Mathematical models for optimal coverage of emergency response services

News - 02 June 2016

Providing the right care promptly in emergency situations. This is what emergency services stand for. On 6 June, the doctoral defence ceremony of mathematician Pieter van den Berg will take place at TU Delft. He developed models for optimising the logistics of emergency response vehicles. In his models he focuses on the following aspects: station location, routing of non-emergency journeys (for ambulance services) and shift scheduling. 'By quantifying the process we can show that making small changes can lead to better quality without adding capacity.'

For his dissertation, Pieter van den Berg conducted research on various emergency services. In the Netherlands, he looked at ambulance services and fire services. In Norway and Canada he developed models for air ambulance services. Van den Berg: 'These services differ tremendously, but they all have one important thing in common: they share the task of delivering fast help in emergency situations.'

Optimal distribution of ambulances

For the ambulance services Van den Berg developed a model that indicates how to optimally distribute ambulances within a single safety zone in order to provide best coverage. Van den Berg: 'An ambulance is on the road approximately half of the time. This means that every ambulance station needs several ambulances. In addition, time-dependent factors also play a role: there is a lot of variation throughout the day, and less traffic at night than during the day.' 
Tool for planned rides
In addition to emergency care, ambulances also have to accommodate planned transport of non-emergency patients from one healthcare institution to another. For these planned journeys, Van den Berg developed a tool that allows ambulance services to plan journeys as efficiently as possible.  Van den Berg: 'Most requests for a planned journey come in around 11 am. The special care ambulances intended for these journeys cannot always handle the demand. But having to use a regular ambulance for a planned journey immediately affects coverage.'

Better quality

Van den Berg also analysed the shift schedules of these so-called care ambulances. Van den Berg: 'The schedule analysis revealed that small changes can lead to better quality without adding capacity.' Van den Berg went on to include the shift schedules of the Canadian air ambulance service in Ontario in his research. This revealed that it is possible to reduce the number of services per day without negatively affecting the level of service. However, due to the size of the area, a large portion of daytime capacity is also needed at night.' 

Location of fire stations

For the fire brigade, Van den Berg developed a model for optimal distribution of fire engines within a given safety zone. He explains: 'This model takes into account some aspects specific to the fire brigade, such as the distinction between volunteer and professional fire services, and the various vehicles used by the fire brigade. This model can contribute to making strategic decisions regarding the location of fire stations. ' 

More information

Pieter van den Berg's doctoral defence ceremony will take place on 6 June at TU Delft, with his dissertation entitled:  Logistics of emergency response vehicles. Facility location, routing, and shift scheduling. His promotors are Professor K.I. Aardal (TU Delft) and Professor R. D. Van der Mei (CWI and VU Amsterdam). Van den Berg conducted his research within the Delft Faculty of Electrical Engineering, Mathematics and Computer Science.



Pieter van den Berg, +31 (0)15 27 86266, 
Juliette Fhij,Communication Advisor, Faculty of EEMCS, TU Delft, +31 (0)15 27 89252, 


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