Solution of Question 1 for reference to Question 2

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, 50 people per hour arrive at the ER, 10% of whom are admitted to the hospital. On average, 30 people are waiting to be registered and 40 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. On average, how long does a patient stay in the ER? On average, how many patients are being examined by doctors? On average, how many patients are in the ER?

	waiting to be registered	Registration	waiting to see a doctor	Doctor Check-in
				ER	Prescription
I = R*T	30p	1.66p	40p	2.5p	3.75p
R = I/T	50p/h	50p/h	50p/h	5p/h	45p/h
T = I/R	36 min	1.66 min	48 min	30 min	5 min

Table 3

a. On average, how long does a patient stay in the ER?

Average staying time in ER = (5patient X (36 + 1.66 + 48 + 30) + 45patient X (36 + 1.66 + 48 + 5)) / 50 Patient

= (5* 115.66 + 45* 90.66 ) / 50 = 93.5

b. On average, how many patients are being examined by doctors?

Number of patients being examined by doctor (see table)= 2.5p + 3.75p = 6.25 Patients

c. On average, how many patients are in the ER?

Total patients in ER (See Table 3)= 30 + 1.66 + 40 + 2.5 + 3.75 = 77.91 Patients

Question #2 A triage system has been proposed for the ER described in Problem above. As mentioned, 50 patients per hour arrive at the ER. Under the proposed triage plan, patients who are entering will be registered as before. They will then be quickly examined by a nurse practitioner who will classify them as Simple Prescriptions or Potential Admits. While Simple Prescriptions will move on to an area staffed for regular care, Potential Admits will be taken to the emergency area. Planners anticipate that initial examination by the triage nurse will take 3 minutes. They expect that, on average, 20 patients will be waiting to register and 5 will be waiting to be seen by the triage nurse. Recall that registration takes an average of 2 minutes per patient. Planner expects the Simple Prescriptions area to have, on average, 15 patients waiting to be seen. As before, once a patients turn comes, each will take 5 minutes of a doctors time. The hospital anticipates that, on average, the emergency area will have only 1 patient waiting to be seen. As before, once a patients turn comes, he or she will take 30 minutes of a doctors time. Assume that, as before, 90% of all patients are Simple Prescriptions. Assume, too, that the triage nurse is 100% accurate in her classifications. Under the proposed plan,

a. How long, on average, will a patient stay in the ER?

b. On average, how long will a Potential Admit stay in the ER?

c. On average, how many patients will be in the ER?

Once the triage system is put in place, it performs quite close to expectations. All data conform to planners expectations except for one set the classifications made by the nurse practitioner. Assume that the triage nurse has been sending 91% of all patients to the Simple Prescriptions area when in fact only 90% should have been so classified. The remaining 1% are discovered when transferred to the emergency area by a doctor. Assume all other information is valid.

d.On average, how long does a patient stay in the ER?

e.On average, how long does a Potential Admit stay in the ER?

f. On average, how many patients are in the ER?