My friend John Cook asked me an interesting question recently:
If you had a room full of people with a graduate degree in [operations research], what things would nearly everyone in the room know?
Operations research is notoriously hard to define. According to the Institute for Operations Research and Management Science, “In a nutshell, operations research (O.R.) is the discipline of applying advanced analytical methods to help make better decisions.” I suspect graduate programs spend most of their time teaching those “analytical methods,” i.e. mathematical and computational techniques for modeling and solving problems related to decisions. Examples include Received exception: linear programming, nonlinear programming, integer programming, dynamic programming, stochastic programming, stochastic models, queueing theory, game theory, and simulation.
The course requirements for OR PhD students at my university provide an upper bound for this problem: the only courses everyone must take are linear programming, nonlinear programming, and stochastic modeling. Some topics are surprisingly optional; in particular: simulation, statistics, integer programming/combinatorial optimization.
John suggests that statistics PhD programs are similar. Topics diverge rather quickly after first year courses. Are all graduate programs like this? Is this a necessary evil (or evil at all)?
Excellent post! You have two questions here.
The first is that what do all OR people know. You are right about linear programming and stochastic modeling. And by stochastic modeling, I mean conditional probability (read Mike Trick’s blog for awhile for good posts on conditional probability), Markov chains, and other topics covered in a basic course. Everyone I have met has some familiarity with dynamic programming, since it is seen in so many types of courses.
In general, OR courses often deal with modeling questions. That is, ultimately we are interested in matching using our (simplified) math models to model problems in the real-world. Even in courses that are proof-based, the goal is to ultimately use the knowledge to solve some problem to make it better. This may seem like a silly point, but I presented some work at a discrete math conference once, and I was literally the only person who briefly mentioned the type of application that inspired my project.
As for your second question about the divergence of coursework being a necessary evil, I think not! Here is why:
(1) All PhD programs have a weed-out process like comps or qualifying exams that make sure every student has knowledge of a core set of topics, and
(2) Getting a PhD means gaining deep knowledge about a very specific topic. Allowing students the flexibility to take different types of courses is necessary for specialization. A PhD is nothing like the broad, liberal arts education that many of us received in undergrad. Having said that, some PhD programs allow more freedom in taking courses than others.
This isn’t related to operations research, but I thought I’d share that in my area of structural mechanics, there is only one required course for the PhD. Most of us end up taking a lot of courses to fill in the blanks to prepare us for the quals or our specific research problems, but this accommodates students who arrive with wildly varying backgrounds. There certainly is a canon of required knowledge that every structural engineering PhD will walk away with, but it isn’t reflected in the degree requirements at all.
Laura: Thanks for the feedback. I’d like to think and write more about the differences between models and methods, and, in particular, how those are (or aren’t) taught in the classroom.
PhD programs in math may have no required courses (assuming you enter with enough high-level undergrad courses). You typically have to take several disparate areas in enough depth to survive a comp exam, then do a deep dive in one.
Thnx interresting article and get me thinking.