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O.R. IN EVERYDAY LIFE

O.R. Inside Your 999 Call

A police force wanted to improve the response of its control room to emergency calls. A problem in dealing with 999 calls lies in the fact that they come in randomly, and the length of time taken to answer a call is variable. This is a classic queueing problem, queueing problems being characterised by random customer (or emergency call) arrivals and variable service times. Queueing problems are very common arising, of course in shops, banks, call centres, traffic lights, airport check-ins and so forth, but also in factories (where work in progress queues up on production lines) and many other contexts. Because of the fact that customer arrivals are random and service times variable, it is impossible to achieve 100% server utilisation without creating infinitely long queues, and so the problem of how to provide a satisfactory level of service consistent with efficiently utilising your servers is not an easy one, which is exactly why organisations that deal with queues need some O.R. inside.

A single queue with a single server is known as a simple queue, and there are excellent mathematical models that can be used to solve such problems very easily. But a police control room with several operators answering many calls, which queue up and are answered in rotation by the first available operator, is analogous to the kind of queue found in post offices, where customers form a single line and then go to the first available server. Queues of this kind being much more complicated and incapable of easy analytical solution, the usual approach is to build a simulation, in which the random arrival of customers, the variable service times and the workings of the queue are simulated on a computer, enabling important measures such as queue lengths and service times to be estimated. Most importantly, the model will enable managers to find out what would happen if they were to change some of the circumstances. For example, 'what would happen to queueing times if we increased or decreased the number of servers by x percent?'

Due to limited resources, the police force's objective was to provide the best possible service from its control rooms with the staff that were available. More specifically, the aim was to maximise the proportion of calls answered within 30 seconds. By building a simulation model and then using the results to ask 'what if' questions about different shift patterns, the O.R. team was able to show that the proportion of calls answered within 30 seconds could be increased by some 10%. Vitally, they were able to do this without putting the public at risk by experimenting on the real system.

When the O.R. inside was implemented by the force in the shape of new shift patterns, the expected performance improvement of 10% was achieved within two months, thus providing better service to members of the public needing emergency assistance, at no additional cost to the taxpayer.

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