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• RalphOberhuber

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3.4. A hospital emergency room (ER) is currently organized so that all patients register through an initial check-in process. At his or her turn, each patient is seen by a doctor and then exits the process, either with a prescription or with admission to the hospital. Currently, 55 people per hour arrive at the ER, 10 percent of who are admitted to the hospital. On average, 7 people are waiting to be registered and 34 are registered and waiting to see a doctor. The registration process takes, on average, 2 minutes per patient. Among patients who receive prescriptions, average time spent with a doctor is 5 minutes. Among those admitted to the hospital, average time is 30 minutes. Flowchart and calculations see below. On average, how long does a patient spend in the ER? T(patient w. admission) = 76.7 min T(patient w. prescription) = 51.7 min T(average over all) = 54.2 min On average, how many patients are being examined by doctors? I(EX) = 6.9

On average, how many patients are there in the ER? I (Total) = I 49.7

Assume the process to be stable; that is, average inflow rate equals average outflow rate. Flowchart: 55/hr 55/hr

Wait for check-in I(W1) = 7 T(W1) = ? min

Initial check-in I(IC) = ? T(IC) = 2 min

I(W1) = R(W1) * T(W1) ;

7 = 55 * T(W1) ;

I(W2) = R(W2) * T(W2) ;

34 = 55 * T(W2) ;

55/hr

55/hr Wait for ER I(W2) = 34 T(W2) = ?

Exam by doctor T1(EX) = 30min T2(EX)=5min Tavg(EX) = ? I(EX) = ?

T(W1) = 7 / 55 * 60 min = 7.6 min T(W1) = 34 / 55 * 60 min = 37.1 min

Tavg (EX) = 0.9*(5)+0.1*(30) = 7.5 T(patient w. admission) = 7.6 min +2 min +37.1 min +30 min = 76.7 min T(patient w. prescription) = 7.6 min +2 min +37.1 min +5 min = 51.7 min T(average over all ) = 7.6 min +2 min +37.1 min +7.5 min = 54.2 min

90%

10%

I(EX) = R(EX) * T(EX) = 55 /60 * 7.5 = 6.9 I(IC) = R(IC) * T(IC) = 55 /60 * 2 = 1.8 I (Total) = I(W1) + I(IC) + I (W2) + I(EX) = 7 + 1.8 + 34 + 6.9 = 49.7