1. IEE 545 Project Report
Title: SM Market Team Members: Alexander Elkholy*(aelkholy@asu.edu)
Dinesh Suryakumar(dsreedha@asu.edu)
Shriram Thamodharan(sthamodh@asu.edu)
Executive Summary
We are presented with a problem statement wherein Sid, an entrepreneur, wants to optimize
his staff schedule at his Deli in order to minimize employee cost and maximize customer
satisfaction. Ideally, Sid would want to minimize the number of full time employees so as to
reduce the cost to company. Based on the arrival rates of both the Normal and the Lunch
crowd, it was found that having 9 employees stationed at the Deli and 5 at the M&F Market
enables us to attain the desirable waiting times of 0.052361 and 1.20963 minutes respectively.
At the same time, this scenario also results in maximum customer satisfaction: 4 full-time
employees are allotted different days of the week, thus making sure only one full-time
employee is working at the store at any given day, all other employees being part-time! As an
additional objective function, we would also like to make sure that the total number of
customers in both the queues not exceed 25, thus preventing potential customers to leave the
store upon realizing that they will have to wait long.
Problem Description and Research Question
Sid’s store has both a deli and a meat/fish counter. Upon arrival, the customers choose which
counter to enter and obtain a token for the respective queue. After being served at one of the
counters, the customers can either leave the store or move to the other counter by obtaining a
token again. The lunch hour customers are those who enter only the deli counter between 11
am and 1.30 pm (at a different rate than normal customers). Normal customers arrive at both
the counters throughout the day. Half of the normal crowd augments their deli purchase with
cold meats from the M&F market. The arrival rate for both the lunch time crowd and normal
time crowd are given for half-hour increments. The most-likely service time for the deli counter
is estimated to be 5 minutes. Deli customers are usually not inclined to stay in the queue for me
than 10 – 15 minutes. Meat and fish customers are patient until 20 – 25 minutes. Another
important characteristic of the customers are that they tend to avoid entering the store when
the total number of customers in both queues exceeds 25. Both part time and full time
employees work at the store for 8$ and 13$ on an hourly basis. A minimum of four full time
workers are mandatory so as to train the part time employees. Although the store closes by 5
pm every day, simulation needs to be running until the last customer is served!
The service times for the meat and the fish market are collected for a total of 1543 entities and
hypothesis testing is performed for goodness of fit. The candidate distributions for the service
times were found using Matlab and are as shown below:
 Lognormal (mu=1.3481 & sigma=0.45112)
 Inverse Gaussian (mu=4.25066 & sigma=18.95)
 Gamma (a=5.211 & b=0.8156)

2.  Birnbaun Sanders (Beta=3.8412, Gamma=0.4614)
For the Deli service time, a Triangular (2, 5, 7) distribution is suggested by Sid. By performing
Chi-square test for goodness of fit test on the M&F service times, it can be concluded that the
service time distribution for the meat and fish market is more likely to follow a lognormal
distribution, which we picked because it seemed to fit best.
The problem statement requires us to minimize the cost of employees by choosing a schedule
for full-time and part-time employees so as to maximize customer satisfaction and minimize the
cost incurred from employment. Because the cost of a full time employee is $13/hr and the cost
of a part time employee is $8/hr. It’s easy to see that the fewer employees the less the cost to
Sid, and so because at least one full time employee is required to be working at all times, we
recommend that we keep as few full time employees as possible. For customer satisfaction, we
look for achieving a trade-off between the number of employees available and the average
queuing time in each queue.
In order to keep a check on the average waiting time in each queue, we create two types of
resources: the Deli staff and the Meat and Fish market staff. An important assumption to be
mentioned here is that each worker of a certain type serves one customer at a time. Also, if
available, each worker serves his/her assigned customer in parallel with other workers who are
serving at any given time. The Queue starts to get filled only after all workers of a certain type
are occupied with customers simultaneously. This simplistic solution offers flexibility in the
customer-employee interface along with reduced queuing times and optimal utilization of the
employees.
We have two start points: one that defines the arrival times for the normal crowd and the other
that defines the arrival times for the lunch crowd. For the second start point, an activity-check
routes the work objects (customers) either to the next queue in the chain, if the system is
operating at lunch time or, to an alternative sink. (As lunchtime crowd is not defined for all
times of the day, and this hack was the only way we could think to do it, and so these
customers are not counted.) This is achieved by the use of the label named ‘IsItTimeYet’.
Another label, ‘CustType’ determines whether the work object arrives from the normal crowd
or from the Lunch-time crowd.
At the Deli store, another label called ‘Normalbuttwo’ decides whether the work object is to
routed back to the meat and fish market (customers who want to augment their deli purchase)
or to the sink. The value for this label is stamped on to the work object at the start point,
normal crowd, with a 50% probability of ‘1’ or ‘2’. Thus all work objects which come to the Deli
activity and have a value of ‘2’ for this label are routed to the meat and fish market queue!
The number of person hours required for early afternoon restocking and the preparation time
for the lunch crowd is also accounted; for various combinations of the number of M&F staff and
the number of Deli staff, we check for availability of 9 person hours in the time slot: 9 am to 11
am.

3. Finally, we would like to get a precise estimate of the Key Performance Indicators (KPI): the
Average waiting time in the queue for both the deli and the meat and fish market; the
Utilization of resources (both the Deli and the M&F staff) and; the Average number of entities
in each queue, over the entire week. In order to do this, we apply the antithetic - variate
sampling technique: 5 independent replicates each having 20 runs in total i.e. 10 runs with
antithetic option checked, and 10 runs with the antithetic option unchecked. This would allow
us to estimate the KPIs with minimalistic variability.
Experimental Summary Results:
# workers
in
Meat/fish
counter &
# workers
in deli
counter
Average
number in
queue
(Meat/fish)
Average
number
in queue
(deli)
Peak
number
in queue
during
lunch
hours
(deli)
Peak
number in
queue
during
lunch hours
(meat/fish)
Average
waiting
time in
queue
(deli)
Average
waiting
time in
queue
(meat/fish)
Miniumum
number of
workers for
preparation
and
restocking
5 & 7 0.05 10.26 Exceeds
30
Within 30 20.41 0.22 >=9
4 & 7 0.3 9.67 Exceeds
30
Within 10 24.75 0.95 <9
5 & 8 0.06 2.11 Within
25
Within 4 7.75 0.27 >=9
5 & 9 0.08 1.88 Within
20
Within 5 4.89 0.32 >=9
Consolidated result from Antithetic Variate sampling for 5 meat/fish workers and 9 Deli
workers:
Meat/fish Deli
Average queue time 0.052361±0.002569 1.2096±0.19302
Peak time in queue 1.5575±0.08421 10.88259±1.1121
Average number in queue 0.08964±0.004639 1.4797±0.249605
Queuing time: Queue for meat/fish

4. Queuing time: Queue for deli
Usage: Meat/fish workers
Usage: Meat/fish workers

5. Conclusion:
 Schedule of workers
 We recommend 5 workers during lunch rush at the Meat&Fish counter.
 The deli requires 9 workers during the lunch rush.
 By this choice the peak number in queue at any given instance doesn’t exceed 25 and at
the same time the average queuing time is within the specified limits.
 For >90% of the time the waiting time in queue is
 below 3.3 minutes for deli
 below 0.28 minutes for meat/fish