Simulation Modeling and Discrete Event Simulation
Project report
Staffing Simulation of Save-a-lot Drug Store
Using Promodel
Pengju Kang
12/19/2002
1
Contents
Problem statement .............................................................. 3
Model development ............................................................. 4
One operator two queue model ....................................................................................... 4
Two Operator Two Queue Model ................................................................................... 6
Three Operator Two Queue Model ................................................................................. 7
Performance Optimization.................................................. 9
Conclusions ...................................................................... 12
Appendix ........................................................................... 13
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Staffing Simulation of Save-a-lot Drug Store Using
Promodel
Pengju Kang
Problem statement
In a recent business plan, it was proposed that a drugstore be built on the Park Street.
According to the plan, the store has walk-in entrance and a drive-in entrance. The store is
intended to serve the needs of customers living in local area. It is expected that the future
store should have a staffing plan that will guarantee minimum customer lost, which is
dependent on the time customer waiting for service. The time a customer spent in the
drugstore is dependent on the time, which a pharmacist fills a prescription, which, in turn,
is determined by the number of items in a prescription varying from customer to
customer.
It is the objective of the present project to model the operation of the drug store to
provide the data regarding various performances of the drug store responsive to the
staffing plan. The following measures are used to assess performance of the business
operation of the store.
1. The average number of customers waiting for service at the drug store.
2. The average time of a customer spends at the drug store.
3. The utilization rate of the pharmacists.
If the average time a customer waiting for service is too long, it may be necessary to add
one or more pharmacists to the store. Through simulation, the optimal number of
pharmacist added to the drug store will be identified. If dedicated pharmacists are
assigned to walk-in and drive-in customers, a comparison will be made on the
performance differences of this arrangement from the previous one. As a matter of fact,
there will be errors in the estimation of process models due to the limited number of data
are used to fit the distribution function. A number of experiments will be run to generate
a profile, which can be used to adjust the business plan in accordance with the model
parameter changes (model uncertainties). This is known as the robust design. Model
based simulation techniques make it possible to accomplish the robust design of the
staffing plan for the store.
It is decided that Promodel package be selected as simulation platform. Statistical models
are to be developed for the processes involved in the drugstore business. The derivation
of the models comes from the analysis of the historical data collected by a store located in
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a different area. Based on the statistical model, different scenarios of staffing plan will be
investigated to identify the optimal plan for the present store.
The present section gives an introduction of the problem the author is studying. In
Section 2, the statistical nature of this problem is analyzed, which includes the process
data collection and processing. Section 3 is dedicated to the description to the
implementation of the model developed for the drug store using Promodel. In Section 4,
the numerical results are given regarding various issues listed above. The final section is
the conclusion of the present work. Listed in the appendix are the text files of Promodel
programs used in this projects.
Model development
One operator two queue model
Starting with one pharmacist working in the store, the drugstore is modeled as a process
with one operator and two queues, one for walk-in customers and one for drive-in
customers. To describe the statistical property of the server, we need to know the service
time of the operator, more exactly the time required by a pharmacist to fill a prescription,
which depends on the number of items in a prescription. The historical records of a
similar store located in a different area were used to identify a statistical model for the
time spent by a pharmacist on filling up a prescription. The data was analyzed using the
Stat::fit utility of Promodel, and the statistic, time required to fill up a prescription, was
found to be best described with a uniform distribution. The fitted distribution function is
shown in Fig. 1. To investigate the utilization rate of the operator, we need to know the
arrival rates of the drive-in and walk-in customers. Historical data of the same store were
used to identify the statistical models for these two statistics. It has been shown using the
Stat::fit that they can be modeled as two exponential processes. The fitting results are
given in Figs. 2 and 3.
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Fig.1 The fitted distribution for the service time of pharmacist.
Fig.2 The fiited distribution for the interarrival time of walk_in customers.
Fig. 3 The fitted distribution for the interarrival time of drive_in customers.
Three locations were selected to model the save-a-lot drugstore. The layout of the
drugstore is given in Fig. 4. Two queues were used to model the entrances of walk in
customers and drive in customers respectively. The queues have limited capacities to
emulate the realistic situation that when there are too many people lining in the queue,
incoming customer may leave for a different store. The capacity of the walk in queue is
10, and the capacity for the drive in queue is 6. The text file for the model layout is
provided in the Appendix. To evaluate the performance of the drugstore, two global
variables are used to track the customers lost due to the overcrowded queues. The
pharmacist is modeled as an operator, whose service time varies according to uniform
distribution.
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Fig. 4 The layout of the save a lot drug store.
To reduce the variance on the estimates of performance measures, random numbers of the
same string were used for simulation. The number of replication is 10 for each simulation
presented in this report, unless specified. The simulation length is 2000 hours, which
corresponds one year business period. The simulation results for the layout shown in
Fig.4 are given in Table 1. With only one pharmacist working in the drugstore, it is
obvious that the store will not be able to deliver a satisfactory service to its customers.
First of all, the waiting times for the customers are too long. Secondly the pharmacist is
overwhelmingly busy, and thirdly too many customers will be lost due to the long queue.
Table 1. Performance measures for one pharmacist scenario
Average time in Average time in Utilization rate
Walk-in
store for walk-in store drive-in
(pharmacist)
customer lost
customer [min]
customer [min]
[%]
303
161
100
7967
Drive-in
customer lost
1981
Two Operator Two Queue Model
From the simulation results of the previous section, we know the store needs additional
staff to improve the waiting time of the customer. For that reason, an additional
pharmacist is included into the simulation. The Promodel text file is provided in the
Appendix of this report. The presumption made in this simulation is that the two
pharmacists have identical prescription filing time distribution. The results of two
pharmacists scenario is provided in Table 2.
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Table 2. Performance measures for two-pharmacist scenario.
Average time in Average time in Utilization rate
Walk-in
store for walk-in store drive-in
(pharmacist)
customer lost
customer [min]
customer [min]
[%]
99
44
99%
2054
Drive-in
customer lost
71
From Table 2, it is observed that the customer waiting time has been reduced after adding
one more pharmacist. Also reduced is the number of customers lost. The utilization rate is
basically the same as the one pharmacist scenario. However this staffing arrangement is
still not good enough to satisfy the customers, due to long queuing time, and the business
interest the store, due to a large number of customers went to other stores for business.
Three Operator Two Queue Model
To further improve the performance of the store, another pharmacist is added into the
simulation. The Promodel text file is given in the Appendix. The service time
distributions of the three pharmacists are considered identical. The simulation results are
given in Table 3.
Table 3. Performance measures for three-pharmacist scenario.
Average time in Average time in Utilization rate
Walk-in
store for walk-in store drive-in
(pharmacist)
customer lost
customer [min]
customer [min]
[%]
21.7
20
75%
6
Drive customer
lost
1
From Table 3, it is observed that the customer waiting time has been reduced
significantly after the adding two extra pharmacists. There are virtually no customers lost
due to the significantly reduced queuing time. The utilization rate is has been reduced to
75%. It is believed that this staffing arrangement is good enough to satisfy the customer,
due to the fact that customer wait time is reasonable, and the business interest of the
store, due to fact that the store does not lose any customers. The utilization rate of the
pharmacists is considered to be acceptable, since 75% utilization rate means that a
pharmacist is totally busying serving the customers 6 hours a day. The remaining two
hours are enough to cover the lunch break time and morning and afternoon coffee time.
It is expected that addition of more pharmacists will not be helpful to the improvement of
the store business operation. Instead, more money will be spent on paying the workers
with low utilization rates. Table 4 gives the simulation results of four pharmacists
working in the store. As expected, there are no significant changes in customer waiting
times, but the utilization rate of the workers has been reduced to 60%, which is
apparently not good to have pharmacists staying idle for 40% part of a year. It is
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therefore concluded that the three-pharmacist staffing arrangement is the best choice for
this store.
Table 4. Performance measures for four-pharmacist scenario.
Average time in Average time in Utilization rate
Walk-in
store for walk-in store drive-in
(pharmacist)
customer lost
customer [min]
customer [min]
[%]
18.24
18.0
60%
0
Drive-in
customer lost
0
Considering the fact walk-in and drive-in customers have two different arriving rates,
simulation was also conducted to compare the scenario of three pharmacists serving the
customers by turn, and the scenario of two pharmacists dedicated to walk-in customers
and one pharmacist dedicated to drive-in customers. The Promodel text file is provided in
the Appendix. The simulation results are given in Tables 5. It is observed that there may
be a significant difference between the two staffing plans. To further confirm the
difference, a hypothesis test was conducted.
Table 5. Performance measures for dedicated pharmacist scenario.
Average time
in store for
walk-in
customer [min]
25.1
Average time
in store drivein customer
[min]
35.1
Utilization rate
Utilization rate
Walk-in
Drive-in
(%) of server
(%) of server
customer
customer
for walk-in
for drive-in
lost
lost
customer
customer
75%
74%
10
55
Two models for the two scenarios were merged together, and 10 replications of
simulations were run. The results are shown in Table 6, in which the 95% confidence
intervals for the difference (D) in customer arrival times are calculated. Because the
confidence interval does not contain 0, it is asserted with 95% confidence that there is a
statistically significant difference between the two scenarios. It is suggested that the
dedicated pharmacist arrangement should not be used.
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Table 6. The results of hypothesis test for two different staffing scenarios.
Walk-in
Scenario 1 Scenario 2
23.98011
24.51343
25.05688
25.83777
25.59524
25.20082
25.68196
25.42603
24.45226
24.96743
21.78467
21.3518
21.52622
22.4179
21.8097
21.69891
22.28685
22.50528
21.75792
21.67911
D
2.195445
3.161626
3.530657
3.419874
3.785537
3.501914
3.395115
2.920747
2.694331
3.28832
(D- D
Drive in
Scenario
1
Scenario
2
)^2
0.109904
0.000805
0.116047
0.052842
0.354664
0.09729
0.042072
0.072497
0.245688
0.009667
D
34.96908
34.95903
36.76688
34.51466
35.25138
34.71155
34.83501
36.29225
33.76848
34.72336
21.60459
22.15908
20.04892
19.98993
20.18548
20.3703
19.91889
20.1979
20.42942
20.71888
(D- D )^2
13.36449
12.79994
16.71796
14.52473
15.06589
14.34125
14.91612
16.09435
13.33906
14.00448
0.145798
0.324922
0.541678
2.41E-05
0.034335
0.003164
0.018326
0.278905
0.152345
0.028394
D
D
3.189357
s(D)
0.349838
14.51683
s(D)
0.412026
s( D )
0.110628
h
0.229842
95% CI
2.959515 3.419198
s( D )
0.130294
h
0.270699
95% CI
14.24613 14.78753
Scenario 1: three pharmacists, two dedicated to walk-in customers, and one dedicated to
drive-in customers.
Scenario 2: three pharmacists serving both types of customers by turn.
Performance Optimization
The staffing plans investigated in the previous section are based on the assumption that
the service times of all pharmacists are the same. It is possible that the pharmacist may be
better trained, or supported with sorting equipment, the service time may be reduced. The
management wants to know if the service time is reduced into the range of 3 and 15 with
a uniform distribution, what will be the optimal plan. Reexamining the performance
measures of the store, the expected staffing plan would be one that has acceptable
queuing time and at the same time the utilization rate of the operators should not be less
than 75%. This staffing planning procedure is modeled as a multi-objective optimization
problem. The objective function terms that were measured are:

Min: 1 * Walk –in customer (Avg Time in Sys)

Min: 1 * Drive –in customer (Avg Time in Sys)

Max: 0.8 * Service-time (operator 1) (% Utilization)

Max: 0.8 * Service-time (operator 2) (% Utilization)
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Different weights are assigned to the objective functions. Unit weight is assigned to the
customer wait time in the system, while 0.8 is assigned to the utilization rate. The
variable in the objective function is the service time of the operator. Starting with twopharmacist plan, the optimization results are partially shown in Table 7, which shows that
if the mean service time is reduced to approximately 10 minutes, the customer waiting
time can be reduced significantly compared with a mean service time of 15 minutes,
while a 75% utilization rate is ensured. With the mean service time being less than 10,
although the customer waiting time is reduced, the utilization becomes too low. Since the
service time of a pharmacist depends on the number of prescription items, as well as the
time to locate and sort the drugs. It is generally difficult to reduce the service time
considerably. However the optimization results provide the management a profile on
which the optimal staffing plan can be established, if the store decides to explore the
option of reducing service time.
Table 8. The multi-objective optimization of the two-operator staffing plan.
Service time
Walk-in
customer avg.
time in sys.
98.88
76.29
54.3
36.46
24.85
17.91
13.84
11.02
15
14
13
12
11
10
9
8
Drive-in
customer avg.
time in sys.
44.06
37.34
30.64
24.67
19.67
15.75
12.91
10.59
Objective
function
Utilization
rate
(pharmacist 1)
99.21
97.78
94.62
89.26
82.41
75.06
67.44
60.17
15.8
42.8
66.47
81.69
87.29
86.37
81.15
74.59
Aervage wait time (walk-in)
Aervage wait time (drive-in)
Objective function
Utilization rate
Utilization
rate
(pharmacist 2)
99.21
97.76
94.63
89.26
82.35
74.99
67.43
60.08
100
100
80
80
60
60
40
40
20
20
0
0
8
10
12
14
utilization rate &
objective function
value
120
Average wait time
[min]
120
16
Mean Service Time [min]
Fig.5 The optimization results.
The detailed optimization results are shown in Fig. 5, which shows how the total
objective function, utilization rate, and average time in system change with the variations
10
in service time. At a service time approximately 10-11 min, the objective function
reaches its peak, which is regarded as the optimal solution. It also observed that is the
service time is reduced below 10 min, the wait time for both customers are roughly the
same.
The performance optimization was also investigated from a different angle. Instead of
considering the customer wait time in the system as the objective function terms, the
number of both types of customers and the server utilization rates are selected as the
objective functions terms. The objective function terms that were measured are:

Min: 1 * total exits of walk-in-customer

Min: 1 * total number of drive-in-customer

Max: 0.8 * server 1 utilization rate (%)

Max: 0.8 * server 2 utilization rate (%)
A number of experiments were run to examine the sensitivity of those terms in response
to the change of service times. The results are provided in Fig. 6. It is interesting to
observe that from the perspective of number of customer having been served, the total
number of drive-in customers is not sensitive to the variations of service time. If the
service time is below 10 minutes, the total number of walk-in customers served is also
insensitive to the change of the service time. It is concluded that the optimal mean service
time is 10 minutes. Continued reduction of service time below 10 will not improve the
operational performance much instead of incurring additional cost required to accomplish
the reduction.
Drive-in Customer
Utlization (1)
Utilization (2)
14000
120
12000
100
10000
80
8000
60
6000
40
4000
20
2000
0
Utilization rate (%)
Customer number
Walk-in Customer
0
8
10
12
14
16
Mean service time [min]
Fig. 6 Optimization results of alternative objective function terms.
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Conclusions
This report describes the Promodel simulations carried out for a drugstore to be built on
the Park Street. The focus of simulation has been on the staffing arrangement for the
store. The data collected for a drugstore located in a different neighborhood were used to
establish a Promodel for the present drugstore. Different scenarios of simulations were
carried out to investigate the effect of number of pharmacists to be hired in the store on
the performance of the business. It has been found that the plan, three pharmacists
working in the store will deliver the best operation performance in terms of customer
waiting time and operator utilization rate, based on the existing data.
Simulations were also conducted to investigate the sensitivity of the service time
variation on the performance on the store. It has been found that if the mean service time
could be reduced, the number of working pharmacists in the store could be reduced to 2,
while ensuring an acceptable business operating performance. Sensitivity simulation is
necessary, since there are always model uncertainties involved in the model derivation,
no mentioning that fact that the primary data are from a another store. Through
simulation experiments, various business plans can be established in response to possible
parameters variations,
It has been demonstrated through this simple project that discrete simulation supported
with the flexibility provided by Promodel is valuable technique for business operation
planning.
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Appendix
The text files and model files used in this project.
The files are saved under the directory of final project.
The model and text file for 1-operator scenario
Final project_1_operator.mod
FinPjt_1_operator.TXT
The model and text file for 2-operator scenario
Final project_2_operator.mod
FinPjt_1_operator.TXT
The model and text file for 3-operator scenario
Final project_3_operator.mod
FinPjt_1_operator.TXT
The model and text file for 4-operator scenario
Final project_4_operator.mod
FinPjt_1_operator.TXT
The model and text file for 2-operator optimization scenario
Final project_2_operator_optimization
FinPjt_2_operator_optimization.TXT
The model and text file for hypothesis test of two 3-operator scenarios
Final project_merge_model.mod
FinPjt_3_operator_MergedModel.TXT
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