Frédéric Semet and his research team Inocs have a real passion for complex problems. Their aim is to use mathematics to find solutions capable of dealing with a range of constraints. Take airline tickets, for example: how should airlines set their ticket prices in order to ensure that they are sold at the highest possible price?
Simply raising all prices indiscriminately wouldn’t work, as this would only drive customers towards other companies. Purchasing mechanisms need to be understood in order to tackle this problem: what is the threshold price beyond which customers are likely to be put off? Is comfort an important enough factor for customers to be willing to pay more? How much more? What are the priorities for certain categories of passengers? Inocs provides solutions enabling companies to offer a pricing structure capable of dealing with all of these issues.
Security: a complex mathematical problem
Such constraints are exactly what the personnel in charge of security on the Lille metropolitan area (MEL) urban transport network, operated by Keolis, were faced with. There are two lines and 60 stations on the Transpole metro network, which transports more than 10 million passengers a month. The MEL, which made the decision to award the network management contract to Keolis, also set the company objectives with regard to security and atmosphere.
The Le Roux - Savary law grants enhanced powers to transport companies when it comes to tackling fraud and security issues, should the supervisory authority choose to allow this. “As a result, we now have dedicated teams - external service providers or Keolis employees - divided up into inspectors, security personnel and mediators”, explains Christophe Laousse, Head of the prevention unit. These agents travel around in pairs across the entire network, from when the metro starts running at 5.17am right up until the last train arrives at its terminus at 12.30am. However, as is stipulated in the contract signed with the council, these agents must be visible every 5 stations and respond within 5 minutes at any station on the network in the event of an issue arising. They must also be capable of responding in exceptional circumstances: installing security checkpoints in stations, public events, etc.
These schedules were previously compiled manually, with staff using their knowledge of the environment in order to ensure that agents could be present throughout the day on the network. Not exactly the perfect solution. “There is a real cost to malevolent acts: firstly, equipment repairs cost several hundred thousand euros each year, while also resulting in business interruption. What’s more, the MEL imposes penalties on us should they feel that we are failing to comply with the terms of our contract”, says Christophe Merlin, director of security and fraud prevention.
An algorithm designed to be flexible
Inocs and Keolis were brought together through Inria’s evaluation unit, the goal being to develop a new algorithm capable of resolving this fortnightly conundrum. “For 5 years now, we have been compiling detailed data on security and all atmosphere-related issues”, explains Nicolas Chausson, Head of the Observatory for Security and Fraud Prevention. “We record precise details as soon as one of our agents becomes aware of an incident”. The first step involved a mass sorting of this data in order to ensure that only relevant information was extracted. The researchers then used this dataset to predict requirements for security personnel. “We began by developing mathematical models using small datasets in order to arrive at the right solution together”, explains Frédéric Semet. “In the beginning everything was abstract, but using prototypes we were able to come up with an idea of what was needed to compile the new algorithm”, says Nicolas Chausson.
The partnership lasted nearly a year and a half, during which time the project was modified, corrected and amended before the ideal solution could be found: the best possible compromise between precision models and speed of execution. “This is the biggest difference between researchers, who are always keen to ensure that everything is perfect when it comes to projects, and operational teams, who need quick, effective solutions”, states Christophe Laousse. As it transpired, the perfect algorithm took 45 minutes to work, while the one that would eventually be used is capable of giving good results in 5 minutes. The way it works is that the algorithm assesses the database, taking reported incidents and atmosphere issues, staff and specific events into account in order to compile a schedule that is then delivered in the form of an Excel spreadsheet. The next stages of development will involve incorporating the tram network, another important mode of transport in the Lille metropolitan area, during the first half of 2019. Finally, agents will soon be able to make changes to their schedules in real-time, flagging up any unexpected events they may encounter over the course of a normal working day.
*Inocs is a joint Inria project team with the CRIStAL laboratory et l'Université Libre de Bruxelles (Centrale Lille, CNRS, University of Lille).