Estima­tion of a customer-specific offer accep­tance proba­bi­lity

Share post:

In this post, a modern approach is presented to derive an indivi­dual proba­bi­lity curve for the accep­tance of an offer from histo­rical accepted and rejected transac­tion data, depen­ding on diffe­rent charac­te­ristics, inclu­ding the number of accepted and rejected transac­tions. of the offer price and incl. of features to diffe­ren­tiate between custo­mers. The proce­dure is illus­trated using an example of the awarding of trans­port contracts by a freight forwarder. I have already described the background to the pricing model and the solution algorithm used in two other posts in this blog.

Let’s assume you want to send a larger shipment in the form of one or more pallets. You commis­sion a freight forwarder to arrange the order with a suitable trans­port company, which demands a so-called shipper price from you. After conclu­ding a contract with you, a forwar­ding agent usually contacts a trans­port company by telephone and makes a price proposal for the trans­port, which is usually renego­tiated. The deter­mi­na­tion of an indivi­dual price taking into account all infor­ma­tion about the shipment, the tour and the trans­port company for a proba­bi­lity of accep­tance of the shipment by the trans­port company expected by the forwar­ding agent is the content of this article.

The infor­ma­tion available on the histo­rical offers consists of 18 charac­te­ristics, which are used to describe the acceptance/rejection target variable:

  • Trans­por­ta­tion price actually paid
  • Number of indivi­dual shipments on the trans­port (shipments are bundled to improve the utiliza­tion of a truck)
  • Total distance of the trans­port
  • Sum of the loading meters (loading meters are a measure of the trans­port volume and describe the load quantity that can be trans­ported on one meter of loading area of the trans­porter)
  • Total weight of the trans­port
  • Average geocoor­di­nates of the loading and unloa­ding points (each consis­ting of latitude and longi­tude)
  • Month of depar­ture of the trans­port
  • Year of depar­ture of the trans­port
  • Weekday of depar­ture of the trans­port
  • Number of working days in the week of depar­ture of the trans­port (inclu­ding bridging days)
  • Distance between the depar­ture of the trans­port and the next public holiday
  • Duration of the trans­port (incl. loading and unloa­ding times, waiting times and breaks)
  • Outward or return journey for the trans­port company (are the loading points closer to the branch of the trans­port company or the unloa­ding points)
  • minimum distance from the trans­port company’s branch to a loading or unloa­ding point
  • Loading and unloa­ding points in the typical action window of the trans­port company

A deep lattice network was used to estab­lish the functional relati­onship between the charac­te­ristics and the target variable and the cross entropy was used as the error function. This not only provides the class assign­ment for a combi­na­tion of charac­te­ristics, but also a proba­bi­lity for a correct assign­ment, which can be inter­preted as an accep­tance proba­bi­lity.

For the valida­tion of the model and the training results, a standard shipment (green curves) was defined, which leads from an econo­mic­ally strong region in Germany to another econo­mic­ally strong region. The distance is around 350 kilome­ters. In the follo­wing figures, one charac­te­ristic was varied as an example; the price on the x-axis is also varied in each diagram in order to expand the accep­tance proba­bi­li­ties into proba­bi­lity curves. It should be noted in the diagrams that the influences of the charac­te­ristics only apply to the selected example. Other
Tour parame­ters will lead to other influences.

It can be seen that the increase in shipments on a trans­port has a major influence on the proba­bi­lity of accep­tance. In the case of loading meters, small and large volumes lead to higher trans­port prices. Low weights lead to lower prices; however, above a certain weight there no longer seems to be any influence. The year and month have little influence on the proba­bi­lity of accep­tance. The day of the week shows that Thursday is the most expen­sive and Wednesday the cheapest.

The curves shown can be used to select the appro­priate trans­port company. They can also be used as a basis for deter­mi­ning an offer price. Assuming that the trans­port has a suffi­ci­ently long lead time, a trans­port company can be offered a price with an accep­tance proba­bi­lity of 50% or less. If the deadline for trans­por­ta­tion is approa­ching and no trans­port company has yet accepted, the proba­bi­lity of accep­tance must be increased and with it the price. Another reason could be a parti­cu­larly suitable trans­port company or a parti­cu­larly reliable company with a good service. The decision for the right trans­port company and the right price can be made by an expert or by artifi­cial intel­li­gence, which we have already successfully tested in a research project funded by the mFund.

Schätzung einer kundenspezifischen Angebotsannahmewahrscheinlichkeit

It can be seen that the increase in shipments on a trans­port has a major influence on the proba­bi­lity of accep­tance. In the case of loading meters, small and large volumes lead to higher trans­port prices. Low weights lead to lower prices; however, above a certain weight there no longer seems to be any influence. The year and month have little influence on the proba­bi­lity of accep­tance. The day of the week shows that Thursday is the most expen­sive and Wednesday the cheapest.

The curves shown can be used to select the appro­priate trans­port company. They can also be used as a basis for deter­mi­ning an offer price. Assuming that the trans­port has a suffi­ci­ently long lead time, a trans­port company can be offered a price with an accep­tance proba­bi­lity of 50% or less. If the deadline for trans­por­ta­tion is approa­ching and no trans­port company has yet accepted, the proba­bi­lity of accep­tance must be increased and with it the price. Another reason could be a parti­cu­larly suitable trans­port company or a parti­cu­larly reliable company with a good service. The decision for the right trans­port company and the right price can be made by an expert or by artifi­cial intel­li­gence, which we have already successfully tested in a research project funded by the mFund.

Picture of Björn Piepenburg

Björn Piepen­burg

Project request

Thank you for your interest in m²hycon’s services. We look forward to hearing about your project and attach great importance to providing you with detailed advice.

We store and use the data you enter in the form exclusively for processing your request. Your data is transmitted in encrypted form. We process your personal data in accordance with our privacy policy.