Category Archives: Research

Optimization Games for the Young (Part 2)

 A couple of weeks ago, I wrote a blog post in which I tell a story that motivated me to start creating games for children and young adults to get them excited about Operations Research/Prescriptive Analytics/Optimization and STEM in general. You can download my first two games here: Lego Furniture and Pack That Bag!

Since then, I can’t stop thinking about other games to create. I have four game ideas in my head right now and today I’m back to share my third one with you: Stop the Fire! This is actually based on a research problem on which I am working right now.

I hope you have a chance to play this and my other games with your young ones. Please let me know your experience with these games and any feedback you may have toward improving them in the comments below.

Keep playing!

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Filed under Analytics, Applications, Games, INFORMS K-12 Outreach, Integer Programming, Mathematical Programming, Modeling, Motivation, Promoting OR, Research, Teaching

Bringing Research into the Classroom: Can Relevant and Impactful be Easy to Explain?

math-equation_chalkboard O.R. researchers and practitioners are constantly churning out papers that tackle a wide variety of important and hard-to-solve practical problems. On one hand, as a researcher, I understand how difficult these problems can be and how it’s often the case that fancy math and complex algorithms need to be used. On the other hand, as someone who teaches optimization to MBA students who aren’t easily excited by mathematics, I’m always looking for motivational examples that are both interesting and not too complex to be understood in 5 minutes. (That’s the little slot of time I reserve at the beginning of my lectures to go over an application before the lecture itself starts.)

Every now and then, I come across a paper that fits the bill perfectly: it addresses an important problem, produces impactful results, and (here comes the rare part), accomplishes the previous two goals by using math that my MBA students can follow 100%, while being confident that they themselves could replicate it given what they learned in my course (the optimization models).

The paper to which I’m referring has recently appeared in Operations Research (Articles in Advance, January 2017): The Impact of Linear Optimization on Promotion Planning, by Maxime C. Cohen, Ngai-Hang Zachary Leung, Kiran Panchamgam, Georgia Perakis, and Anthony Smith (

If I had to pick one word to describe this paper, it would be BEAUTIFUL.

I immediately proceeded to put together a 5-minute summary presentation (8 slides) to cover the problem, approach, and results. I’ll be showing this to 100 of my MBA students on this coming Tuesday (Valentine’s Day!). I hope they love it as much as I did. Feel free to show this presentation to your own students if you wish, and let me know how it went down in the comments.

A recent Poets & Quants article explains how business schools with the highest quality teaching strive to bring their faculty’s research into the classroom so that students get to learn the latest and greatest ideas. The O.R. paper above is a perfect example of when this can be done effectively.

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Filed under Analytics, Applications, Integer Programming, Linear Programming, Modeling, Motivation, Promoting OR, Research, Teaching

Semantic Typing: When Is It Not Enough To Say That X Is Integer?

Andre Cire, John Hooker, and I recently finished a paper on an interesting, and somewhat controversial, topic that relates to high-level modeling of optimization problems. The paper is entitled “Modeling with Metaconstraints and Semantic Typing of Variables“, and its current version can be downloaded from here.

Here’s the abstract:

Recent research in the area of hybrid optimization shows that the right combination of different technologies, which exploits their complementary strengths, simplifies modeling and speeds up computation significantly. A substantial share of these computational gains comes from better communicating problem structure to solvers. Metaconstraints, which can be simple (e.g. linear) or complex (e.g. global) constraints endowed with extra behavioral parameters, allow for such richer representation of problem structure. They do, nevertheless, come with their own share of complicating issues, one of which is the identification of relationships between auxiliary variables of distinct constraint relaxations. We propose the use of additional semantic information in the declaration of decision variables as a generic solution to this issue. We present a series of examples to illustrate our ideas over a wide variety of applications.

Optimization models typically declare a variable by giving it a name and a canonical type, such as real, integer, binary, or string. However, stating that variable x is integer does not indicate whether that integer is the ID of a machine, the start time of an operation, or a production quantity. In other words, variable declarations say little about what the variable means. In the paper, we argue that giving a more specific meaning to variables through semantic typing can be beneficial for a number of reasons. For example, let’s say you need an integer variable x_j to represent the machine assigned to job j. Instead of writing something like this in your modeling language (e.g. AMPL):

var x{j in jobs} integer;

it would be beneficial to have a language that allows you to write something like this

x[j] is which machine assign(job j);

To see why, take a look at the paper ;-)

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Filed under Modeling, Research

Improving Traveling Umpire Solutions the Miami Heat Way: Not one, not two, not three…

Those who know me are aware of my strong passion for basketball, so I had to find a way to relate this post to my favorite sport. Fans of basketball in general, and of the Miami Heat in particular, might be familiar with this video clip in which LeBron James makes a bold prediction. Back in 2010, when asked how many titles the Heat’s big three would win together, he replies “Not one, not two, not three, not four, not five, not six, not seven, …” While I’d love to see them win 8 titles, it sounds a bit (a lot) unlikely. But I can’t complain about their record so far. Winning 2 titles in 3 finals’ appearances isn’t bad at all. But what does this have to do with baseball umpires? Let’s get back to OR for a moment.

A couple of years ago, I wrote a post about scheduling baseball umpires. In that same article I co-authored with Hakan Yildiz and Michael Trick, we talked about a problem called the Traveling Umpire Problem (TUP), which doesn’t include all the details from the real problem faced by MLB but captures the most important features that make the problem difficult. Here’s a short description (detailed description here):

Given a double round-robin tournament with 2N teams, the traveling umpire problem consists of determining which games will be handled by each one of N umpire crews during the tournament. The objective is to minimize the total distance traveled by the umpires, while respecting constraints that include visiting every team at home, and not seeing a team or venue too often.

And when I say difficult, let me tell you something, it’s really hard to solve. For example, there are 16-team instances (only 8 umpires) for which no feasible solution is known.

Two of my Brazilian colleagues, Lucas de Oliveira and Cid de Souza, got interested in the TUP and asked me to join them in an effort to try to improve the quality of some of the best-known solutions in the TUP benchmark. There are 25 instances in the benchmark for which we know a feasible solution (upper bound) and a lower bound, but not the optimal value. Today, we’re very happy to report that we managed to improve the quality of many of those feasible solutions. How many, you ask? I’ll let LeBron James himself answer that question:

“Not one, not two, not three, … not ten, … not eighteen, … not twenty-three, but 24 out of 25.”

OK, LeBron got a bit carried away there. And he forgot to say we improved 25 out of the 25 best-known lower bounds too. This means those pesky optimal solutions are now sandwiched between numbers much closer to each other.

Here’s the approach we took. First, we strengthened a known optimization model for the TUP, making it capable of producing better bounds and better solutions in less time. Then, we used this stronger model to implement a relax-and-fix heuristic. It works as follows. Waiting for the optimization model to find the optimal solution would take forever because there are too many binary decision variables (they tell you which venues each umpire visits in each round of the tournament). At first, we require that only the decisions in round 1 of the tournament be binary (i.e. which games the umpires will be assigned to in round 1) and solve the problem. This solves pretty fast, but allows for umpires to be figuratively cut into pieces and spread over multiple venues in later rounds. Not a problem. That’s the beauty of math models: we test crazy ideas on a computer and don’t slice people in real life. We fix those round-1 decisions, require that only round-2 variables be binary, and solve again. This process gets repeated until the last round. In the end, we are not guaranteed to find the very best solution, but we typically find a pretty good one.

Some possible variations of the above would be to work with two (or more) rounds of binary variables at a time, start from the middle or from the end of the tournament, etc. If you’re interested in more details, our paper can be downloaded here. Our best solutions and lower bounds appear in Table 10 on page 22.

We had a lot of fun working on the TUP, and we hope these new results can help get more people excited about working on this very challenging problem.

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Filed under Applications, Heuristics, Integer Programming, Research, Sports, Traveling Umpire Problem

MLB Umpire Scheduling

There are two purposes to this post. First, I’d like to follow-up on Michael Trick’s post on the importance of teaching and its relationship with research. One of the points Mike makes is that your next exciting research or consulting project may come from current or former students. Those of us who teach undergraduate and MBA classes have the opportunity to network with (future) managers and practitioners who will eventually put their training to the test, producing actual answers to real-life problems. And if one of those problems requires more OR knowledge than what they had the opportunity to learn in school, they might remember their friendly neighborhood OR professor. Another way research can come out of teaching is during hands-on projects. Back in 2006, Mike was in charge of an elective OR-project class that allows MBA students to try their hands on a real-life problem; in that case umpire scheduling. To my delight, Mike invited me to be the TA for that course and I gladly accepted. The rest is history.

The second purpose of this post is to help myself keep track of the recent news stories about our umpire scheduling paper. Thanks to an excellent job by the PR departments at the University of Miami School of Business (thanks, Catharine!) and Michigan State University, the story has appeared in numerous outlets. As a matter of fact, I’m very excited to report that Scientific American had a 60-second science podcast about our work:

August 18Scientific American: Researchers Tell Umpires Where to Go (PDF version)

Here are a few other news outlets that covered the story (I’m trying to keep this list up-to-date for my own sake). I’m also providing a link to a PDF version of each story in case the web pages are taken offline:

April 2012, The Spring issue of Business Miami Magazine has an article about our work entitled Road Trip (PDF version).

October 19, WAMC Northeast Public Radio Academic Minute. I recorded a 1:45-minute explanation of the problem, approach, and results which aired as one of WAMC’s Academic Minutes on the same day of the first game of the World Series. That was a lot of fun! Click on the link to listen. If the link doesn’t work, here’s the MP3 file.

September 6, Miami New Times: Tallys Yunes, UM Professor, Solves MLB’s Umpire Scheduling Dilemma (PDF version). This article also appeared in print, in the September 8-14 issue of Miami New Times. Here’s a PDF scan of that.

August 3, PhysOrg: University of Miami Business Professor Helps Create a Successful Scheduling Method for Umpires in Major League Baseball (PDF version)

August 3, HPCwire: Business Prof Solves Traveling Umpire Problem for Major League Baseball (PDF version)

July 31, University of Miami School of Business: School’s Management Science Research Resolves Major League Baseball’s Umpire Scheduling Challenges (PDF version)

July 21, ScienceDaily: Scholar Helps Make Major League Baseball Umpire Schedule a Hit (PDF version)

July 21, ThePostGame: MLB Umpires Have a Turkish Secret Weapon (PDF version)

July 20, PhysOrg: Michigan State Scholar Helps Make MLB Umpire Schedule a Hit (PDF version)

July 20, Michigan State University News: Michigan State Scholar Helps Make MLB Umpire Schedule a Hit (PDF version)

I greatly enjoy the teaching side of my job because I believe it complements the research side quite well. I’m looking forward to bringing articles like the ones above to my classes in the Spring and I’m sure they’ll be well received.

Further acknowledgments: thanks to those who also helped spread the word about the umpire scheduling problem on Twitter, especially Paul Rubin (@parubin), Aurélie Thiele (@aureliethiele), and @INFORMS (is that you, Mary Leszczynski? :-).


Filed under Applications, Heuristics, Promoting OR, Research, Sports, Teaching, Traveling Umpire Problem

There and Back Again: A Thank You Note

There were sub-freezing temperatures, there were snow flurries, there was a hail storm, and there was a tornado watch. No, I’m not claiming that my visit to Pittsburgh last week was as full of adventures as Bilbo Baggins’s journey, but it was very nice indeed.

I had the great pleasure of being invited by John Hooker and Willem-Jan van Hoeve to give a talk at the Operations Research seminar at the Tepper School of Business. Since John, André Ciré, and I are working together on some interesting things, I took the opportunity to spend the entire week (Mon-Fri) at CMU; and what a joy it was.

The Tepper School was kind enough to have a limo service pick me up from, and take me back to, the airport. I guess this is how the top business schools roll. It’s a great way to make a speaker feel welcome. Besides, my driver turned out to be an extremely friendly and easy-to-talk-to fellow. Thanks to him (and his knowledge of off-the-beaten-path roads), I managed to catch my return flight. Otherwise, a cab driver would have sat through miles of Friday rush hour, and I’d certainly have missed the flight.

I walked to campus every day and actually enjoyed the few minutes of cold weather (wow! I can’t believe I just said that!). Stopping at the Kiva Han to grab an almond biscotto and a small coffee, right across the street from Starbucks, was a daily treat. Walking around campus brought back great memories from my PhD-student days. It’s nice to see all the improvements, and all the good things that remain good. Upon leaving Miami, I had the goal of having Indian food for 10 out of my 10 meals (excluding breakfast). Although I managed to do it only 4 times, I’m pretty happy with my gastronomic adventures in Pittsburgh. The delicious semolina gnocchi served at Eleven is definitely praiseworthy.

Work-wise, it was a very productive week. We had interesting ideas and conversations. I’m very grateful to all of those who took time off their busy schedules to meet with me, be it to catch up on life, talk about research (including some excellent feedback on my talk), or both. Thank you (in no particular order) to Alan Scheller-Wolf, Javier Peña, Michael Trick, Egon Balas, Sridhar Tayur, Masha Shunko, Valerie Tardif, Lawrence Rapp, and of course John and Willem. Many thanks also go to André, David, and all the other PhD students who joined me for lunch on Friday. I really enjoyed meeting all of you and learning a bit about your current projects.

I noticed that John got rid of his chalk board and painted two of his office walls with some kind of glossy white-board paint. It’s pretty cool because it allows you to literally write on your wall and erase everything with a regular white-board eraser. Now I want to do the same in my office! (My white board is pretty small.) But I’m not sure if they’ll let me. Gotta check on that!

Overall, it was an awesome week and I hope I can do this again some time.

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Filed under People, Research, Travel

Getting Freshmen Excited About OR

The vice dean for undergraduate programs at the school of business asked me to make a presentation to a group of freshmen. My job is to tell them about the field of Management Science and the research that goes on in my department. The main goal is to get these students excited about research early on. Hopefully, they’ll get involved in undergraduate research projects and even consider joining our PhD program further down the road. My understanding is that every department in the school will make a similar presentation, but I’ll tell the students that OR is by far “the coolest topic” (sorry “other departments”, but I think it is!).

I think this is a great idea, especially because Management Science (or OR) is not a required class for all business majors and I believe that every business school graduate should at least know what OR is and what it can do for you (fortunately, OR is a required class for all MBA students in our school).

I’m putting together a presentation with the following outline:

  1. Introduction (who I am, my background, etc.)
  2. What is Management Science? (that’s where I tell them to use the name OR instead :-)
  3. Real-life applications of OR
  4. Research interests of the Management Science department (with a focus on my interests, at the request of the vice dean)
  5. Research opportunities for undergraduate students

The room is booked for 1 hour and 45 minutes, and I was told I can use as much time as I want. Boy, that’s a lot! For item number 3, I’ll pick a diverse collection of applications covering a wide range of topics. For item 4, I’ll tell them about things my colleagues have worked on, things I’ve done, and things I’m currently doing. Then I’ll move on to item 5 and close the presentation with problems on which I’d like to work with an undergraduate student (nothing that requires advanced OR knowledge, of course). One caveat is that I must tell them that my projects require some knowledge of computer programming and basic understanding of linear and integer programming (which they could get by taking one of our classes or by reading on their own).

I’ve also put together a Google document entitled A Hyperlinked Introduction to the World of Operations Research and Management Science, which I’m going to hand out at the end of the talk.

The purpose of this document is to function as an organized list of links to OR resources and interesting applications that the students can easily navigate to. It contains a superset of the real-world applications I’m going to tell them about, and it’s supposed to complement my talk. I hope this turns out to be useful to other people as well. Feel free to use it and let me know if you have any suggestions for improvement. I’m sure there are many interesting links that I forgot to include there.


Filed under Motivation, Promoting OR, Research