Estima­tion of a customer-specific offer accep­tance proba­bi­lity

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.