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The medical director of a large emergency clinic faces a problem of providing treatment for patients who arrive at different rates during the day. There are several doctors available to treat patients when needed. If not needed, they can be assigned to other responsibilities (for example, lab tests, reports, x-ray diagnoses) or else rescheduled to work at other hours.
It is important to provide quick and responsive treatment, and the medical director feels that, on the average, patients should not have to sit in the waiting area for more than 20 minutes before being seen by a doctor. Patients are treated on a first-come, first-served basis and see the first available doctor after waiting in the queue. The arrival pattern for a typical day is:
These arrivals follow a Poisson distribution. The treatment time is 24 minutes on the average with an exponential distribution. Consider the service cost (by doctors) to be $130 per hour. For each patient, the waiting cost when waiting for service (only count the time waiting in line but not the time in service) is estimated to be $65 per hour.
Questions
- How many doctors should be on duty during each period to maintain the level of patient care expected? Present calculations in Excel and explain your results.
- What other elements of managing queues would you apply to reduce the negative effects of waiting?
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