# Let maths count: it can, and should, play a role in health care

Whether it is doctors’ rotas, the MRI scanner, distribution of beds or outpatient appointment scheduling, Zonderland offers practical solutions derived from mathematics. Her research was applied at Leiden University Medical Centre (LUMC). On 27 January, she will defend her thesis at the University of Twente.

“The aging population, the shrinking workforce and the current efficiency level in the majority of hospitals is making it difficult, if not impossible, to guarantee adequate care for the elderly and sick in our society”, maintains Maartje Zonderland. “Given what’s at stake, it’s hard to believe that, as a rule, hospitals avoid making explicit decisions on the allocation of scarce goods. Ad hoc responses are often given to problems which seem to arise spontaneously and are coupled with adverse side effects, such as the cancellation of patient treatments or extremely long waiting times.”

Solutions
Much of the research is based on issues arising on a daily basis at LUMC. One of the challenges, for example, was to develop an appointment schedule for the outpatient clinics which continued to restrict the waiting time for patients without an appointment, while maintaining an acceptable access time for those with appointments. The same scheduling could be applied to the popular care pathways, thereby creating a kind of ‘one-stop-shopping’ in the hospital: an excellent starting point, but sometimes difficult to combine with regular care. Maartje Zonderland has developed a queuing model for optimizing the flows of regular patients and those on a care pathway, thereby avoiding scheduling conflicts. She then went on to tackle timetabling for the MRI scanner. Scarce MRI capacity can only be divided equally when all medical departments can give a good estimate of the amount of scans they will be requiring.

Speed and planning
Intersecting patient flows in hospitals are always in conflict with one another. Emergency patients almost always take priority over planned patients. But how can you organize this without causing frustration? Take the following example. Every week, hospitals are confronted with an unknown quantity of semi-urgent patients requiring operating time. If there are large numbers of semi-urgent patients, the operations for scheduled patients will be cancelled. On the other hand, reserving operating theatres in advance for semi-urgent patients on a “just-in-case” basis can lead to under-utilization. Zonderland is able to regulate this planning process by using a queuing model to find a balance between these two factors.

The mathematical models presented in this thesis will enable hospitals to conduct a quantitative analysis of their capacity problems. Zonderland concludes that mathematical modelling can make a positive contribution to improving decision-making processes in health care.

Further information
Maartje Zonderland will defend her thesis on 27 January 2012 at 14:45 in the G.J. Berkhoffzaal in the Waaier Building at the University of Twente. For further information, or an electronic version of the thesis entitled ‘Curing the Queue’, please contact the science information officer Janneke van den Elshout on +31-(0)53-4895432.