# Mathematical models for optimal coverage of emergency services

Providing proper care in time in emergency situations. This is what emergency services stand for. On 6 June mathematician Pieter van den Berg defends his PhD thesis at TU Delft. He developed models for optimising the logistics of emergency response vehicles.

Publication date: 06-06-2016

Providing proper care in time in emergency situations. This is what emergency services stand for. On 6 June mathematician Pieter van den Berg defends his PhD thesis at TU Delft. He developed models for optimising the logistics of emergency response vehicles. In his models he focuses on the  location of the stations, routing of non-emergency rides (for ambulance services) and shift scheduling. "By quantifying the process we can show that making small changes can lead to a better quality without adding capacity." Part of this research was conducted at Centrum Wiskunde & Informatica (CWI).

For his thesis Pieter van den Berg studied various emergency services. In the Netherlands he looked at ambulance services and fire brigades. 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 providing help fast in emergency situations."

Optimal distribution of ambulances
For the ambulance services Van den Berg developed a model that shows how ambulances can be distributed within a safety zone for the best coverage. Van den Berg: "An ambulance is  about half of the time on the road. 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 at night there is less traffic than during the day."

Tool for scheduled rides
In addition to emergency care, ambulances also have to accommodate planned transport of non-emergency patients between healthcare institutions. For these planned rides, Van den Berg developed a tool that allows ambulance services to schedule rides 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 meet the demand. When a regular ambulancehas to be used for a planned ride, this  has obviously a direct impact on the coverage."

Higher quality
Van den Berg also analysed the 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." Subsequently, Van den Berg included 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 slightly without negatively affecting service levels. However, due to the size of the area a large portion of daytime capacity is also needed at night.

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 positioning of fire brigade equipment and personnel."