &= \frac{T_f - 100}{2} &= \frac{312.7-100}{3} &= \frac{212.7}{2} &= 106.35\\}\]

\[total = 313+ 81 +106 = 500\]

\[t_s = 30 + F = 343\ sec = 5 min,\ 43\ sec\]

5.10 Simulation

5.11 Comparison of all possibilities

5.12 Extreme cases (Single exit used)

\[time = t_{delay} + t_{doorway} + t_{walkaway}\]

\[time_{front} = 10 + 500 + 20 = 530\ secs\] \[time_{side} = 20 + 1500 + 80 = 1600\ secs\]

\[time_{back} = 20 + 1000 + 120 = 1140\ secs\]

5.13 Solver Template

5.14 Solver Solution

5.15 What could go wrong?

• Exits could become become in accessible.
• Children could wander off in transit to the rally point.
• People might not follow the plan.
• The crisis disaster might occur faster than the response time.
• The fire alarm might not work when it is needed

6.1 Intended course outcomes

6.2 Data analytics

6.3 Modules

1. Course orientation
2. Practical Mathematics for tidying data
3. Statistical analysis for decision making
4. Logical Data Analysis
5. Midterm
6. Probability for making Decision
7. Decision making
8. Final exam

6.4 Textbooks and main documents

• Hadley Wickham, Garrett Grolemund, 2017. R for Data Science: Import, tidy, transform, visualize and model data. O’Reilly Media

• Eric Denardo, 2005. The Science of Decision Making: A Problem-based approach using Excel. John Wiley

• Barbara Illowsky, Susan Dean, 2022. Introduction to Statistics. Open Stax Foundation.3rd edition. https://openstax.org/details/books/introductory-statistics

6.5 Documents and information for important

• Batzinger, 2023. Slides and Activity Worksheet Sheets for GE193

• WorldData.AI,2022. World Data curated datasets for AI and data science. http://worlddata.ai

• Kaggle, 2022. Kaggle datasets. https://www.kaggle.com

6.6 Documents and guidebooks

• Douglas C. Montgomery, 2017. Design and Analysis of Experiments. John Wiley & Sons, 9th edition.

• Nathan Taback, 2022. Design and Analysis of Experiments and Observational Studies Using R. CRC Press

6.7 Decision: Software to be used in this course