the secretary problem is a useful model for selling a house

Realtors sometimes think that the optimal solution is to convince their clients to accept the first offer made on their house. The marginal increase in the realtor’s fee is tiny if the sellers wait to get a small increase in the selling price (a 3% commission on the extra $2000 that the sellers are holding out for is a measly $60. The realtor may invest more than $60 to better market the house while waiting for a slightly better offer to arrive. See the video from the Freakonomics documentary below for more on this subject.

We ended up using the optimal Secretary Problem policy to sell our house. It wasn’t our plan on the offset, but it’s what happened. An optimal policy to the Secretary Problem maximizes the probability of ending up with the best offer. The idea is to first estimate the number of offers you would expect to receive, at least in the timeframe that you have to sell a house; let’s call this n. Then you observe and reject the first n/e offers. After that, you accept the first offer that is the best you’ve seen so far. I thought n would be small (2-3), but there was a lot of traffic in our house and I had to increase my estimate of n to maybe 6.

The first person to look at our house made us an offer almost immediately. It was a good offer, but the buyer wanted to close a month earlier than we were ready, which would lead to some substantial costs on our end (not counting the stress of having to make immediate moving plans and find temporary housing). The net offer was good, but not good enough for us to sell our house. We let it go. At the time, this seemed like our n/e, which meant that we should accept the next offer that was better than our first one.

We had a second offer on our house that eventually worked its way up to match the net value of the first offer. It was too low, so we rejected it (and almost gave our realtor a heart attack in the process). We then had a third offer on the house that was not worth entertaining. Later that day, we received our fourth offer. After some negotiation, it became our best so far, and we accepted it.

It’s not often that I get to personally collect empirical evidence to validate an OR model. I’d like to say that it was fun, but it was mostly a stressful experience. I’m glad it worked out in the end. During the process, it was helpful to know that math backed us up on our offer rejections. We ended up with that extra $2000 (less $120 for both realtors).

Comment: When I say we “rejected” offers, I mean that we counter-offered with what we were willing to settle for and were turned down. Accepting/rejecting offers is a little more complicated when selling a house as compared to the secretary problem, where there is no negotiation.

Incidentally, the Wall Street Journal recommends using the Secretary Problem for finding a rental [Link].

The current state of math in the United States

I was shopping at Target and noticed a baby scale for sale for people who are unwilling or unable to do subtraction (see image below). The scale works by first weighing a person holding the baby, then weighs the person without the baby, and performs subtraction to yield the weight of the baby. Most digital scales these days are accurate enough to give a good estimate of a baby’s weight using the 2-weigh method for people who can do subtraction. The need for such a scale  reflects poorly on the state of math in the US.

I posted this to twitter [here is the thread], where it was warmly greeted, so I decided to add it to the blog to give it a more permanent location.

On the upside ,the scale was on clearance for $11.98, down from $39.99. The shelf at Target was full of these scales. Perhaps new mothers are not too tired to do subtraction after all.

Baby scale for those who are unable or unwilling to do subtraction.

things I found in my office while packing

I found a number of things in my office while packing up for UW-Madison. I officially move later this week.

Giant Illinois flag (go Illini!) and my office slinky. I’m definitely hanging up my Illinois stuff in my new office, even it upsets the Wisconsin students.

Printed announcements for my dissertation defense on April 4, 2006. Also, see the next item.

A large filing cabinet full of papers. I definitely killed a small grove of trees, potentially a small forest. It took a few days to move all of the papers out of my office. This was 1 of 3 rounds. Most of the papers were very old – from my first year or two on the job. I got better at minimizing paper as I got older.

Office bulletin board filled with PhD comics and an Onion article.

The Onion article is entitled “Mead Releases New Grad-School-Ruled Notebook:”

“We here at Mead understand that as students get older and wiser, they need notebooks with increasingly narrow lines,” Mead CEO John A. Luke told reporters.  ”How can we expect graduate students to learn to gather information and construct knowledge independently within their specialized field of study using college-ruled notebooks?” he added. “These students need a narrower-lined notebook, and at long last, they have it.”

Lots and lots of Post-It notes and paperweights. Number of times I have used paperweights to keep paper from blowing away: 0. It’s never windy in Richmond, Virginia. These might be more useful back in the Midwest.

I have emergency sunscreen within arm’s distance at all times.

Pictures drawn by my oldest daughter. This is her and me in the elevator in my old building. She drew this 5ish years ago. I also found a few outdated pictures of my kids in my office (not too outdated — all three kids are in the pictures). The background images on my computers pictures of my kids taken last month.

The giant hairy spider that lives outside my office window whom I’ve occasionally tweeted about. I probably won’t miss him.

land O links

Here are a few links:

• When is the best time to purchase airline tickets? On average, 49 days before your departure for domestic flights, 81 days for international flights.
• What day of the week is the best for purchasing airline tickets? The weekend, according to a paper published in the Journal of Economic Behavior and Organization.
• When is the optimal time to purchase concert tickets? Usually right before the concert when they may be discounted. This assumes perfect information that is free. After taking the cost of information into account, such as the cost of checking ticket prices every day, I wonder if it’s not really best to wait until the last minute. Plus, waiting to the last minute may lead to other problems, like finding a babysitter at the last minute. Good luck with that.
• American Airlines is toying with the idea of first boarding customers without bags that go into the overhead bins, thus improving efficiency at the expense of irking their elite customers. How far should the airlines go to board the plane a few minutes (seconds) earlier?
• McDonalds is going to reduce its menu of 145 items to reduce complexity and improve service.
• In Berlin, Occupy Germany is taking on Barbie and her dreamhouse:

At the final “Occupy Barbie” meeting Tuesday, Franziska Sedlak, 25, wondered why the Dreamhouse only lets girls act out careers like model and pop star, instead of jobs like engineer and mathematician.

Mattel’s Ms. Cota said the decision was one of logistics and entertainment. “Pretending to be an engineer is a hard concept for a 4- or 6-year-old to play out,” she said. She notes that the Dreamhouse has a space where children can impose their faces on outfits for Barbie’s 135 careers, including astronaut, engineer, doctor and chancellor.

• It’s the time of year for advice for graduates. Here is TIME’s Top 10 commencement addresses ever. For something more recent, here are Jason Gay’s 29 pieces of advice for college graduates. Take the link to Mary Schmich’s Wear Sunscreen column. You’ve likely heard or seen Schmich’s column – Baz Luhrmann turned it into a music video in the late 90s (wait until about 30 seconds into the video for the music to start).

queuing, cutting in line, and social justice

Page Six ran a story about wealthy Manhattanites who hire “black-market Disney guides” for $130 an hour (or $1,040 for an eight-hour day) to cut in line for the rides at Disney World. The guides are people with disabilities who, according to Disney rules, are allowed to take up to 6 people to the front of the ride lines.

At face value, this may seem like a good trade – people who pay do not have to wait in line. People who do not pay more have to wait. But of course, this is not how we really feel about queuing.

This story became popular because hiring guides with disabilities violates the social justice principle we associate with queues. First come first served, no exceptions! This is especially important since single line FIFO queues, like the ride queues at amusement parks, have the highest expectations of social justice. We are someone less concerned with grocery store lines with multiple servers and multiple lines, where a late-comer to one line can be served before someone who has been waiting longer in another line. We reluctantly accept the Law of Lines.

I blogged about the psychology of queuing long ago based on Dick Larson’s research on the intersection of operations research and psychology [Link]. Dr. Larson and his collaborators found that people are willing to wait longer on average to ensure that no one gets special treatment. Special treatment means that someone violates the first-come-first-serve queuing rule. Multiple servers with a single queue preserve social justice.

In reality, we accept many deviations from FIFO/FCFS queues. For example, frequent fliers can register with the TSA and pay an annual fee to get expedited screening at many hub airports. We accept this. Frequent fliers skipping the security queue is not unlike the wealthy people who purchase a “guide” at Disney to avoid waiting. The difference is that the TSA expedited screening is an official way for cutting in line whereas the Disney guides are working around the way the rules are intended to work (cutting via a technicality).

What are your favorite ways to avoid queuing?

 

how to use data mining and simulation to win at Jeopardy

The single most lucrative single day prize for any contestant in Jeopardy’s history was indirectly based on data mining and simulation. Roger Craig, who has a PhD in computer science, used data-mining algorithms to train himself on a database of training questions. His source data was The Jeopardy Archive, which has every question and answer from all of the Jeopardy episodes. He parsed the whole site to create one large data set composed on unstructured test data. He reverse engineered the game to identify which categories of questions to study based on how valuable these questions are in the game. He randomly sampled from the set of training questions and tried to answer the questions correctly. His answered questions were used to predict which questions he would get right and wrong and to identify which subjects to study.

Roger Craig clustered the training questions based on their category and their value. For example, low-valued questions are often based on food whereas high-valued questions are often based on art. He constructed a nonlinear algorithm to identify the optimal “path” for beating the average contestant on Jeopardy. The algorithm was based on the probability of getting questions correct for his “predicted self” using simulation. He focused on improving his answers on the high-valued questions by studying topics that were shaky.

Training for Jeopardy was also a knapsack problem: Roger Craig had a limited amount of time to study. One way to effectively use his studying time was to limit the amount of time spent on each question. This had the side benefit of preparing him to answer the questions as quickly as possible, improving his odds of being the first to buzz in with the correct question. Then, he used his algorithm to identify which topics would help improve his score the most.

The video below shows how Roger Craig prepared for Jeopardy. If you have discovered more details about his specific model and implementation, please leave a comment.

the day-old bread supply chain

This is yet another post about the intersection of operations research and my frugality.

I occasionally stop by Jimmy John’s to pick up some day-old bread for $0.50 per loaf. I purchase a loaf for each one of my kids and then let them do whatever they want with it for dinner. They love it. Whenever I am in a Jimmy John’s, there is a huge stack of day-old bread. When I try to pick up some day-old bread at the grocery store, there are limited loaves and they disappear quickly. I often have to pay full price.

Is there an optimal strategy for how much bread to sell/bake each day?

The answer must be yes. The costs and revenues seem to be different for the grocery store and Jimmy John’s. At the grocery store, selling too much bread one day will eventually lead to a glut of  day-old bread sold at a discount, since it’s unlikely that all of the bread will be sold for full price. Bread is usually discounted to 1/3 – 1/6 of the original price. Those who buy the bread at a discount may have purchased bread at full price if no discounted bread was available, thus leading to lost revenue. Over time, the regular availability of discount bread may make frugal shoppers like me unwilling to pay full price. I suppose a variation of the newsvender problem can be used here.

I don’t think the grocery store is analogous to Jimmy John’s (JJ). There is no “full price” bread available at JJ, since the fresh bread is used in sandwiches. The day-old bread also doesn’t seem to discourage people from buying sandwiches. This is interesting, since the bread is about 1/10 of the price if a sandwich – why not make my own sandwich with JJ bread and pocket the savings?  I’m not sure that most sandwich consumers think the way I do. If the extra bread costs < $0.50 per loaf (cost = production + storage costs + labor cost to sell it), then JJ makes a profit for everyone who comes in to buy a sandwich and leaves with an extra loaf. Perhaps this is the dynamic that JJ aims for. Interestingly, the day-old bread I purchased yesterday clearly had just been taken out of the freezer, so Jimmy John’s preserves the day-old bread for future sales, rather than selling leftover bread that has been sitting out at a discount and possibly donating whatever is left.

Do you enjoy day-old bread? Do you see it priced in a way that would lead to lost revenue from the seller’s point of view?

Day old bread at Jimmy John’s.

should there be a science laureate in the US?

Senator Mazie Hirono (Hawaii) introduced a bill to create a “Science Laureate” position in the US, similar to the “Poet Laureate” (except for one obvious difference).

This new honorary position would be appointed by the President from nominees recommended by the National Academy of Sciences and serve for a term of 1-2 years. Using this national platform, the Science Laureate would be empowered to speak to Americans on the importance of science broadly and scientific issues of the day. Like the Poet Laureate, the Science Laureate would be an unpaid, honorary post. The scientist would also be encouraged to continue their important scientific work.

I think this is a great idea, and I’m happy to see that it is supported by AAAS and other science organizations. Unofficial science laureates like Neil DeGrasse Tyson and Carl Sagan have inspired many people to go into the sciences. One could argue that an official science laureate position is unnecessary with social networking tools that make scientists more accessible. However, science literacy in the US is poor, and many Americans view belief in science as optional. An official science laureate would add a layer of credibility that, sadly, might be needed for optimal outreach.

Science, engineering, and technology fields are often lumped together under the STEM umbrella. My only concern is that a science laureate position would mainly benefit physical and life sciences. I’m selfish – I’d want OR, CS, math, and engineering to get some exposure, and these fields really could use a laureate. It would be hard to justify awarding, say, a computer scientist with this role when climate change is still so controversial. Data science could also use some more organized and targeted exposure, since even to those of us in STEM fields are still defining what constitutes data science [Link] and big data [Link to JF Puget, Link to me].

We already have a few excellent STEM ambassadors who are not science laureates. In the past year, Bill Gates, Mark Zuckerberg, and others teamed up for computer science education through the non-profit code.org (see their video below). I’ve written before about how will.i.am bought airtime to broadcast a science and technology special on ABC [Link]. Some people in OR have done a wonderful job of publicizing their work. Anna Nagurney and Sheldon Jacobson come to mind, but there are many others.

What do you think about a science laureate?

Related posts on OR outreach:

• operations research, disasters, and science communication
• researchers should embrace talking about their research in 140 characters or less
• OR on social networks
• science vs. swimsuit competitions

Braess’ Paradox can be applied to physical systems and professional basketball

Braess’ Paradox is a famous result in game theory which states that in a network where users selfishly seek to lower their travel times, the Nash equilibrium flows may increase after a new arc/road is added.

Braess’ Paradox can be demonstrated physically with springs, as seen in this nifty YouTube video:

When searching for information about Braess’ Paradox, I found a delightful post on Anna Nagurney’s blog.

In the basketball world, according to Bill Simmons of ESPN, there is the Ewing Theory. According to Simmons: The theory was created in the mid-’90s by Dave Cirilli, a friend of his who was convinced that Patrick Ewing’s teams (both at Georgetown and with New York) inexplicably played better when Ewing was either injured or missing extended stretches because of foul trouble. Simmons has a primer, Ewings Theory 101, which lists examples in basketball history where the removal of a top player (paradoxically) results in a better outcome for the basketball team.

Brian Skinner, a physicist at the University of Minnesota, wrote an article, “The Price of Anarchy in Basketball” in which he developed an analogy, through a model, between certain basketball plays and the Braess paradox, in order to further explore the Ewing Theory.

I’ve been enjoying the NBA basketball playoffs since my favorite team (the Chicago Bulls) won their first round series and beat the Miami Heat in the first game in the second round. The Bulls are without Derrick Rose, the best player on the Bulls. I hope there is not a “Derrick Rose Effect” that would cause the Bulls to be worse when he returns.

Are you aware of other interesting applications of Braess’ paradox?

new department in IIE Transactions: Government, Public Policy, and Society

There is a new department in IIE Transactions called “Government, Public Policy, and Society” that may be of interest to some of you. The new department is in the Focused Issue on Operations Engineering and Analysis. I urge you to submit your papers to this new department. I’ve included some information about the new department here.

Other new departments include Analytics and Emerging Applications [Link to the pdf of IIET departments].

I am the department editor for “Government, Public Policy, and Society.” My associate editors are Kash Barker (University of Oklahoma), Maria Mayorga (Clemson University), and Tom Sharkey (Rensselaer Polytechnic Institute).

Here are the types of papers we hope that you send us:

Systems that benefit society require the effective, efficient, and equitable allocation of resources for operating public services, improving homeland security systems and protecting critical infrastructure, responding to natural disasters and terrorism, and recovering from disasters, among other policy concerns.  These processes and systems can operate every day (such as public schools and fire services) or perhaps exist only as plans for possible scenarios (such as the mass dispensing of medication in response to an epidemic and evacuating a large population in advance of a natural disaster).  In either case, the models and methodologies of operations research can be applied to design better processes and systems that serve public interests.

This department intends to publish papers that describe innovative operations research models and methodologies that address problems of societal benefit.  This department defines government, public policy, and society broadly but is focused on advanced quantitative and analytical methods to design processes and systems, make better decisions, and solve problems of public concern.  Accordingly, papers describing straightforward applications of existing techniques should be submitted to other venues.

The department’s scope includes the protection of critical infrastructure; border, maritime, and port security; transportation security; food safety; emergency preparedness and response; humanitarian logistics; evacuation modeling; recovery efforts; public sector and public services operations research; decision making for homeland security; and non-profit and community-based operations research, among other related topics in government, public policy, and society.  Papers submitted to this department must clearly motivate the problem’s relevance to society and should make substantive and innovative contributions to solving the problem.  Papers that describe collaborations and applications of the research and papers that evaluate public policy alternatives are particularly desired.

Authors interested in submitting a paper to this department are encouraged to contact the department editor at lmclay@wisc.edu.  For more information about IIE Transactions and the manuscript submission process, visit the journal web site at
http://www.tandfonline.com/toc/uiie20/current
.