# Arnoff Lecture

I am just back from Cincinnati, where I gave the 17th E. Leonard Arnoff Memorial Lecture on the Practice of Management Science. When I look at the list of presenters, with my name on it, I am reminded of the Sesame Street tune “One of These Things (Is Not Like the Others)“. I was honored to be asked, and very happy to give the talk. There were about 85 in the audience, despite armaggeddon-like lightning and thunder outside.

The lecture is named after Len Arnoff, best known for his 1957 book “Introduction to Operations Research” with Churchman and Ackoff, one of the first (or the first) operations research textbook. He had a varied career: faculty member at Case and others, partner at Ernst and Ernst, and Dean of the Business School at the University of Cincinnati, before retiring to Florida in 1988. He died in 1991. (David Rogers is preparing a short biography of Arnoff, and I am grateful for the early version he sent me).

I was very pleased that his wife Ann flew up to attend the lecture, and that his daughter Susan could also attend.

The title of my talk was “Sports Scheduling and the Practice of Operations Research”. In addition to telling some stories about working with various sports leagues (you will have to attend one of my talks to hear those!), I spend some time on some of the technical issues. The main theme was that if you only knew operations research from ten years ago, you probably don’t have the techniques needed to solve real-world sport scheduling problems. In particular, the following methods don’t work very well:

1. “Routine” integer programming: let x[i,j,t] = 1 if i plays at j in time t, etc. etc. Weak formulation that does very poorly
2. Greedy heuristics. Generally do not lead to anything close to feasible.
3. Local search. Simple exchange generally leads to infeasible solutions, making it hard to use simulated annealing, tabu search or other metaheuristic approaches.

The following do make a big difference (and are much more recent ideas):

1. Complicated variables (like in branch and price): Let a variable represent a road trip, a schedule section, or a whole schedule for a team.
2. Large neighborhood search. Relax large pieces of a schedule and reoptimize keeping the rest fixed.
3. Constraint programming, ideally combined with integer programming, in order to quickly find feasible solutions.

## 4 thoughts on “Arnoff Lecture”

1. I’d love to hear more about good and bad choices of decision variables! I’m teaching my senior-level elective on advanced operations research techniques again this Fall (it’s about modeling and implementing on the computer, not much on algorithms) and that would be a great addition to the integer programming section – most of my IP problems are on cost structures (extra-unit vs all-unit discounts, fixed ordering cost, etc). Any paper or slides that would help? And maybe you can come and give a talk!

2. Wow, this is pretty interesting to read. I had a soccer coach in college who ranted and raved about Arnoff but i never knew who he was talking about. This is the first time i actually put 2 and 2 together. Pretty interesting!

3. Soccer God says:

My mom once mentioned the name, Leonard Arnoff. I never really got it until I did some research. i coach a little soccer team, I implement a few of Mr Arnoff’s principles. It’s good to see his legacy lives on in our educational system