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Our client was an Emergency Response Management organization who handles medical, police and fire emergencies through the " 1-0-8 Emergency service". Currently the organization runs around 690 ambulances. An analysis is run on historic data extracted from client's management database. The live data input is fed to a simulation model to propose an optimal ambulance allocation providing an opportunity of cost reduction for the organization.

In probability theory and statistics, the exponential distribution is the probability distribution that describes the time between events in a Poisson process, i.e. a process in which events occur continuously and independently at a constant average rate. It has the key property of being memory less. In addition to being used for the analysis of Poisson processes, it is found in various other contexts.

We used exponential distribution to model inter-arrival times of the calls and ambulance service times as well. The model parameter lambda is estimated as the average of the historical data from client database. Given an allocation of ambulances across 23 centers a simulation is repeatedly run with 10,000 calls arriving at call centers in each simulation. Ambulances are run to the cater the calls. In case the nearest ambulance center doesn't have any idle ambulance the call is catered by another ambulance center with a configurable higher value of lambda. The waiting times where a call had to wait to be allocated an ambulance are added up and reported. Higher the number of simulations more accurate are the results reported.

The entire exercise is repeated with reduced ambulance counts. It is found that with 54% reduction in ambulance counts across ambulance centers we still achieve zero waiting time. But with 55% reduction there appears a positive waiting time and the risk is not worth taking in case of emergency services.

Suggested 54% reduction in ambulance counts providing our client a cost reduction opportunity keeping the existing SLA un-impacted. Surely scrapping ambulances from service would not have helped in cost reduction but future procurements of new ambulances were reduced and that was an effective cost cutting mechanism adopted by our client. 

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