Overbooking is a basic model in yield management and is always a fun example to do in class. If you are selling tickets to a flight and there is some chance that passengers will be no shows, it is optimal to oversell the flight, i.e., sell more tickets than you have capacity to serve. Model it right and you have a tidy little newsvendor problem in which the seller weighs the cost of accommodating a bumped passenger with the opportunity cost of flying with an empty seat. The optimal amount of overbooking will also depend on the distribution of the number of no shows on the flight since no shows represent “demand” for oversold seats.
An academic institution may not look like an airplane, but it faces a problem similar to determining how many seats to sell on the 9:15 flight from O’Hare to LaGuardia. The admissions office can invite students in but it cannot guarantee that they will show up. A student may be admitted to a different school that they prefer or simply have a change of plans so enrolling no longer fits their immediate plans. On the other hand, they may all decide to show up.
That gets us to MIT (Bad Math: MIT Miscounts Its New B-School Students, Wall Street Journal, Sep 25).
The Sloan School of Management’s full-time M.B.A. program, usually about 400 students, was oversubscribed by an unusually high number of students this year. Rather than expand the class size, the school asked for volunteers willing to wait a year to enroll, sending out an e-mail just a couple of weeks before the Aug. 23 kickoff barbecue. By that point, many expectant students had quit jobs and secured housing in the Boston area. …
After realizing they had a student surplus, school officials emailed the incoming class on Aug. 7, offering “guaranteed admission to the class of 2015 for the first 20 admitted students who request it.” The school gave them until Aug. 13 to respond, according to one student’s copy of the letter, which was reviewed by The Wall Street Journal. But it didn’t get enough takers.
So, like an airline offering vouchers to travelers willing to hop off oversold flights, the school put money on the table, offering students who expressed an interest a $15,000 scholarship to be applied to next year’s tuition. Students still balked, and on Aug. 21, a day after pre-term refresher courses began, Sloan raised the offer to $20,000 for the first 10 respondents. (Tuition for the 2012-2013 academic year is $58,200, with total expenses—including books, housing and food—estimated at just under $89,000.)
To take the suspense out of the discussion, only four students took Sloan up on its offer.
I must first confess that it is really hard to write something that does not reek of schadenfreude. But the truth is that this could have easily happened at my school or just about any other.
If we think of this from an operations perspective, it is somewhat surprising that severely over-sized classes don’t happen more often. The cost of not filling out a class is relatively big. If the “capacity” of the program is 400 students, having just 399 does nothing to really change the cost of the program. The school, for example, is not going to cancel a section of the core ops class just because there is one less person. So being shy a students costs the school two years of tuition that is almost pure profit.
Of course, defining capacity of a program is tricky. Said another way, being a little bit over should be relatively cheap. Having 401 students in a class can be handled with putting some section of a core class in a bigger room or providing whichever professor whines the most with an extra TA. What the MIT example suggests is that the costs involved are non-linear. One extra student is easily accommodated but 20 or 25 extra are not. At some point, you do need extra sections or you run out of large classrooms. And this is just emphasizing teaching capacity. If you throw in worrying about institutional culture and the experience of students knowing each other, costs could get very high very quickly.