1. Given lambda = 5 patient arrivals per hour (Poisson) and mu = 3 patients served per hour per physician (Poisson), your assistant has used an M/M/c/ ¥ / ¥queueing analysis to provide the following information about the operating characteristics of your clinic under varying numbers of physicians providing service. Nothing else about the system has changed except the number of physicians -- the service rate per physician and arrival rate have both stayed the same.
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2 Physicians
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3 Physicians
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4 Physicians
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Ave Wait Time in Clinic
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.35 hours
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.41 hours
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1.09 hours
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Ave Total Time in Clinic
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.01 hours
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.07 hours
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.75 hours
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Ave # Waiting in the Clinic
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1.7
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2.0
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5.5
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Ave # in the Clinic
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.07
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.37
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3.7
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Physician Utilization
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42%
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55%
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83%
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What conclusions can you draw from this table? Why?
2. Match the appropriate modeling technique with the problem that best matches its appropriate use. On the Excel sheet called Q2 are 5 modeling methods we have discussed in class. Read the 5 descriptions below and type the letter next to the name of the modeling method that would be the most likely model for that problem. Each method should be used only once.
a. You need to determine the number of weeks people will have to wait for surgery at your new outpatient surgical services clinic. You know that requests for the surgery are well approximated by a Poisson distribution with a mean of 5 per day and the number of people the surgeon can operate on per day is well approximated by a Poisson distribution with a mean of 6 per day.
b. You are trying to determine an inventory ordering policy that will minimize your inventory management costs.
c. Your hospital is revising its staffing policies in the Emergency Room. It is trying to determine the number of staff needed to ensure that patient waiting time is within 20 minutes even if an emergent case arrives that must take priority over patients already waiting.
d. You need to determine whether you will have enough hospital beds to meet weekly demand over the next 6 months.
e. You are trying to schedule visiting home nurses (both RNs and LPNs) to minimize their distances traveled. Some of the homebound patients require RN skills every visit, while others do not.