Logical hospital

Running an emergency room (ER) requires the careful planning and management of resources in order to efficiently meet the demand for services. Appropriately designing the ER can mean the difference between profit and loss.

Suppose patients arrive at a waiting room with an interarrival time of six minutes (normally distributed with a standard deviation of two). Each patient is prescreened and classified into one of three severity types: high, medium and low. The severity types are evenly distributed at 33.3 percent each.

The prescreening station determines the following: For the high severity patients, 80 percent will need to go an ER station and 20 percent will be discharged without requiring any treatment. For the medium severity patients, 50 percent will need to go to an ER station and 50 percent will be discharged without requiring any treatment. For the low severity patients, 20 percent will need to go to an ER station and 80 percent will be discharged without requiring any treatment.

There are two ER stations available to treat patients. Treatment times, on average, take 21 minutes (normally distributed with a standard deviation of four). An open ER station will take the highest severity patient first from the waiting room. Once a patient is admitted to an ER station they cannot be bumped out by a higher priority patient. An ER station can only treat one person at a time.

Question: What is the average wait time in minutes for each of the three patient types (high, medium and low)?

Send your answer to [email protected] by March 30. The winner, chosen randomly from the correct answers, will receive an “Analytics: Driving Better Business Decisions” T-shirt.