*We scheduled some time for this Q&A with Principal Data Scientist Evan Lynch, where we explored the many cross-industry challenges that scheduling optimization aims to solve and the robust scheduling techniques that lie at the junction between mathematical optimization and machine learning. *

#### 1. What are your official title, role, and responsibilities at Mosaic Data Science?

Evan Lynch is Principal Data Scientist at Mosaic who has been with the company for about three years.

“Although we wear many hats, I’d say my specific area of focus on the team includes projects related to developing and integrating machine learning and mathematical optimization models, which I’m excited to dive deep into today,” says Evan.

#### 2. How did you first come across optimization in your data science journey? What was your first project?

Evan states his interest in optimization began during his school years. Many of his undergraduate professors were very passionate about the subject and passed this same curiosity on to him, which he continued to pursue throughout his professional career.

“My first real optimization project was for a distribution center in North Jersey, where I built a model to optimize the allocation of a small set of warehouse employees across a large set of loading docks,” Evan adds. “Given the random nature of where packages were going to come off of the conveyor belts over the next hour, the goal was to dynamically reassign personnel to an adjacent set of doors to make sure everyone had enough work to do.”

#### 3. How did you uncover the idea of integrating machine learning and mathematical optimization, and what does it mean actually to integrate the two?

To answer this question, Evan describes how early in his data science career, he perceived two needs. These are outlined below:

“Let’s start with optimization. For an optimization model to really be actionable, it needs to have reliable inputs, not just assumptions – and often the inputs to optimization models are not deterministic,” he explains. “Going back to the loading dock example, I could assume the number of packages going to each loading dock is equal to the average over the past week, but that is not what is actually going to happen. Instead, if I can accurately predict the number of diverted packages by dock over the next hour, that optimization model is a lot more useful. Therefore, reliable inputs to optimization models are the first need.”

“The second need is for ML models to be actionable. Meaning, explicitly actionable, and therefore more useful,” Evan continues. “The standard process for many ML use cases is to build a model to predict X and serve that prediction to a decision maker, leaving the weight of the actual decision on the user without offering any suggestions. We refer to this as ‘actionable insights.’”

Evan adds that, ultimately, the decision maker should make the final decision, but it is often incredibly helpful to follow up a prediction with a recommended action or a set of possible pathways to pursue an objective or set of objectives that a decision maker has.

Therefore, integrating machine learning and mathematical optimization involves starting with an ML model that is predicting the input of an optimization model. In that sense, Evan says, we are chaining together predictive and prescriptive models.

#### 4. How does scheduling play into all of this? How do integrated ML and optimization help companies solve scheduling problems?

“Scheduling problems are super interesting because they are really hard to solve from an optimization standpoint, and there are a bunch of ML input problems that often precede a schedule optimizer,” Evan explains.

“Let’s start with defining what a schedule is. Essentially, a schedule is just a sequence of events. The events may just be ordered or may need to start at specific times of the day or year.”

He goes on to explain how there may be times when one may need to start considering an allocation of resources (such as rooms or staff), and how different use cases can have complicated constraints that come into play. This includes what types of events may be able to be sequenced before others.

“And you pretty much end up playing this complex game of Tetris,” Evan says. “So that is sort of your standard scheduling problem that you would use mathematical optimization techniques to solve.”

Evan adds that there are a lot of standard prediction problems that precede a scheduling optimization problem, such as:

- Predicting the duration of events. For example, we scheduled this interview for half an hour today. We predicted we would need a half hour when we did that.
- Predicting resource demand and availability.
- Predicting how many events need to be scheduled at all.

#### 5. Why do you think scheduling optimization problems are critical to solving?

Evan calls out three main reasons why scheduling optimization problems can be challenging.

“Schedules are everywhere and almost always very complex,” states Evan. “Many organizations have entire scheduling departments, and most of the time, a scheduler has to sit there for 45 minutes every time they create a schedule to find something that works, let alone something that optimizes multiple implicit objectives. Because objectives are typically implicit, it’s hard to realize that you may juggle 10 or 20 different objectives when you build a schedule.”

“Additionally, the constraints that one tries to abide by can be very nuanced. For example, you might not be allowed to schedule two different types of events back to back,” Evan explains. “Events requiring a scarce resource might not be able to be scheduled simultaneously. Or, maybe Joe and Bob might not work well together, or they have the same skillset, so maybe you should put them on different shifts. The list of constraints can go on and on with scheduling problems.”

“Lastly, the number of possible schedules you could try is often astronomical,” Evan says. “You could look at a schedule like shuffling a deck of cards. As mentioned, a schedule is just a sequence. A deck of cards has likely never been shuffled the same way twice. So if you want to create an optimal schedule that abides by all your constraints, you can’t do that without some sort of algorithm helping you out.”

#### 6. What’s the coolest thing you have seen with a scheduling optimization solution?

Evan’s answer can be found in the world of sports, such as the NFL or the World Cup, which rely on schedules for teams to play each other.

“In the NFL, you have 32 teams and an 18-week season,” he says. “Seems simple, but you also have all of these weird constraints and objectives that come into play like stadium conflicts, or a rule that you can’t play more than two road games against opposing teams who are coming off their bye week, or the objective to maximize the number of late-season division games.”

This is a super interesting, high-profile scheduling problem – and the NFL uses optimization to get it done!

#### 7. What are the different techniques and most promising use cases associated with this technology? Which industries can benefit?

Evan believes there is a lot of content out there around ML techniques, but from an optimization standpoint, there are merely a few. Below, he lists them in order of complexity:

- The first is heuristics. We’d start here with simple rules-based techniques that are well-known for providing good starting solutions to an optimization problem. “First in, first out” is a well-known heuristic in the food industry for making sure that the freshest food is always available.
- The second is meta-heuristic-based custom algorithms. There are different classes of algorithmic approaches that you can implement to solve an optimization problem. These can’t guarantee you have an optimal solution but will get you a really good solution quickly. A lot of these are based on optimization that happens in nature. Evolution and genetic traits that are passed down are optimizations that happen in your own body, as an example. You can use the same concept of genetics to solve all sorts of other optimization problems.
- The last is mixed-integer programming, which covers a range of algorithmic approaches. At a high level, you are defining decisions, objectives, and constraints in purely mathematical terms and are able to guarantee an optimal solution. So you’ll want to use this approach if it’s absolutely critical you aren’t leaving benefits on the table, whether that is in the form of things like monetary savings or time savings.

“In terms of which industries can benefit, I would say any industry where you’ve hired multiple people to bang their heads against the wall to find a good way to allocate resources and come up with a schedule,” Evan laughs. “Which I would say is most industries.”

#### 8. How do you think scheduling optimization ties into other deep learning/machine learning applications?

“There is definitely an opening for reinforcement learning to come into play to help solve really complex scheduling problems,” answers Evan. “It’s something we’ve done in-house research on, and I think it would be really cool to start implementing within a commercial setting.”

#### 9. Why is Mosaic so well-positioned to help with scheduling optimization use cases? What sets Mosaic apart?

“I think Mosaic is in a great position because we have a lot of folks in-house with a background in operations research and optimization,” Evan says. “We’ve done a ton of work in that space historically. And then we also have a powerhouse of a data science team that has a ton of experience working on really interesting ML use cases.”

Unlike the competition, Evan adds that Mosaic is in a unique and powerful position where the company has both skillsets in-house. Many traditional OR consulting firms do not possess in-house ML expertise, while many data science teams are only focused on ML and not optimization.

“We’re definitely in a great position from a resourcing standpoint. You don’t have to go to two places to solve the same problem.”

#### 10. Where do you see the future of mathematical optimization going? How does Mosaic play into this?

“I think the future of optimization is heavily dependent on the ability of the OR world to ride the coattails of the machine learning and AI world,” Evan speculates. “I think the technology is there, and it’s honestly more of a marketing problem.”

Evan comments on how he is starting to see a lot of teams investing in individuals with an optimization background and how data science programs at schools are adding optimization courses into their curriculum.

“So it’s definitely an exciting time for me as someone who lives in both worlds,” Evan concludes. “When I first started pushing the idea of integrating ML and optimization three or four years ago, I thought I was the only one, and it’s really cool to see companies in both fields sort of repositioning themselves and more people jumping on board.”

Without a doubt, the future of optimization looks more exciting than ever – especially for passionate individuals like Evan, who are playing their part.