Page 75 - Six Sigma Advanced Tools for Black Belts and Master Black Belts

OTE/SPH
OTE/SPH
Char Count= 0
JWBK119-05
60 August 31, 2006 2:55 Fortifying Six Sigma with OR/MS Tools
Source

Checking
Typing
Packing Dispensing
Legend:
: Queues : External
: Servers : Internal Flows
Sink
Figure 5.2 Queuing network representation of drug dispensing process.

For the Analyze phase, estimates of average waiting times and queue lengths can
be derived using basic queuing methodologies based on the patient arrival rates and
service rates. Steady-state queuing analysis is adequate here as the arrival and service
rates are fast enough to ensure the system reaches its steady state in a short time. Inter-
arrival and service times were assumed to be exponentially distributed. The entire
processcanthusberepresentedasasystemofinterconnectedM/M/1andM/M/sser-
vice stations. M/M/1 and M/M/s are standard abbreviations to characterize service
stations in queuing methodologies, M/M/1 denoting service stations with a single
server, and M/M/s stations with a finite number s of servers (s >1). Both of these types
of stations experience Markovian arrival and service processes, with service processes
in an M/M/s system being independently and identically distributed. Furthermore,
the queuing buffer is assumed to be of infinite size and each server can only serve
one customer at a time and selects waiting customers on a first come, first served
basis.
Given the preceding assumptions, mean total waiting times for the entire drug
dispensing process in the pharmacy can be computed by first computing the mean
sojourn times using standard queuing formulas for each service station, 28 and then
summing these mean sojourn times. In the computations, the mean total waiting time
for the entire process does not include the mean service time of the final dispensing
and checking process. This is because the waiting time of a patient is defined as the
period from the time he submits the prescription to the time when service by the
dispensing pharmacist is initiated.

5.4.1 Sensitivity analysis
At the Improve phase, the impact of different manpower configurations on the over-
all waiting times can be assessed by varying the number of packers and dispensing