Questio T Consider the following (simplified) flow diagram of an emergency department (ED) at a local hospital. Patient Arrivals W Triage 5 min/patient 00 O O 10 000 - 12 patient Ar Hospitalize C 50% 50% Discharge 75% 80% Doctor B Non-Severe Symptoms 10 min/patient 1000 6 patient/hr 25% 20% Severe Symptoms 15 20 0 25 2 Arriving patients go through the following sequence of steps: Lab Tests 20 min/patient 3 patient/hr 0.2x +0.820.25 = 0.430 1400 Triage: A preliminary diagnose is made to determine the severity of the symptoms. On average, 20% of the patients have severe symptoms and they are sent directly to the Lab for testing (blood, X-rays, etc.), while the remaining 80% of the patients move to meet the doctor. Currently, there is a single nurse in charge of patient triaging and it takes her five minutes per patient to complete this step. Doctor: In this step, a single physician examines patients to diagnose a treatment and to decide whether to discharge or to hospitalize them. Out of those patients that meet the doctor without Lab tests (i.e., those who were diagnosed non-severe symptoms in the Triage step) 75% are immediately discharged while the remaining 25% are sent to the Lab for testing. Out of those patients that meet the doctor with Lab tests, 50% are hospitalized and the remaining 50% are discharged. On average, the doctor spends 10 minutes on every encounter with a patient. Lab Tests: A single nurse is assigned to perform all Lab tests. The average time it takes her to complete this step is 20 minutes per patient. 2 * Based on this information, answer the following questions. a) (10 points) What is the flow time (in minutes) of a patient that is diagnosed with severe symptoms in the Triage step? What is the average flow time (in minutes) of a patient that is diagnosed with non-severe symptoms in the Triage step? (When you compute these flow times you may assume that a patient never has to wait before undergoing the next step.) Severe symptoms: 35 Average of non-severe : min (5+20+10) 15 min for 75% who is immediately discharged 3 +10 +20 + 10 = 15x0.75 + 45 min 450.25 for 25% who gets lab tests = 22.5 minutes Can assume all non-severe Symptoma? b) (points) What is the maximum throughput (in patients per hour) that this ED can serve? What is the bottleneck? What is the utilization of the nurses and the doctor? Maximum throughput: 7 patients/hr e Y Bottleneck is the Lab tests Utilization rate Triage: 1/2 = 58.3% lab tests: 40% of patients end of getting lab test 5 70.4-93.3% Doctors Triage cap: 12 patient /hr (0.2x + 0.8xx0-23= 0.4x) 80% of patients see doctor Lab tests Cap: 3 patient/ hr 3 6 7x0.8 = 933% Doctor cap= 6 patient /hr 6.5 c) (points) On a peak day, there are 30 patients per hour entering the ED. Determine what is the minimum number of doctors and nurses that need to be staffed on each of the three steps to serve this inflow of patients? Currently, each step can handle this many visiting patients 12 Triage: 2 patients/hr. Lab tests: 1x3 = 7.5 patients/hr Poctors: 10 26= 7.5 patients/hr. 8 Hence, we need 3 triage nurses, 4 lab tests nurses, and 4 doctors ent Lab Dec 3 0.5 d) (10 points) Since nurses handle both Triage and Lab Tests, there is a proposal to combine these two steps into a single one. How would your answer in part (c) change under this new configuration? Would you support this proposal? 4