Eighty-Four Mathematicians Walk into a Lecture Hall…

And tackle four industrial problems, including a programmatic TV problem proposed by clypd, during a week-long workshop. This happened on June 12-17, 2016 at Duke University during the 32nd Annual Mathematical Problems in Industry (MPI) Workshop. This year, the MPI workshop attracted 84 mathematicians from universities, industry, and national laboratories from Canada, the UK, and the US.

The workshop activities start weeks before the meeting with four invited US companies submitting real-world problems for attendees, including the participating companies’ representatives, to work on for a whole week. At the meeting, each problem is first introduced by the industry representatives in a general presentation, then the participants split into four smaller groups to work on a single problem. At the end of the workshop, an executive summary of the work is given to the company’s representative, and a few months later, a full-length report is produced.

The MPI workshop is an event of great value for all the attendees. Academic mathematicians learn about and work on problems outside their research field, while industrial mathematicians get feedback and new ideas from other experts who choose to work on their problem. This year, W.L. Gore and Associates proposed a problem about chemical reactions in porous materials such as catalysts, Revon Systems participated with a problem related to the prediction of medical diagnoses of asthma events, Covar Applied Technologies submitted a signal processing problem for explosive devices detection, and clypd suggested the problem of designing a programmatic TV marketplace where buyers optimize their linear TV campaigns and send their highly specific requests to sellers who try to maximize their inventory yield (more about this problem below).

This is the second consecutive year that clypd, represented by one of our data scientists, submits a problem to MPI. We participate in these kinds of events because programmatic TV as a mathematical problem is not fully solved yet. As an industry, we have certainly made a lot of progress in terms of transaction automation and data-driven optimization, but programmatic TV is more than that. It is full of interesting mathematical problems that can keep dozens of professional mathematicians engaged and interested for weeks.

Some of the problems that we explored in depth at the last two MPI editions include forecasting of advanced (i.e., beyond age and gender) viewership volumes, frequency of viewership spikes, and reach and frequency distributions. We also have worked on optimization models with specific reach and frequency goals, and various mathematical methods for better understanding viewership and inventory (see the MPI 2015 report  for details about last year’s problems).  

This year, we focused on a scenario that we believe will be commonplace in the near future: media buyers will use various data sources, predictive analytics, and optimization to generate optimal TV schedules (but without access to media owners’ inventory). These schedules might be very specific, which contrasts with the current practice of defining requested schedules via general constraints. Since buyers build these schedules without knowledge of what media owners have available, there might be competition for certain spots. Therefore, buyers need to complement their submission with an offer that they hope will convince the media owner to accept their schedules without modification, and as a result, reject the requests of other buyers. See below for an example.

Bidders compete for certain spots. The greater the competition, the lighter the shade is. This competition increases the market value of the slots in question.

Bidders compete for certain spots. The greater the competition, the lighter the shade is. This competition increases the market value of the slots in question.

Bidders compete for certain spots. The greater the competition, the lighter the shade is. This competition increases the market value of the slots in question.

Given that the buyers’ optimized schedules might include inventory from various media owners, it is best for the buyers to send these requests through a sell-side platform, such as clypd, which has access to inventory from different media owners.

Here’s where the mathematical problems that we tackled at MPI arise: In the presence of competition among two or more buyers for the same inventory, how is the media owner suppose to respond? Which order(s) should the media owner accept? What kinds of counteroffers should the media owner propose to the buyers whose orders cannot be accepted without modification? If the counteroffers consist of alternative (portions of) schedules, how should the alternatives be determined? Among others.

At clypd, the data science team addresses these and other questions of similar nature. We try to learn as much as possible about our problems in order to develop the necessary mathematical models and methods that might drive the future of programmatic TV.

We look forward to participating in events like MPI where we can interact with and learn from subject matter experts in an effort to better serve not only our clients, but also the TV industry as a whole.

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