Precision Manufacturing

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ME290

Homework 1.

Homework #1

Prof. Omar Romero-Hernandez / GSI Katie McKinstry

Please answer the following questions. Make sure you write the answer in the underlined

space. You must also show your calculations. This homework is due on Thursday Sep 27th, between 11.00am and 11.10pm in the classroom. Late submission is not accepted.

Make sure you refer to the ME290 syllabus

for more rules related to homework:

Homework: Homework will be assigned in lecture and will be due as indicated on each homework (usually one week later). Please do plan in advance since no questions concerning the homework problems, projects, exams, presentations etc. will be accepted 24 hrs prior to the corresponding deadline. Late homework will not be accepted. You must turn in all problems together (i.e. you can’t turn in some on time and others late). Make sure that procedure and reasoning behind your answer is included.

Problem 1. (exercise 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 d octor and then exits the process, either with a presentation or with admission to the hospital. Currently, 55 people per hour arrive at 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 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. (a) On average, how long does a patient spend in the ER? (b) On average, how many patients are being examined by doctors? (c) On average, how many patients are there in the ER? Assume the process to be stable; that is, average inflow rate equals average outflow rate. Problem 2 (exercise 3.5)

A triage system has been proposed for the ER described in Exercise 3.4. As mentioned earlier, 55 patients per hour arrive at the ER. Under the proposed triage plan, entering patients 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 the initial examination (triage) 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. The triage nurse is expected to take an average of 1 minute per patient. Planners expect the Simple Prescriptions area to have, on average, 15 patients waiting to be seen. As before, once a patient’s turn comes, each will take 5 minutes of a doctor ’s time. The hospital anticipates that, on average, the emergency area will have only 1 patient waiting to be seen. As before, once that patient’s turn comes, he or she will take 30 minutes of a doctor ’s time. Assume that, as before, 90% of all patients are Simple Prescriptions. Assume, too, that the triage nurse is 100% accurate in making classifications. Under the proposed plan, (a) how long, on average, will a patient spend in the ER? (b) On average, how long will a Potential Admit spend in the ER? (c) On average, how many patients will be in the

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ME290

Homework #1

Prof. Omar Romero-Hernandez / GSI Katie McKinstry

ER? Assume the process to be stable; that is, average inflow rate equals average outflow rate. Problem 3 (exercise 3.6)
Refer again to Exercise 3.5. 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...
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