# PROS Science Showcase Using Competitors' Prices to Improve Revenue Management & Pricing

Our scientists have been busy over the last year, and we have a lot to share. PROS provides insight into the work conducted recently with Etihad surrounding our willingness-to-pay model. This is an excellent opportunity for airline revenue managers to gain an overview of how the data was used and the important outcomes from the research.

**About the Speakers**

**Ravi Kumar** serves as Lead Scientist at PROS responsible for the research and development of Reinforcement Learning methods for dynamic pricing, methods for demand forecasting and consumer choice modeling with applications to airline revenue management, ancillary pricing and offer optimization. His research interests are in the area of stochastic modeling, statistical inference, optimization, reinforcement learning and Markov decision processes with applications in the areas of revenue management, pricing and energy efficient operation of computing systems providing SaaS solutions.

**Siva Arunachalam** is a Revenue Management professional with 12 years of experience at Etihad Airways. He has deep expertise in operations research, forecasting and demand planning.Arunachalam is a committed professional with extensive project experience from concept to development and implementation. He is a highly action-oriented individual with a strong ability to communicate effectively with technology, executive and business audiences.

**Full Transcript**

**Ravi Kumar:** Hello, everyone. My name is Ravi Kumar. And welcome to the prime PROS Science Showcase. Today, we are going to talk about how to use competitive price to improve Revenue Management and pricing. We have done a lot of work on this over the past year and a half with the Siva from Etihad. So he will be my co-presenter in this talk. So let's get started. So it's part of what we are going to talk about. We are going to give a brief background and motivation related to this work. Some of the challenges which make adding competitive pricing and Revenue Management difficult. And then we are going to dive a little bit deeper into the mathematical details of how to model these computer of demand models. And then we are going to talk about the studies that we have, extensive studies we have conducted with Etihad on figuring out what benefits we can obtain from such models on real data set. So to start you off, let me hand it over to my co-presenter Siva from Etihad....

**Siva Krishnan Arunachalam: **Thank you Ravi, good day, everyone, I hope you're all enjoying the virtual PROS Outperform conference, which is running for the second year successfully. As Ravi introduce I'm Siva, I work in Etihad Airways Senior Manager Operations Research. So coming to the research in particular, this has been a three year journey and something that we've worked extremely closely with PROS, as always, co-innovating and collaborating in the space of Revenue Management and offer management. So on this study in particular, when we think about enhancing the Revenue Management systems, it's already in a mature state and you always start to think of what's next. So you add the pricing complexity into it, then you begin to see with the technology advancements, there are far more things that you can have an evolution in that space. So one thing that comes to you quickly is this data. And when you look at data, there are a lot of non-traditional data sources that the Revenue Management systems can benefit. For example, one thinks of travel trends from social media like think about Twitter data. Think about Facebook and think about many such things. We are talking more technically about the airline scenario where what's the average delay that's ongoing between aircrafts? What sort of schedule information that's happening in the outside world? But besides all this, you know, US airline colleagues would agree with me that one of the most important third party data that. You could say it, give a bang for the buck is the competitive price information. This is something that's kind of, you know, in the breadth and depth of every single RM analyst who is looking at the data and market strategy time and again. So handling competitive effects from a model perspective is quite important and something that we all dream about. How do we do it? So thankfully, what are we going to see here is an attempt where we have solved it in an interesting way and more importantly, you know, in a very successful way, I would say. So when we look at these processes in terms of how this is managed today in the airline, these are done largely manually or a lot of offline analytics being done by the analytics divisions in each airline. And then the information is fed back to the analyst, who then decides how do they handle it in each of their markets, starting with, let's say, the market analysis on competition, then to determine what sort of benchmark they have for their carrier, where they need to also review the product positioning and the brand offering in place, then to finally look at what sort of prices I'm actually influencing using various different tools in the space. So when one looks at that in that space, you start looking at the very detail the analysts and mostly the demand analysts in the organization are trying to figure out what's the impact of a change in competitive price or brand position, which is finally reflected in the price on the airlines own airlines observe demand, then they need to start thinking about answering questions like, you know, the demand that I observe, is it, is it a low demand? Is this observed because of my competitive position? Are they trying to undercut me in this? Did I not receive my market share because of the competitive position in the last one or two weeks? Did I see this in all channels now knowing this information, do I, as an analyst, go about influencing my demand? Or am I also in a similar situation on this flight? And you know, by how much am I? How much do I need to feed my system for a change that I've observed with competitor? So these are quite tacky for an analyst in nature. And finally, when you look at the market price that they need to kind of adjust they are looking at the availability in most scenarios where they actually can influence. So in this example, if you look at, you know, the lowest fare, if I'm offering is 350 and the competitive air is 320. The question begs in the analyst mind, should I match it or should I ignore or should I stay with a higher price? And if I match with the competitor, do they usually respond to that? And then you could think of a cyclical reaction and knock on effect. So clearly, the slide outlines to you that introducing some automation around these processes would largely benefit most of the analysts in this process and help them to make better decisions in the space. So that's something that we tried to highlight. And if you've seen in this slide, when when one does a generic shopping in Google or elsewhere, you quickly see a lot of the competitor information for the airline, as well as what the competitors positioning. So in this changed environment, with what COVID has brought to all of us, it made us think in a completely new way. How a competitive effect will play out is even more significant for an airline to absorb. Is it going to make a competitive effort to be stronger? Or is it going to be weaker? That's it's an interesting scene. So if you see on the left, I just did a Google search on many markets and you would see on many of these markets, the airline seems to be indicating a strong inclination on matching, right. Maybe by coincidence here. But if you try to make some sense overall, you see that with covid, the demand has produced something we all acknowledge and all of the airlines are competing to get the same diminished demand. And moreover, on a large faction, if you think about it, it's more of a early leisure demand or you have business demand, which have more and more and more over time diminished in the space because of, you know, thanks to the Zoom that we are all actually talking now. We have not attending the PROS conference this year face to face. We have chosen to sort of do this, you know, given all the restrictions, in a virtual forum. So this explains even more that, you know, the business traffic is not back it and not definitely not back in the way that we have seen it before. So it does seem that in this change environment, competitive effects may become even more important, and it'll be even more important for airlines to actually figure out when to actually stop doing price matching because there are more in the offering that you don't just look at price, you look at the brand overall. And there are many things strategically for an airline to say, you know, have the book sufficiently in the way we think we should be profitable and future trends. So with a lot of changes in the airline operating scenario and changes in manpower dynamic competition, our Revenue Management model is something strongly called for.

**Siva Krishnan Arunachalam:** So I'm going to take you through when one tries to solve. The problem of this nature, what sort of complexity actually arise, so it starts with challenges, and there are far more research assumptions that one need to make because the information is not the same in a Revenue Management system, with third party data sort of integrating overall. So let's look at some of the challenges when incorporating competitive information. So the first and foremost challenge that comes in the mind when related to competitive prices is that we see that the information is not the same what you receive from various sources. So a lot of the times. You're always seeing a miss for certain entities. And for certain durations like you observe here, there are many price points missing. It's not that the computer was never available. It could be that the data of sanity that you get from the feeds that you receive, but it could be various sources why something is missing in that place. And secondly, when you see pricing includes a lot more dimensions that than what item and availability systems typically manage. So there is a lot that the airline needs to decide, or the model needs to decide how to aggregate the right set of dimensions. And for the right set of competing products. Right so when I mean, we all understand Fibonacci series and everything in mathematics, where if you add one more dimensions, the whole equation explodes to put it in simple terms. Finally, when you look at, you also need to look at how to identify the right price to use. Right? Is it is it just a passenger only? Or is it with some brands and the type of passenger codes? All these and so on increases the complexity. So for all this, there is a strong requirement that we need to have a process in place to improve the data quality input. And, you know, over and over, we need to assess and refine it and have analytical solutions that paves the way for the rich input data that will always come to be modeled in a better way, where the output is more reliable and, you know, not leave the model in a state of outcome where there's not much of information in the space. So now that let's say we have this large amount of data. We've looked at, how we should start thinking about modeling this, this piece of work. In fact, when we looked at quite a few markets that we wanted to present the PROS in this space, it wasn't easy for us to provide streamlined data to start with where the analysis could be carried out. So all these challenges and assumptions are something that we had to work through. And in terms of data, it's a huge amount of data and we talk about having competitive prices across the calendar horizon for a departure date. It's huge. And when we're trying to assess that from a model perspective, we are most exploding. But thanks to big data and improvements in that space, these are challenges and assumptions are something that you know, are reasonably met. Then, you know, we open to the next set of challenges, which are, you know, you rightly look at the microeconomic theory and to say, how do we actually model right? Modeling this is probably then the biggest challenge once you are able to sort out the data in the competition landscape. So one assumption that we did consider in this process is, you know, when you're trying to determine the optimal pricing policies, we do not consider the game theoretical effects and equilibrium pricing because that sort of limits a lot of the things that we try to do with the model. And we think the way the market behaves, these sort of concepts are, you know, sort of being moved away from or in the evolution in that space. So in the models themselves, so when we look at the typical model on demand and price relationship and a simple exponential model in this space, one quickly realized that these models are very hard to fit from a data perspective, as we do see non-zero demand, you know, when we price higher than the competitor because there are various other obvious reasons that the customer is influenced that is not captured in data, for example, right? So the model cannot assume that, you know, when I'm priced higher than competition, I get nothing. Many an analysis even in, you know, various different simulations in the industry do show us that the results are different in that space. So there is a large like you can't drop a large amount of data which does not follow. This is just choice behavior, and that's the point that we're trying to highlight here. So from here on, you would see that how? And what type of models that we look at and what are the type of vessels that we have seen in this space? So to know more on the advanced way of how we solve this particular problem. I now hand over back to Ravi to discuss the various models and how we solve for this opportunity that has been in the industry for a while.

**Ravi Kumar:** Thank you, Siva. That was really a great background and motivation for this work, and as Siva mentioned, we have collaborated extensively on refining these models over a year and a half with Etihad and the insights they have provided. And these backgrounds have shaped how we have developed these methodologies that I'm going to show and talk about next. So as Siva mentioned that, you know, modeling consumer behavior is a very important point to consider. And the models cannot be simplistic enough that as soon as you start pricing higher than the competitor, your demand goes down to zero. So there is some need for modeling complex consumer choice behavior. But at the same time, we cannot make the models that complex that we cannot even estimate or forecast them. So there is a balancing act that needs to be performed here. So in view of this, we consider the model where the overall demand volume is divided into two kind of customer populations. There's one customer population, which is called the loyal customers, and these customers will prefer to buy from the airline of choice, even if the airline is pricing higher than the competitor. And this fraction is denoted by delta fraction. And then there is another kind of customers called flexible customers, and these are the customers who prefer to buy the lowest price in the market. So across various airlines and this fraction of customer is one denoted by 1 minus delta. In addition to this, we assume that both these kind of customer populations are fully price sensitive in a sense that they have a willingness to pay distribution that might be differentiated across the two customer population. So for the loyal customers, the willingness to pay is exponentially distributed with parameter alpha f whereas for flexible, it's exponentially distributed with parameter alpha L. This means that we can write the purchase probability given a price, which depends for either the loyal or flexible customer in this exponential form. Now, putting it all together, we get this sort of demand curve where lambda now denotes the overall market volume. So if everybody is pricing the lowest, what is the demand at which the market is going to saturate? That's lambda. And if the airline is pricing lower than the competitor, then they get both loyal and flexible kind of customers, right? But because they are price sensitive, we still get a downward sloping demand curve with this exponential form. And now, as soon as the airline starts pricing higher than the competitor, we see a discrete demand drop because we lose our flexible customers and all we have is our loyal customer population. Again, because they are price sensitive, we get a downward sloping curve, which is exponential in nature. So this demand model is realistic enough to capture some of the challenges Siva was mentioning. But at the same time, it is not complicated that we are introducing a lot of parameters and we cannot estimate it. Now, in addition to this model, which we call loyal market price model, which is shown on top panel here. We also work with another kind of model called a competitive price ratio model. So in this model, in contrast to the low oil market price build model where we have the discrete drop, when we start pricing higher than the competitor, the demand shifts more smoothly in response to how the competitor is pricing. In particular, as the competitor is increasing their prices, the demand curve is moving upwards, it's shifting upward. So for any given price, the airline is going to get more and more demand as the smoothly increasing demand as the competitor is increasing their price. The reason why this is called price ratio is that the interaction of my price to the airline price in the formula shown on bottom right comes in the form of this price ratio of my price to the competitor's price. And then there is a parameter called eta, which controls this elasticity, how they respond to my price and in this ratio of my price to the competitor's price. Now, in the science that we have developed, we have been able to enhance our willingness to pay forecaster to include estimation and forecasting for both these kind of models. So this means that, you know, in our willingness to pay forecasting previously, we were just estimating and forecasting the volume parameters, the price sensitivity parameters. But in addition, both these models also introduce parameters which control competitive effects, for example, the Delta parameter in the market price model or the eta parameter in the competitive price ratio model. So this is an additional parameter which needs to be estimated and forecasted. And we have been able to extend the science methodology for willingness to pay forecaster to include these effects. Now, another important factor when we are thinking about constructing an integrated solution for competitive air forecasting, some of the challenges Siva mentioned, right? Point to issues with data quality. The other thing is that we are including so many other dimensions. So on each market, there may be four or five customers. So we need and that leads to storage and computational related complexities. So that may also need the solution. So in this integrated solution, we design the competitive market analytics and signal generation model. And this module does first of all it, it deals with the data issue. That is, it tries to figure out what the data quality is. Where do I need to fill the missing prices? And these missing prices are filled through advanced algorithms like expectation, maximization and so on. In addition to this, this module also provides an analysis of the market through the analysts that may be handling them. So things like how is the distribution of various airline as well as competitive prices are in the market right? Or what is the correlation heatmap? That means which airline is prices are more correlated to me and which airline is maybe ignoring me and not following as much. Also, it gives a view into the historical pricing strategy that your competitors may have put in place. So what fraction of time in the history they were undercutting, what fraction of time they were matching me, and what fraction of time they were ignoring and over pricing? And this could have many dimensions. For example, in winter months, they might be ignoring me. But in the summer months, the competition strong. So this module is designed to give that insight to the analyst that about how the competitive landscape looks like. In addition to these analytics modules, one of the important tasks that this does is, as I mentioned, there could be many competitors in the market. So four or five what in our model, we compress all of these poses and construct a single statistic. And this is done by evaluating many statistics which are constructed of competitive price. For example, let's consider minimum of all, the price of all the competitors or which competitor is closest to me or individual competitors and things of that nature. So we evaluate 30 to 40 statistic and do an analysis to figure out, well, this is the competitive statistics which impacts my demand the most. And once we identify this, this statistic, we are we call it the competitive reference signal. This signal is then fed into the downstream systems. So, so for example, the enhanced willingness to pay forecaster takes this reference competitive signal along with bookings and other traditional co-variants, and then does the estimation and forecasting process, which can relate it to the models that I just presented to you earlier. And these can be then fed into the RM optimizer if you want to have the effect of competitive prices in the bid price creation. But in addition to that, and one of the very important tasks that also were mentioned is how to create a competitor aware real time pricing strategies. So you can feed these parameters, which are estimated by the model into the availability and the pricing system. And now, given the real time bid price and the actual competitive prices in real time, the model tells you what is the optimal strategy? Is it to undercut? Is it to match, is it to ignore? And if you do so, what is the right margin over bid price to charge? So what is the right competitor, a fair price that you should be charging? So all of this becomes now possible because of some of these models.

**Ravi Kumar:** So we have done extensive testing of the enhanced willingness to pay forecaster with Etihad and the data that they have provided. So I'm showing you an example of real data forecast for a particular market. The top panel is showing you the volume forecast. The middle panel is showing you the price sensitivity forecast and the bottom panel is showing you the competitive parameter forecast. So we have seen in all of these extensive testing that the forecast to produce performs very stably, and it captures the historical seasonality trends and patterns and forecast them reasonably well. So now, apart from doing all of this qualitative testing, we have also done extensive quantitative testing. So in particular, we have looked at how these competitive models improve forecast accuracy. To do that, we have taken the real data and we have divided it into training sets and test sets. We have trained our models on the training sets and then evaluated the forecast accuracy, constrain demand forecast, accuracy on the test sets. And what we find when we compare these models to our normal monopolistic willingness to pay forecaster is that whatever metrics that we have considered in these, for example, root mean squared error or mean absolute deviation or bias. The competitive willingness to pay forecaster improves performance on all of these statistics uniformly, and the improvement is statistically significant. What we have seen in our analysis is that the improvements that you can get range anywhere from 5 to 10 percent, depending on the markets. But these are statistically significant improvement that we saw in performing all of these tests. Now, apart from these forecast accuracy studies, as we mentioned that you can use the competitor of air demand models in constructing pricing policies. So in order to do that, typically given the real time bid price and the real time competitive price, one solves an optimization problem to maximize the expected margin contribution. So here the bid price is denoted by BP. The competitive price is pc, and you're trying to find a price which maximizes, given the demand model parameters, what price you should charge. Now, in the loyal, flexible model that we talked about, another interesting thing is it leads to very intuitive pricing policies. In particular, the kind of pricing policies lead to very natural things, like whether to undercut, match and ignore or price higher. Right so these are kind of policies that typically are intuitive and have been used in airline industries and other industries quite often. So I'm giving you an example from a real data. So for example, when your bid price is low, you have a lot of seats. Maybe the right thing to do is to undercut the competitor because you don't want to lose the flexible customer base. You still have a lot of seats remaining. In the medium or hybrid price situations, particularly hybrid price situations. When you have less seats remaining, you might want to, you know, only price for your loyal fraction. So you can start taking that risk that, OK, fine, I have sufficient seats booked and therefore I can start thinking of pricing just for my loyal fraction and ignore and price higher. So, you know, these competitive prices, competitive demand models can enable you to construct such pricing strategies.

**Ravi Kumar:** Another interesting aspect is related to the fact that, you know, so in this particular example, again, from a real data situation, everything is same, but we are trying to show you the effect impact that fraction of loyal customers have on pricing policy. So on the left panel, the fraction of loyal customers is 0.4. On the right panel, the fraction of loyal customers is 0.9. So quite high right. So the left panel, we have relatively lower amount of loyal customers. Now here we see given the same price in the two scenario, and other factors are also same. Competitive prices the same as well as the price elasticity parameters are the same in the situation where you have low fraction of loyal customers. The model is recommending you to match while in the high fraction loyal customer scenario. The model is recommending you to ignore and price higher for the loyal customers, right? Because you have a lot of loyal customers to in your demand. So these competitive demand models enable you to construct these competitive price over policies which tell you the right strategy, given the bid price and the real time competitive price, and also depending on the loyal fraction of customers. These policies give you a very refined estimate of what the pricing should be. So let me summarize the stock. So we considered this problem of how to incorporate competitive prices and Revenue Management and pricing. We try to make the case that the models that we need should be realistic enough to be useful. But at the same time, they cannot be as complex, that they cannot be estimated reliably and through the loyal, flexible and the price revenue model, we. Demonstrated that these models fit the bill in terms of being realistic, but at the same time, we have been able to construct willingness to pay for casting methodologies or enhance our willingness to pay forecaster to reliably and stably estimate the parameters for these models. And thanks to Etihad, we have been able to conduct and refine these models and conduct large scale data studies to demonstrate not only from the qualitative perspective, how these models can behave, but also from the quantitative perspective. We have shown that these models can provide you substantial benefits, both in terms of forecast accuracy as well as revenue performance. We have been able to write the paper in collaboration with Etihad on all of the things that we talked about, and this paper was published very recently in 2021 in the Journal of Revenue and Pricing Management. So if you are interested, I've given the link to that and please feel free to email either Siva or me if you and we can provide you a copy for the paper as well. So with that, I'll thank Siva and all of you for joining me for this session.