Getting Started!

1. Getting Started! Edward H. Kaplan William N. and Marie A. Beach Professor of Management Sciences, Yale School of Management Professor of Public Health, Yale School of Medicine Professor of Engineering, Yale Faculty of Engineering

2. Getting Started! • What makes a problem worth working on? • Scholars of creativity note a simple bias • typical researcher thinks his/her problem is the most interesting/important thing there is • Of course, something is wrong here... • My problems are the most important!

3. Where Do Good Problems Come From? • The world is full of good problems! • Read the newspaper! Surf the web! • The trick is to learn how to recognize and structure them, since they often do not appear pre-formulated • Think of the difference between being able to answer all of the questions in an assignment, and creating the questions in the assignment

4. Where Have Some Of My Best Problems Come From? • Public housing: classmate’s boyfriend was planning liason to tenant’s association • IVF policy: my wife’s doctors • Needle exchange: Yale biology prof who also chaired mayor’s task force on AIDS • Electoral college: sidewalk discussion with Arnie Barnett • March Madness: I kept losing office pools! • Bioterror: Heart-to-heart with Larry Wein about 9/11 and what OR/MS could do, plus an inquiry from NIH asking for help

5. How Do You Know If You Have Picked A Good Problem? Does the problem satisfy Larson’s list?

6. Larson’s List: Three Rules For Picking A Good Problem • You have to think your problem is interesting and important; otherwise you won’t get excited about it • You need to have the ability to do something about it • Someone besides yourself, and preferably many such people, also think the problem is important

7. The Value-Added Criterion • Can you point out something with an OR/MS mindset that others have yet to see?

8. That Vision Thing... • Can you sense the nature of your results? • This is not the same as pre-determining your results, nor do I mean reverse-engineering an analysis to meet desired conclusions

9. Getting Started Checklist • Larson’s list: • Important to me? ü • Ability to contribute? ü • Others think it’s important? ü • Value-added: • OR/MS new and different?ü • Envision the results: • Sense possible findings? ü

10. Needle Exchange • Intervention designed to prevent HIV transmission via needle-sharing among drug injectors • pre-1990 studies were all based on participants’ self-reported behavioral accounts • Larson’s list: • Important to me? ü • Ability to contribute? ü • Others think it’s important? ü

11. Needle Exchange: Value-Added • OR approach: let the needles do the talking! • focus on the behavior of the needles instead of the people • design needle-tracking system akin to inventory tracking • focus on how needle exchange operations change the transmission of HIV, switching evaluation focus from changes in behavior to changes in HIV incidence

12. Needle Exchange: Envision Results • needle exchange reduces needle circulation times • as a consequence, needles share fewer people • as a further consequence, fraction of needles that are infected should decline • easy to capture this logic with simple model • what was not so easy was to verify it with actual data from the needle exchange program

13. Tracking Needles And Clients

14. Needle Circulation Times

15. Circulation Theory: An Operational Model

16. Electoral College • Question: given polling data, predict the probability that a given candidate will win the presidency • recognize how the electoral system really works! • Larson’s list: • Important to me? ü • Ability to contribute? ü • Others think it’s important? ü

17. Electoral College: Value-Added • OR approach: what is the probability distribution of electoral college votes? • Pr{Win} = Pr{Get > 269 Electoral Votes} • OR approach: how many likely voters should be surveyed from each state to best estimate the electoral college distribution? • how large a sample is needed overall to achieve sufficient accuracy?

18. Electoral College: Envision Results • Could focus on electoral college lead to different results than conventional polling approach based on the same data?

19. Electoral College Distribution:Jan-Mar 2000 EC Votes for Gore

20. Figure 1 E(T51) = 340; s = 21 2.5%ile = 296 50%ile = 340 97.5%ile = 378 Pr{Gore wins} = 99.9%

21. Sensitivity of Probability of Winning to Popular Vote

22. How Many Samples?

23. Bioterror • How should we prepare now for possible bioterror attacks (e.g. anthrax, smallpox)? • Larson’s list: • Important to me? ü • Ability to contribute? ü • Others think it’s important? ü

26. Bioterror: Value-Added • OR approach: while epidemiology worries about what infectious agents do to us, bioterror response logistics worries about what we can do to deliberately released infectious agents • logistics matters just as much as epidemiology! • OR approach: the idea is not to choose a policy for the most-likely scenario; rather the idea is to choose policies that yield good results robustly across many scenarios

27. Bioterror: Envision Results • Casualties depend on operations • smallpox: how quickly can you vaccinate; how accurately can you trace contacts; how effectively can you isolate cases, etc. • anthrax: how quickly can you dispense antibiotics; what should the queueing discipline be for distributing antibiotics, and for hospital care • smallpox and anthrax: how quickly can you recognize an attack; are costly detection technologies beneficial (e.g. syndromic surveillance, biosensors)

28. Contact Tracing:The Race To Trace!! • “Contact identification is the most urgent task when investigating smallpox cases since vaccination of close contacts as soon as possible following exposure but preferably within 3-4 days may prevent or modify disease. This was the successful strategy used for the global eradication of smallpox.” -CDC Interim Plan, Guide A, p. A-10 • Our model estimates the probability of finding a contact in time; for contact tracing to be effective, the race to trace must be won repeatedly!

29. Smallpox: Contact Tracing or Mass Vaccination? • Favor MV for any R0 > 2

30. Wein, Craft and Kaplan Anthrax Model (PNAS, 2003)

31. Aggregated Queue Dynamics: Mass Service Policy

32. Sensitivity to Total Time to Distribute Antibiotics • Lose about 10,000 lives per day over pre-attack distribution of antibiotics for first two days, gets worse after that

33. March Madness • Hey – I’m from Connecticut!! • and I always was pretty lousy at filling out the bracket for the office pools • Larson’s list: • Important to me? üüü • Ability to contribute? ü • Others think it’s important? 

34. March Madness: Value-Added • OR approach: in contrast to typical “greedy algorithm” approach of filling out bracket from start to finish, dynamic programming considers downstream consequences of earlier decisions, enabling optimal tradeoffs • this is especially valuable in pools with complicated rules awarding upset points, or points for correct picks further into the tournament

35. Envision Results: March Madness • For the same tournament, should get different picks for different pools! • Maybe with the model I could even win sometime!            

36. Optimizing in Real Office Pools

37. 2000 NCAA Tournament Results

38. So, Did I Make Any Money?

39. Tactical prevention ofsuicide bombings in Israel • What combination of tactics prevents suicide bombings? • focus on Israel, 2001-2003 • Larson’s list: • Important to me? üüü • Ability to contribute? ü • Others think it’s important? üüü

40. Suicide Bombings • Suicide bombings deliberately targeting Israeli civilians inside the “Green Line” caused 471 deaths during 2001-2003, more than half of all Israeli fatalities (including deaths in the West Bank and Gaza) Source: International Policy Institute for Counter-Terrorism, Herzliya, Israel http://www.ict.org.il/

41. Suicide Bombings In Israel

42. Suicide Bombing: Value-Added • Many studies of suicide bombers, and suicide bombings • typical database: for every suicide bombing, 100 different variables ranging from fatalities to number of bomber siblings to square inches of newsprint devoted to coverage of event • No studies of suicide bombing hazard rate • today was a special day – there was not a suicide bombing – how come??? • Where and when do terrorists attack given the deployment of defensive measures over time and space?

43. Suicide Bombing: Envision the Results • What is the marginal impact of a preventive action on future suicide bombing attempts? • which actions are most effective? • note: some actions could lead to more attempts • How do defensive measures tighten in response to anticipated attacks?

44. Tactical Israeli Countermeasures Include • Preventive military operations to destroy bomb-making “laboratories” and arrest terrorists if possible, kill if necessary • Targeted hits on “ticking bombs” and senior terrorist commanders • Border closures • En-route interception of suicide bombers (road blocks, terror alerts, hot pursuit) • Security fence

45. Model Schematic Preventive Actions Intercepts Launches Base Rate Stop? Suicide Bombings Hits

46. Is Hit-Dependence Artifactual? • Suppose that there is an intelligence signal s regarding suicide bombings, that a hit is ordered if s > s*, and hits are effective • Then one would expect elevated suicide bombing rates following hits due to timing

47. Intercept Probability Increases With Expected Suicide Bombings

48. On-Target Hit-Dependent vs Constant Recruitment Model • On-target (red) versus constant (blue)

49. On-Target Hit-Dependent Model

50. Getting Started Checklist • Larson’s list: • Important to me? ü • Ability to contribute? ü • Others think it’s important? ü • Value-added: • OR/MS new and different?ü • Envision the results: • Sense possible findings? ü