1. A hospital emergency room is currently organized so that all patients registe
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Question
1. A hospital emergency room 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% 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 registrations 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. We assume a stable system -average inflow equals average outflow at every stage. a. Draw a flowchart of this emergency room. (10 pts) b. On average, how long does a patient spend in the ER? (15 pts) c. On average, how many patients are being examined by doctors? (15 pts) d. On average, how many patients are there in the ER? (10 pts)Explanation / Answer
solution-
We assume a stable system. This implies that average inflow equals average outflow at every stage. In this case you are given inventory numbers I and flow rate R= 55 patients/hr. There are two flow units:
(1) Those that are potential admits: flow rate = 55*10% = 5.5/hr.
(2) Those that get a simple prescription: flow rate = 55*90% = 49.5/hr.
To find the average flow times, we use Little's law at each activity for which the flow time is unknown:
(1) Buffer 1: R = 55/hr (both flow units go through there), I = 7, so that waiting time in buffer 1 = T = I/R = 7/55 hr = 0.127 hours = 7.6 minutes.
(2) Registration: flow time T = 2 min = 2/60 hr. All flow units flow through this stage. Thus flow rate through this stage is R = 55 / hr. Average inventory at registration is given by I = RT = 55*2/60 = 1.83 patients.
(3) Buffer 2: R = 55/hr (both flow units go through there), I = 34, so that waiting time in buffer 2 = T = I/R = 34/55 hr = 0.62 hours = 37.1 minutes.
(4) Doctor time: depends on the flow unit:
4a: potential admits: T = 30 minutes
4b: prescription folks: T = 5 minutes
OK, now we have everything to find the total average flow times: find the critical path for each flow unit. In this case, each flow unit only has one path, so that is the critical path. We find its flow time by adding the activity times on the path:
(a) For a potential admit, average flow time (buffer 1 + registration + buffer 2 + doctor) = 7.6 + 2 + 37.1 + 30 = 76.7 minutes
(b) For a person ending up with a prescription, average flow time (buffer 1 + registration + buffer 2 + doctor) = 7.6 + 2 + 37.1 + 5 = 51.7 minutes.
The answer to the other questions is found as follows:
a. On average, how long does a patient spend in the emergency room?
We know the flow time of each flow unit. The average flow time over all flow units is the weighted average: 10% of total flow units spend 76.7 minutes while 90% spend 51.7 minutes. Thus, the grand average is:
T = 10% * 76.7 + 90%*51.7 = 54.2 minutes.
2. On average, how many patients are being examined by a doctor?
This question asks for the average inventory at the doctor's activity. Again, first calculate inventory of each type of flow unit:
(a) Potential admits: R = 5.5 patients/hr, T = 30 min = 0.5 hr, thus, I = RT = 5.5/hr*0.5 hr = 2.75 patients
(b) Simple prescription: R = 49.5 patients/hr, T = 5 min = (5/60) hr, thus I = RT = 49.5*(5/60) = 4.125 patients
Thus, total inventory at the doctor is 2.75 + 4.125 = 6.865 patients.
3. On average, how many patients are in the ER?
This question asks for total inventory in ER = inventory in buffer 1 + inventory in registration + inventory in buffer 2 + inventory with doctors = 7 + 1.83 + 34 + 6.865 = 49.695 patients.
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