​a) How many doctors should be on duty during each period to maintain the level of patient care​ expected?   The least number of doctors required during the 9 A.M.−3 P.M. shift to meet the set waiting time goal is ▼   4 2 3 1 . The least number of doctors required during the 3 P.M.−8 P.M. shift to meet the set waiting time goal is ▼   4 3 2 1 . The least number of doctors required during the 8 P.M.−Midnight shift to meet the set waiting time goal is ▼   3 1 2 4 . ​b) What condition would exist if only one doctor were on duty between 9 A.M. and 3 P.M.​?     A. Since λ>μ​, the line would back up indefinitely.   B. Since λ<μ​, the line would back up indefinitely.   C. Since λ>μ​, the average wait time would increase slightly.   D. Since λ<μ​, the average wait time would increase slightly.

Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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Ted​ Glickman, the administrator at D.C. General Hospital emergency room faces the problem of providing treatment for
patients who arrive at different rates during the day. There are 4 doctors available to treat patients when needed. If not​ needed, they can be assigned other responsibilities​ (such as doing lab​ tests, reports,​ X-ray diagnoses) or else rescheduled to work at other hours.
 
It is important to provide quick and responsive​ treatment, and Ted feels​ that, on the​ average, patients should not have to sit in the waiting area for more than
4
minutes before being seen by a doctor. Patients are treated on a​ first-come, first-served basis and see the first available doctor after waiting in the queue. The arrival pattern for a typical day is as​ follows:
 
Time
Arrival Rate
9
A.M.−3
P.M.
8
​patients/hour
3
P.M.−8
P.M.
3
​patients/hour
8
P.M.−midnight
13
​patients/hour
 
Arrivals follow a Poisson​ distribution, and treatment​ times,
12
minutes on the​ average, follow the negative exponential pattern.
​a) How many doctors should be on duty during each period to maintain the level of patient care​ expected?
 
The least number of doctors required during the 9
A.M.−3
P.M. shift to meet the set waiting time goal is
 
4
2
3
1
.
The least number of doctors required during the 3
P.M.−8
P.M. shift to meet the set waiting time goal is
 
4
3
2
1
.
The least number of doctors required during the 8
P.M.−Midnight
shift to meet the set waiting time goal is
 
3
1
2
4
.
​b) What condition would exist if only one doctor were on duty between
9 A.M.
and
3 P.M.​?
 
 
A.
Since
λ>μ​,
the line would back up indefinitely.
 
B.
Since
λ<μ​,
the line would back up indefinitely.
 
C.
Since
λ>μ​,
the average wait time would increase slightly.
 
D.
Since
λ<μ​,
the average wait time would increase slightly.
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