[MUSIC] Hello and welcome to the module on aviation management. Before we dive into the specific topics, I'd like to very briefly introduce myself so you know which direction I'm coming from. I started out very early while I was still at school listening to my first mathematics lectures on very, very abstract mathematics. Which are very much fancy at the time after this I went to England to study mathematics properly. And during my studies I started to more and more emphasize that I need to see the application of what I'm studying. And so I started to focus on optimization and statistics for example. Once I finished my degree, I went to Ireland to IBM for three months where I did an internship which had a very close connection to this module as we see in a moment. More importantly though, gave her first introduction to machine learning techniques, which I then took along for my further career. After this, I went back to München and basically stayed there since then. I did my PhD in 2018 on a combination of operations research and machine learning and started my junior professorship on operations research and prescriptive analytics. In May this year, which in case you're watching this in the future is 2021. I'm not an expert on aviation. I'm an expert on various kinds of mathematical techniques that can be used for applications. And today we're discussing aviation management through this perspective. So what are you going to hear about? Well, we're first going to talk about some of the problems you might be facing and embed them in the processes of say an airline on airport. And then we're going to abstract this to three core approaches to these problems and you will have a section on all of these. So we have prediction optimization and control at the very last section. We are then going to take a broader look at all of this. And look at the very important topic of accessibility at least very briefly and then summarize everything and I'll give you some pointers on where to go next. What are typical problems you might be facing in aviation management? Well, the first one I picked was fleet assignment. Imagine from which airport you want to fly as airline and roughly how many people want to fly there. Your next task will be to assign various aircraft types or models to each connection. And you can imagine it's not a quite trivial problem because you have to for example. Consider that certain types can only fly certain distances like long range or short range. Or you have to accommodate a certain number of passengers all the while keeping your own revenue in mind. A similar problem that's even more complicated would be crew scheduling. Once we know which aircraft is flying from where to where and when we now need to assign our cabin crew and flight personnel to each flight. And this is even more complex because you not only have the very obvious problems. Like if you fly a crew from München to New York, the same crew can't fly an hour later from London to Berlin. But also you have certain restrictions put in place by for example, the law that people are only allowed to fly a certain number of hours on a given day, week or month. I need to consider all of this and in addition they might change regularly and so you have to have a solution that can adapt to that easily. This is why this is one of the problems that started very much in literature and we can find a whole variety of approaches to this. So how do we embed these into a whole process for the airline. While the airline would start by first figuring out where to fly from and to when, how often for how many people. So the flights schedule, once you have the flight schedule, then we get the flight assignment that we've just discussed. But before we assign the cruise, we need another step in between and that's yet another problem to solve. And that is the aircraft routing problem, meaning we know where we want to fly from, a tune with what type of aircraft. However, we still have to assign the specific tails meaning which aircraft is exactly flying from where to where. And again, we get a lot of site constraints here, for example, regular maintenance for aircraft that can only be done in specific airports. So that needs to be taken into consideration as well. And then once we've done that, we can finally do the crew scheduling now for an airport things are even more complex. And we just pick out a very small example here. And the most well known one should be gate assignment or gate scheduling, meaning figuring out which gate a certain aircraft should be de boarding and boarding it. And again you have to take into consideration things like walking distances for connecting flights. The size of the gate, the destination, for example, if you're flying in a European, there might be a different security measure than flying to the States. And so you need to consider all of this in your planning and there are a lot of things that depend on this from then on. One example would be going from gate assignment to then bus planning, if your parking position is not at the gate. But further out in the field, you would have to schedule busses to take passengers there. And once that has happened, you can then assign personnel to security points, the busses and so on and so forth for the airport. This is only a small small part because there are many, many more processes that inter with with this one. But I think for now this should be enough. We can't discuss all the specific problems today. So we're going to abstract these to three classes of problems. All of them fall into the first one is prediction, meaning we want to somehow estimate future values. We've seen an example in the flight planning, we need to estimate how many people roughly want to go from A to B. And there are two basic approaches. We can either go database or model based, but we look into more details in this, in the respecting sector. Another problem classes, optimization. These two should be fairly obvious given what we've just discussed optimizations. For example, fleet and crew assignments. We want to find some kind of ideal static values to variables. And again, we were going to look at different methods of approaching this. The basic to being exact and heuristic on methods. The third category is maybe a little bit more non obvious compared to the other two and that is optimal control. Why optimal control? Well, we're seeing a specific example why we might need this. However, the basic distinction to optimization is that we now want to find ideal dynamic values. And that might make the solution of certain problems much easier. And now we're going to look at all of these three in detail. [MUSIC]