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Statistics 802 Quantitative Methods Spring 2007

Statistics 802 Quantitative Methods Spring 2007. Final Thoughts. Goal (Syllabus). To provide students with a description of the advanced quantitative models which are routinely used for managerial decision making. Goal (Syllabus).

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Statistics 802 Quantitative Methods Spring 2007

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  1. Statistics 802 Quantitative Methods Spring 2007 Final Thoughts

  2. Goal (Syllabus) • To provide students with a description of the advanced quantitative models which are routinely used for managerial decision making

  3. Goal (Syllabus) • To provide students with examples of the application of these models • Interfaces • Forecasting Project • Videos (web problem) • AHP Guest Lecture

  4. Companies in Interfaces presentations

  5. Samples of Models(From Lectures, Text, Homework and Exams) • Market share • Brand loyalty (Markov chain) • Advertising (Game) • Scheduling • 1 to 1 (Assignment) • 1 or many to many • Transportation • Integer Program (Set covering)

  6. Samples of Models(From Lectures, Text, Homework and Exams) • Advertising • Media selection (linear programming) • Competitive • Game/Market Share/$ • Game/Price Guarantees – Guarantees guarantee HIGH prices!

  7. Samples of ModelsPrice Guarantees

  8. Samples of ModelsPrice Guarantees

  9. Samples of Models • Inventory planning • Newsboy problem (single period inventory model) • Decision table (in notes, we did not get to it) • Simulation (in notes, we did not get to it) • (we did more on decision trees than I have done in the past) • Production planning - linear programming • Bidding • Simulation (in notes, we did not get to it) • (we did the in-class simulation exercise) • Capital budgeting - integer program

  10. Samples of Models • Enrollment management/forecasting - Markov chain • Public services • Mail delivery, street cleaning/plowing • School bussing – transportation • Finance/accounting • Cost/volume - simulation • Portfolio selection – linear/integer programming

  11. Samples of Models • Production • Product mix/resource allocation - linear programming • Blending - linear programming • Employee scheduling- related problems • Workforce scheduling • Workforce training • Assignment • Health • Diet problem

  12. Samples of Models • Location • Game theory • Transportation • Agricultural planning • Noncompetitive - linear programming • Competitive - non zero sum game

  13. Bonus Models - Sports • Baseball • Assignment of pitchers - linear programming • Football • Fourth and goal - decision tree • Optimal sequential decisions and the content of the fourth-and • Desperation - decision analysis - maximax • Ice hockey • Pull the goalie sooner • Desperation - decision analysis - maximax • Basketball • Desperation - decision analysis - maximax

  14. ModelsIn Some Cases There Is One Specific Goal • Linear programming • Transportation • Assignment • Integer programming

  15. ModelsIn Some Cases There Is One Specific Goal • Networks • Spanning trees • Shortest path • Maximal flow • Traveling salesperson problem • Chinese postman problem • Analytic Hierarchy Process (AHP)

  16. ModelsIn Other Cases There May Be More Than One Specific Goal/Measurement • Decision analysis • Expected (monetary) value • Maximin (conservative, pessimistic) • Maximax (optimistic, desperate) • Maximin regret (conservative, pessimistic) • Forecasting • Error measurement (technique evaluation) • Mean absolute deviation (MAD) • Mean squared error (standard error) • Mean absolute percent error (MAPE)

  17. Prescriptive Vs. Descriptive Models • Some models PRESCRIBE what action to take • Linear programming based • Transportation, assignment, integer programming, goal programming, game theory • Network based • Shortest path, maximal flow, minimum spanning tree, traveling salesperson, Chinese postman • AHP – sort of • Zero or constant sum games • Flip a coin!!! –

  18. Prescriptive Vs. Descriptive Models • Some models DESCRIBE the consequences of actions taken • Decision analysis • Forecasting • Markov chains • Simulation • Non zero sum games • Matching lowest price leads to high prices ! • Competition leads to low prices

  19. Probabilistic vs. Deterministic Models • Some models include probabilities • Markov Chains • Decision Analysis • Decision tables • Decision trees • Games • Forecasting

  20. Probabilistic vs. Deterministic Models • Other models are completely deterministic • Linear programming • Transportation • Assignment • Integer programming • Networks • AHP

  21. Long Run • Some models/measures require steady state (long run) in order for the results to be useful • Games • Decision analysis • Expected value • Expected value of perfect information

  22. A Notion of Fair • Game videos • Splitting a piece of cake • In two • Statistician • Game theorist • In more than two • Team work division • Splitting work for projects

  23. ModelsTradeoffs • Ease of use vs. flexibility • Transportation (easier) vs. LP (more flexible) • Decision table (easier) vs. Decision tree (more flexible) • QM for windows (easier) vs. Excel (more flexible) • Model correctness vs. solvability • Integer programming/linear programming

  24. ModelsTradeoffs • Model exactness vs. Flexibility • Analytical method vs. Simulation • Development cost/time vs. Exactness • Analytical method vs. Simulation

  25. Model Sensitivity • Forecasting & simulation • Standard error/standard deviation • Linear programming • Dual values/ranging table • Decision tables/decision trees • Data table (letting probabilities vary)

  26. Data Table With a Decision Tree

  27. Solving Backwards • Decision tree • Game tree (sequential decisions) • Let’s make a deal

  28. Models – Number of Decision Makers • One • Most models • More than one • Games • Let’s make a deal !!

  29. Excel Addins • Solver • Linear & integer programs • Networks (shortest path & maximal flow) • Zero sum games • Decision trees • Crystal ball • Simulation/risk analysis

  30. Excel Tools • Data analysis • Forecasting • Simulation • Can be used for generating random numbers • Scenarios • Data tables • Simulation • Decision tables • Decision trees

  31. Computer Skills • Microsoft office • Word • Excel • PowerPoint • Blackboard • Listserv • Software • Download? • Installation

  32. Less important computer skills (but skills nonetheless) • QM (POM-QM) for Windows • Will be used in MSOM 806 – Operations Mgt in Fall 2006 • Excel 802 • Available for use in MSOM806

  33. SURVEY/EVALUATION RESULTSCLASS OF 2008

  34. Consistency • Note the consistency between your evaluations and those of the previous 2 classes!!

  35. Survey Results – ForecastingClass of 2008/2007/2006 • Workload • Too much time – 2/1/5 • Just right – 22/17/18 • Too little time – 2/0/0 • Value • High – 16/18/17 • Medium – 8/1/6 • Low – 0/0/0 • Conclusion: keep as a requirement

  36. Interfaces presentations • Workload • Too much time – 2/1/2 • Just right – 23/18/20 • Too little time – 1/0/1 • Value of reading; listening • High – 14;10 /10;6 /7; 6 • Medium – 10;10 /7;6 /14; 11 • Low – 1;2 /1;1 /2; 1

  37. Interfaces presentations • Interfaces Question 4 • Continue as is – 2/2/17 • Discontinue – 20/10/1 • Power point – 1//10 • Conclusion: drop the Interfaces assignment • Bad news – will lose flavor of applications and large $ savings • Good news – more time for lecture in class • Comment – I don’t understand answer to this vis-à-vis previous answers

  38. LP interpretation - self • Workload • Too much time – 0/0/2 • Just right – 26/18/20 • Too little time –0/0/0 • Value • High – 17/13/14 • Medium – 6/6/8 • Low – 3/0/0 • Conclusion: Keep as a requirement

  39. LP interpretations - team • Workload • Too much time – 1/1/7 • Just right – 23/17/16 • Too little time – 2/0/0 • Value • High – 13/11/12 • Medium – 9/5/8 • Low – 3/3/3 • Conclusion: Keep as a requirement

  40. Decision tree (team) • Workload • Too much time – 4 • Just right – 22 • Too little time – 0 • Value • High – 15 • Medium – 9 • Low – 1 • Conclusion: Keep as a requirement • (keep anyway since it will be used in Finance)

  41. Simulation (team) in class • Workload • Too much time – 1 • Just right – 8 • Too little time – 17 • Value • High – 10 • Medium – 4 • Low – 12 • Conclusion: Keep as a requirement but do it outside of class as originally planned • Note: Simulation will be used in Finance in fall

  42. Group Take home exam • Workload • Too much time – 3/2/6 • Just right – 23/16/17 • Too little time – 0/0/0 • Value • High – 22/16/21 • Medium – 3/3/2 • Low – 1/0/0 • Conclusion: Keep as a requirement

  43. Homework/Exam • Workload • Too much time – 4/2/14 • Just right – 17/12/8 • Too little time – 5/4/1 • Value • High – 15/12/14 • Medium – 11/7/7 • Low – 0/0/2 • Conclusion: Keep as a requirement

  44. Guest Lecture • Repeat next year – 22/13/13 • Do not repeat – 3/6/9 • Conclusion – repeat next year!

  45. Overall Course Workload • Compared to Econ, Elective • Above average – 11/7/15 • Average – 15/11/8 • Below average – 0/0/0 • Compared to Stat 800 • Higher – 14/3/6 • Same – 9/14/16 • Lower – 3/1/1 • Conclusion: Workload is slightly higher than other comparable courses; needs slight reduction which may happen with dropping of Interfaces assignment

  46. Videos – sorted by score – Cl 2008

  47. Video ratings – comparing last 4 years

  48. THE FINAL EXAM & GRADES • Howard, now is the time to return the exams!

  49. Final Exam Statistics

  50. Final exam curved as if base was 100. E.g., a raw score of 90/120 was treated as a score of 90/100 or 90% Student Grade Sheet

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