Deutsche Bahn (DB) was asked to propose a new timetable for its public transit contract in Toronto, where the algorithm used to determine the quality of the timetable was known. Naturally, the contracting authority also imposed a number of constraints to the timetables to meet their minimum operating standards. Therefore, DB approached Lynxx with the challenge to optimise an urban timetable for economic growth.
Optimisation of urban timetable
Industry, Data science, Capabilities
Deutsche Bahn (DB) was asked to propose a new timetable for its public transit in Toronto, where the algorithm used to determine the quality of the timetable was known. Naturally, the contracting authority also imposed a number of constraints to the timetables to meet their minimum operating standards.
Therefore, DB approached Lynxx with the challenge to optimize an urban timetable. The aim is to design a timetable in which – according to the wishes of the contracting government – optimizes specific characteristics (which are confidential and thus will not be shared here).
To test a timetable, different input types were considered each with its set of constraints. Optimizing this problem by hand would have been impossible given the amount of variables and potential combinations, so Lynxx used Operations Research (OR) models to tackle this issue. First of all, we determined the so-called ‘target function’ in order to fully understand how the different railway operating characteristics contributed to the target optimized output. Then, together with the DB team, we developed the model, which solved the optimization problem given the above-mentioned constraints, decision variables and objective values and produced the corresponding timetables.
We developed various timetable concepts in order to:
- Quickly get an indication of which type of scenarios were desirable
- Iterate with stakeholders which further input and output of the model is desired
- Gain insight into how different scenarios affect the target function
To achieve this, we organized biweekly workshops with the DB team to define different scenarios. That is, suppose we increase our input sensitivities and upgrade infrastructure at station X, and we reduce the available resources, then (1) what would the corresponding optimal timetable be, and (2) what is the value of the target function in this scenario?
By iteration of different scenarios, we have helped DB to develop a timetable that meets the requirements, is feasible with regard to resource inputs and optimizes the required outputs within these preconditions. This project helped DB win the Toronto tender.