Mike Trick talked about his experience setting the Major League Baseball (MLB) schedule at the 2014 German OR Conference in Aachen, Germany. Mike’s plenary talk had two major themes:
1. Getting the job with the MLB
2. Keeping the job with the MLB
The getting the job section summarized advances in computing power and integer programming solvers that have made solving large-scale integer programming (IP) models a reality. Mike talked about how he used to generate cuts for his models, but now the solvers (like CPLEX or Gurobi) add a lot of the cuts automatically as part of pre-processing. Over time, Mike’s approach has become popping his models into CPLEX and then figuring out what the solver is doing so he can exploit the tools that already exist.
Side note: I am amazed at how good the integer programming solvers have become. I recently worked on a variation to the set covering model for which a greedy approximation algorithm exists. The time complexity of the greedy algorithm isn’t great in theory. In practice, the greedy algorithm is slower than the solver (Gurobi, I think) and doesn’t guarantee optimality. I can’t believe we’ve come this far.
Mike also stressed the importance of finding better ways to formulate the problem to create a better structure for the IP solver. Better formulations can be more complicated and less intuitive, but they can lead to markedly better linear programming bounds. Mike achieved this by replacing his model with binary variables that correspond to team-to-team games (does team i play team j on day t?) with another model whose variables correspond to series (a series is usually 3 games played between teams on consecutive days). Good bounds from the linear programming relaxations help the IP solver find an optimal solution much quicker. Another innovation focused on improving the schedule by “throwing away” much of the schedule (usually about a month) after making needed changes and resolving. Again, this is something that is possible due to advances in computing.
The keeping the job section addressed business analytics and its role in optimization. Mike defined business analytics as using data to make better decisions, something that OR has always done. What is new is using the power of data analytics and predictive modeling to guide prescriptive integer programming models in a meaningful way. The old way was to use point estimates in integer programming models, the new way uses more information (such as the output of a logistic regression) to guide optimization models. The application Mike used was estimating the value of scheduling home games at different times (day vs. night) and day of the week. When embedded in the optimization modeling framework, the end result was that creating a schedule using business analytics could add about $50M to MLB in revenue.
Mike summed up his talk but talking about how educating the marketing folks is part of the job now. Marketing likes to measure “success” as the number of games that sell out. Operations researchers recognize that sold out games are lost revenue, so the goal has become to schedule games such that games are almost sold out, and making sure that marketing understands this approach.