Modern pricing in the revenue manage­ment environ­ment

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Tradi­tio­nally, offer prices for products or services are charged on the basis of the costs incurred, plus a target margin. Since the end of the last century, there has been a second approach to setting offer prices: How much is a customer willing to pay for a product or service? In the best case scenario, this price covers the costs incurred and also includes the targeted margin. The driving force behind this develo­p­ment was passenger trans­por­ta­tion by air. Due to the increase in so-called low-cost airlines, the renowned airlines were forced into action and had to come up with an approach to cover their costs and still be compe­ti­tive with their rivals. The idea was that, for example, business trave­lers who decide to travel at short notice pay more money for a ticket than city trave­lers with a long planning horizon. Today, this idea is sprea­ding to diffe­rent indus­tries and products such as hotel accom­mo­da­tion, rental cars and freight trans­por­ta­tion. The central question of the approach is how much a specific customer or customer group is prepared to pay for a product or service.

Reasons for accep­table prices vary greatly depen­ding on the industry and customer. In passenger trans­por­ta­tion or, more generally, in the tourism industry, it is certainly the lead time of the booking, flexi­bi­lity, cancel­la­tion condi­tions, additional services such as catering and other influences. An exact indivi­dual accep­tance proba­bi­lity depen­ding on all influences incl. of the price cannot be calcu­lated exactly. Even for a specific person, the weighting of the influences can change between two days. If, for example, the weather forecast deterio­rates, the likeli­hood of last-minute city trave­lers buying tickets decreases. A reduc­tion in price could neutra­lize the influence, but an upgrade to a diffe­rent class of trans­port or room size could also influence the decision.

The task of a Data Scien­tist (m/f/d) is to estimate indivi­dual accep­tance proba­bi­li­ties for a customer or customer group from histo­rical transac­tion data, depen­ding on all available infor­ma­tion. The accep­tance proba­bi­li­ties as a function of the price, taking all influences into account, are referred to as the price sensi­ti­vity curve. This generally has an S-shaped (sigmoid) course.

Moderne Preisgestaltung im Umfeld von Revenue Management

An example of the curve shown is a service company that places orders with trade­speople. In the case of a product price, the curve would have to be mirrored so that low prices lead to a high proba­bi­lity of accep­tance and high prices to a low proba­bi­lity.

The curve can be mapped using a multi­di­men­sional (non-linear) regres­sion model: a function is sought that maps the influen­cing charac­te­ristics in relation to the target variable (or also in relation to several target varia­bles) and minimizes the devia­tions from the target variable actually measured. This is known as super­vised learning. In our case, the target variable would be the proba­bi­lity of accep­tance and the influen­cing charac­te­ristics of all infor­ma­tion (inclu­ding the price) available in the transac­tion data and in the customer data. There is only one problem: the target size is unknown. Although we have the infor­ma­tion for each offer as to whether it was accepted or not, we do not know how far the offer price was from the customer’s accep­tance thres­hold. To solve the problem, we change the target variable to the binary charac­te­ristic accep­tance / rejec­tion. This gives us a so-called logistic regres­sion model, which we can train. What is missing now, however, are the required accep­tance proba­bi­li­ties.

To obtain these, we change the solution method again. By using the binary target variable accep­tance / rejec­tion, we can also model the assign­ment of a data set to one of the two classes accep­tance or rejec­tion instead of the regres­sion curve – a classi­fi­ca­tion problem. Similar to regres­sion, the classes are ordered in such a way that the devia­tions between the actual assump­tion behavior and the model are minimal. In mathe­ma­tics, there are proven measures for the error of a model. The best known is probably the root of the mean square error over all data sets. With the goal that we somehow need a proba­bi­lity that a specific combi­na­tion of charac­te­ristics will lead to an accep­tance of the offer, we choose the cross entropy as an error measure instead. The cross entropy compares an empirical with a theore­tical distri­bu­tion and returns not only the class assign­ment, but also the proba­bi­li­ties that a combi­na­tion of charac­te­ristics belongs to one of the two classes. We can inter­pret this proba­bi­lity as the proba­bi­lity of accep­tance.

There is another peculia­rity within our task: accep­tance proba­bi­li­ties should not fall with rising prices, all other things being equal. We there­fore need a monoto­ni­city criterion which ensures that if a charac­te­ristic increases, the target value also increases or at least does not decrease (this also applies to decre­asing charac­te­ristics).

One method that fulfills all of the above requi­re­ments is a deep lattice network, which I described

in another post in this blog

 in another post in this blog. After training the network, in which values are estimated for the variable parame­ters of the model on the basis of training data, the available infor­ma­tion on a current offer, inclu­ding the current price, can be used as a basis for the calcu­la­tion. of the offered price and incl. infor­ma­tion about the poten­tial customer, a proba­bi­lity of accep­tance can be estimated. If the price is varied while other charac­te­ristics remain constant, the accep­tance proba­bi­lity is extended to a price sensi­ti­vity curve. I will present an example of the appli­ca­tion in another post in this blog in this blog.

The curve must be used to decide what proba­bi­lity of accep­tance is expected from the offering company. Let us return to the example of the service company that places orders with trade­speople. If, for example, you assume an accep­tance proba­bi­lity of 50%, the craft­sman will accept 50% of the order and reject 50%. If you want to increase the proba­bi­lity of accep­tance (e.g. because there are only a few trade­speople with the required quali­fi­ca­tions or because the trade­sperson is known from experi­ence to deliver work of a very high quality), the price and thus the proba­bi­lity of accep­tance must be increased. On the other hand, you may be lucky and the tradesman is currently under­uti­lized and accepts the job even if the price quoted has a 40% proba­bi­lity of accep­tance. We are there­fore dealing with an optimiza­tion problem here, which we have solved, for example, in a research project funded by the mFund using artifi­cial intel­li­gence approa­ches.

Picture of Björn Piepenburg

Björn Piepen­burg

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