Getting Started!

Edward H. KaplanWilliam 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

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!

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

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

How Do You Know If You Have Picked A Good Problem?

Does the problem satisfy Larson’s list?

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

The Value-Added Criterion

Can you point out something with an OR/MS mindset that others have yet to see?

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

Getting Started Checklist Larson’s list:

– Important to me? – Ability to contribute? – Others think it’s important?

Value-added:– OR/MS new and different?

Envision the results:– Sense possible findings?

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? – Ability to contribute? – Others think it’s important?

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

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

Tracking Needles And Clients

Needle Circulation Times

Circulation Theory: An Operational Model

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? – Ability to contribute? – Others think it’s important?

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?

Electoral College: Envision Results

Could focus on electoral college lead to different results than conventional polling approach based on the same data?

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

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Electoral College Votes

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Figure 1

Probability Distribution of Gore's Electoral College Votes (based on ARG Survey of 9/5-9/20, 2000)

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Electoral College Votes

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E(T51) = 340; = 21

2.5%ile = 296

50%ile = 340

97.5%ile = 378

Pr{Gore wins} = 99.9%

Sensitivity of Probability of Winning to Popular Vote

Gore's Popular Vote vs Pr{Gore Wins}

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How Many Samples?

Optimal State-Specific Sample Sizes

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n = 2000

Bioterror How should we prepare now for

possible bioterror attacks (e.g. anthrax, smallpox)?

Larson’s list:– Important to me? – Ability to contribute? – Others think it’s important?

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

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)

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!

IndexRemaining Infectious Period Index Case Detection

Contact Vaccine Sensitive Period Contact Detection -- Too Late!

Smallpox: Contact Tracing or Mass Vaccination?

Favor MV for any R0 > 2

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Initial attack size (I(0))

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rod

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MV optimal

TV optimal

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

Aggregated Queue Dynamics: Mass Service Policy

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

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? – Ability to contribute? – Others think it’s important?

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

Envision Results: March Madness

For the same tournament, should get different picks for different pools!

Maybe with the model I could even win sometime!

Optimizing in Real Office Pools

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2000 NCAA Tournament Results

So, Did I Make Any Money?

Tactical prevention ofsuicide bombings in Israel

What combination of tactics prevents suicide bombings?– focus on Israel, 2001-2003

Larson’s list:– Important to me? – Ability to contribute? – Others think it’s important?

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)

Location/Type Deaths

Gaza (all) 73

West Bank (all) 240

Israel (suicide bombings)

471

Israel (all other types) 94

Total 878

Source: International Policy Institute for Counter-Terrorism, Herzliya, Israel http://www.ict.org.il/

Suicide Bombings In Israel

Terrorist Group # Suicide Bombings in

2001-2003

Israelis

Killed

Hamas 32 286

Islamic Jihad 25 81

Al Aqsa Martyrs 24 91

Pop Front Lib Pal 4 13

All Groups 85 471

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?

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?

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

Model Schematic

Launches

Preventive Actions

Hits

Stop?

Intercepts

Suicide Bombings

Base Rate

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

Daily Attack Rate

s*

Signal Value (s)

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Hazard Without Hits

Hazard With Hits

Intercept Probability Increases With Expected Suicide Bombings

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On-Target Hit-Dependent vs Constant Recruitment Model

On-target (red) versus constant (blue)

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Cumulative Suicide Bombing Launches

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Getting Started Checklist Larson’s list:

– Important to me? – Ability to contribute? – Others think it’s important?

Value-added:– OR/MS new and different?

Envision the results:– Sense possible findings?

One Last Thing... Having spent all this time discussing how

to get started...

Now it’s time to quit!