This document describes a case study using simulation to model a take away restaurant. It presents the entity and attributes in the model, including customers, orders, and time. It describes the flow model of customers entering and moving through the restaurant. It then provides statistics from running the simulation at different times, including the state of the system, gains, efficiencies, and queue lengths. The goal is to use simulation to help address issues like long wait times and improve the restaurant's performance.

1. Case study using simulation
Presented by
S.Sanjay (18MF32)

2. Contents
• Abstract
• Introduction
• Entity & Attribute
• Flow model
• Other attributes
• Delay
• Formulae & Findings
• The State of System at 8:00:20 PM
• The State of System at 8:00:40 PM
• The State of System at 9:00:00 PM
• Interpretation on case study of take away restaurant
• Conclusion
• Case1 No queues
• Case 2 Improved Service time
• Reference

3. ABSTRACT
• Model: A model is proposed here for The Take away Restaurant.
• Assumptions: The model is developed under the assumption that there is no limit
for the number of customer’s arrival and there is limited number of servers who
will attend customers.
• Problem: Overcrowding is major problem, which may effect profit as well as
goodwill of restaurant.
• Analysis: Studying and analysing for long period of time, we have noticed
continuous increase in number of customers as well as in number of restaurants.

4. Cont.
• Question/Confusion: So it is a big question for management how to provide best
service in lesser time so that their customer could not move to other options.
• Cause: Long waiting queues is a big issue for a customer as he is not ready to
wait for a long time.
• Reason: When we asked to many customers the reason for switching to other
restaurants from a particular restaurant, they pointed on issues like insufficient
personnel and long waiting time.
• Solution/Simulation: To overcome these situations, we will use queuing model
which can provide reasonably accurate evaluations of our system’s performance
in the light of Simulation modelling.

5. Intro
• Overcrowding at Restaurants is a problem worldwide as the human being
move to restaurants to enjoy or relax from their routine jobs.
• The number of problems which customers as well as staff of the restaurants
are facing regularly is related to fast service and long waiting lines.
• Delays in the customer’s service may cause drastic outcomes for business.
• Restaurant’s performance in terms of customers flow and of the available
resources can be improved using the Queuing Theory and Simulation
modelling.
• Restaurants can be regarded as a network of queues.
• The waiting threads and evaluation of gain or loss, will be effective tools to
support management decisions related to the capacity planning of restaurant.

6. • This paper presents
• Since here a model presented to solve the problem of long waiting lines
and control losses in financial, it will be a useful tool for capacity
planning for these type of service organizations
First part
• Study of a
take away
restaurant
with the help
of simulation
technique
Second part
• Results of the
literature
search
Third part
• Some
solutions to
improve the
performance
of service
organizations

7. • Limitations: Most simulation studies limit themselves to either a single
technique or a single application area where more than one technique is
used. It is worth nothing, so here we tried to consider the empirical aspect
of studies.
• Model Proposed: We developed this model of Take Away Restaurant with
the help of work done by (Ingalls 2002; Ingalls & Kasales 1999; Ingalls
1998) who created dynamic models in various fields for understanding
and evaluating the performance of system and follow the step by step
approach of (Nembhard 1999) to complete our model.

8. Entity & Attribute
Customer
• Primary entity
Order
• Secondary entity
• When the order is placed and When the payment is done
*Entity - has a relatively short life, the time the order is taken until it is received from
the counter.
Time of day
• The customer enters the restaurant in billing section at order counter.
• Also called as Time Of Enter.
Order
• Value Of Order

9. Simulation model for customer’s flow in take away restaurant
Enter the billing counter at the restaurant
Leave the restaurant as the
dissatisfied customer
Wait in queue for payment
When arrive at billing counter – pays for order
Order is made at kitchen counter
Wait until the customer in
front of you moves
Get in line for order receive counter
Is the queue very
long ?
Is there place to
move forward
Arrive at order receive counter to receive order
Leave the restaurant as the happy customer
Start
Stop
Order meets
customer
at order Receive
counter Yes
Yes
No
No

10. Other Attributes
• The common attribute would be the time that the order would take in the kitchen.
• Each order would have a unique time that it started in the kitchen.
• It may also have other attributes such as
 priority,
 the type of dish, and
 cost incurred to produce the dish.
• In a restaurant simulation that is tracking each individual dish, it would not be
unusual to have thousands of entities active in the simulation simultaneously

11. Delays
• There are three major types of activities in a simulation: delays, queues and logic.
• Delay occurs, when the entity is delayed for a definite period of time.
• In this example, there are three type of delays.
 When Customer is ordering at the order counter.
 When the order is being cooked in the kitchen.
 When customer receives his order at the order receiving counter.

12. Formulae & Findings
• The formulae for these random values are as follows:
1. Time between arrivals of customers to the restaurant = (Rand×115) seconds
2. The value of the order for the customer = (Rand×1,000) Rs
3. The delay at the order placing counter = (Rand×120) seconds.
4. The delay at the kitchen = (Rand×96) seconds.
5. The delay at the order receive counter = (Rand×120) seconds.
• In our model, we count the number of Lost Customers because the line was too long.
• A common variable to track the performance of various severs in the restaurant is the
Efficiency of a resource.
• Here we will also calculate average queue length at various counters.
• If we are to improve this system, we should minimize waiting line without the loss of sale.

13. • We have assumed that there is no fixed size for queue, so there is no requirement for a customer
to stay in the restaurant for a long time.
• And a customer would leave restaurant if he has to wait to place an order (more than 15 minutes).
• Customer 1 was at the Order Receive counter receiving its order.
• Customer 2 and Customer 3 were in line waiting for the Order Receive counter.
• Customer 4 was ordering at the Order counter (Billing counter).
• Customer 5 and Customer 6 were waiting in line for the Order counter.
• The Order for Customer 2 was being cooked in the Kitchen of the restaurant.
• The Order for Customer 3 was waiting in line for the Kitchen.
• Customer 7 was schedule to arrive at the restaurant in the future.
• Customer 8 was also ready to arrive at the restaurant very soon.

14. Entity Events Time of event
Customer 7 Arrival at restaurant 8:00:20 PM
Customer 1 Order receive counter-Complete 8:00:40 PM
Customer 2 Order’s Cooking in Kitchen-Complete 8:00:56 PM
Customer 4 Billing counter-Complete 8:01:10 PM
The planner of this system is made up of the entities that are scheduled to complete an
activity with a specific time duration in Table 1

15. Entity Time Of Enter Value Of Order
Customer 1 7:54:20 PM Rs. 335
Customer 2 7:55:50 PM Rs. 958
Customer 3 7:57:10 PM Rs. 338
Customer 4 7:58:20 PM Rs. 874
Customer 5 7:59:30 PM Rs. 895
Customer 6 8:00PM Rs. 218
Customer 7 - -
Customer 8 - -
Our two attributes Time Of Enter and Value Of Order for each of the entities in the system
is shown in Table 2.

16. Statistics Value Time Duration
Gain Rs. 35357 1:00:00
Loss 0 1:00:00
Billing Counter Efficiency 0.9956 1:00:00
Kitchen Efficiency 0.9971 1:00:00
Order receive counter
Efficiency
0.9966 1:00:00
Billing Counter waiting in line 1.8205 1:00:00
Kitchen Waiting in line 1.1040 1:00:00
Order Receive Counter
waiting in line
1.3261 1:00:00
The statistics of the restaurant after one hour from the start of simulation i.e. from 7:00:00
PM

17. The State of System at 8:00:20 PM
• Since, the first event on the planner is scheduled to occur at 8:00:20 PM,
that is the arrival of Customer 7 to the restaurant, so firstly set the
attributes for this entity.
• Time Of Enter is set to 8:00:20 PM, and the Value Of Order is set using
the formula [(Rand()× 1000)].
• The Rand() gives us a 0.1490, so the value of the order is Rs.149.
• If we have assumed that the customer 7 enters in the system. Then the
value of variable Gain is incremented from Rs. 35357 to Rs. 35506.
• Now, the time between arrivals of two customers to the restaurant is set
using the formula (Rand()×115) = 0.6937×115 = 80 seconds.

18. Table 4. The Planner at 8:00:20 PM
Entity Events Time of event
Customer 1 Order receive counter-Complete 8:00:40 PM
Customer 2 Order’s Cooking in Kitchen-Complete 8:00:56 PM
Customer 4 Billing counter-Complete 8:01:10 PM
Customer 8 Arrival at restaurant 8:01:40 PM

19. Calculations
• Here are two types of statistics, they are
 the calculation of Gain and Loss,
 the resource Efficiency statistics and
 the queue length statistics.
• Gain has gone to Rs. 35506 while the Loss is Zero, till now.
• The other statistics are time-dependent statistics that are time-weighted
averages of a given value.
• We calculate the new value of the average number of customers waiting in
line for the billing counter.

20. Calculations
• At dinner time, the simulation had been running for one hour. From 8:00:00
PM to 8:00:20 PM, only 1 customer left the billing counter and the number of
customers waiting in line for the billing counter has been 2.
• So the new time-weighted average for Billing Counter Efficiency and number
of customers waiting in line for the billing counter is
((.9956×1:00:00)+(1×0:00:20))/1:00:20 = .9957 and
((1.8205×1:00:00)+(2×0:00:20))/1:00:20 = 1.8247.
• formulae from time format into seconds, these would be
((.8982×3600)+(1×20))/3620 = .9957 and
((1.2292×3600)+(2×20))/3620 = 1.8247.

21. Statistics Value Time Duration
Gain Rs. 35,506 1:00:20
Loss 0 1:00:20
Billing Counter Efficiency 0.9957 1:00:20
Kitchen Efficiency 0.9971 1:00:20
Order receive counter
Efficiency
0.9966 1:00:20
Billing Counter waiting in line 1.8247 1:00:20
Kitchen Waiting in line 1.0842 1:00:20
Order Receive Counter
waiting in line
1.0397 1:00:20
Table 6. Statistics at 8:00:20 PM

22. The State of the System at 8:00:40 PM
• Customer 1 finishes its time at the Order Receive Counter at time 8:00:40
PM. So the Gain value is increased and Order Receive Counter is no
longer used.
• Hence, Customer 2 is allocated the Order Receive Counter. But order for
Customer 2 is still in the Kitchen. So even though the Order Receive
Counter is occupied, no productive work is going on.
• At the next step in the simulation, the order for Customer 2 will complete
in the Kitchen and Customer 2 will be able to start the process of picking
up its order.

23. • Since Customer 2 has moved forward, Customer 3 moves to first place in
the line waiting for the Order Receive Counter. Customer 4 still occupies
the Billing Counter and is still in the process of giving its order.
• Customer 5 and 6 do no change their position in the line and Customer 8
is still scheduled to arrive at the restaurant at time 8:01:40 PM.
• To determine new values for the statistic, we take average number of
customers waiting for Order Counter is 2 (2,3) because from time 8:00:20
PM to 8:00:40 PM there were 2 customers waiting in line (5,6).

24. Statistics Value Time Duration
Gain Rs. 35506 1:00:40
Loss 0 1:00:40
Billing Counter Efficiency 0.9957 1:00:40
Kitchen Efficiency 0.99572 1:00:40
Order receive counter Efficiency 0.99662 1:00:40
Billing Counter waiting in line 1.8202 1:00:40
Kitchen Waiting in line 1.0892 1:00:40
Order Receive Counter waiting
in line
1.0450 1:00:40
Table 6. Statistics at 8:00:40 PM

25. The State of the System at 9:00:00 PM
• Now, continuing the same procedure we keep on collecting the statistics
for one more hour i.e. up to 9:00:00 PM
• We observed that our Global variable Gain is incremented to Rs.42974 but
Loss has also been introduced and reached up to Rs. 16168.

26. Statistics Value Time Duration
Gain Rs. 42974 2:00:00
Loss Rs. 16168 2:00:00
Billing Counter Efficiency 0.9970 2:00:00
Kitchen Efficiency 0.9980 2:00:00
Order receive counter Efficiency 0.9977 2:00:00
Billing Counter waiting in line 1.3666 2:00:00
Kitchen Waiting in line 1.1510 2:00:00
Order Receive Counter waiting
in line
1.0624 2:00:00
Table 7. Statistics at 9:00PM

27. Statistics Value Time Duration
Gain Rs. 43325 3:00:00
Loss Rs. 43946 3:00:00
Billing Counter Efficiency 0.9979 3:00:00
Kitchen Efficiency 0.9986 3:00:00
Order receive counter
Efficiency
0.9984 3:00:00
Billing Counter waiting in line 1.5606 3:00:00
Kitchen Waiting in line 1.1500 3:00:00
Order Receive Counter
waiting in line
1.0540 3:00:00
Table 8. Statistics at End of Simulation (7:00:00-10:00:00PM)

28. Interpretation on case study of take away restaurant
• This data is saying that every day, from 7:00 PM to 10:00 PM, the Gain for the
restaurant will be Rs. 43325.
• Now, the conclusion value is “These numbers give us a random performance of
the system.” For the validity of the answer we will repeat the whole procedure for
25 iterations to have an accurate result because the outcome of each iteration is
not constant.
• So, we obtained Confidence interval for each of our statistics after 25 iterations.
• The revenue can be doubled if we fully decrease the number of lost customers.
• So, we need to find the new techniques to decrease the number of lost customers.

29. • Billing Counter and Order Counter are highly utilized, lines are forming in
front of those two resources.
• The minimum average theoretical time for a customer would be 120
seconds at the Order Counter and 96 seconds at the Kitchen Counter,
which is 216 seconds, or 3.6 minutes. So, about 4 minutes of the
customer’s time is simply waiting.
• Our objective is to minimize the
amount of waiting time to meet the
customer satisfaction.

30. Statistics Value Lower limit of
Confidence
Interval
Upper limit of
Confidence
Interval
Gain Rs. 43325 Rs. 41492 Rs. 74418
Loss Rs. 43946 0 Rs. 94172
Billing Counter Efficiency 0.9982 0.6982 0.9982
Kitchen Efficiency 0.9988 0.8004 0.9988
Order receive counter Efficiency 0.9984 0.7672 0.9986
Billing Counter waiting in line 1.7599 1.0493 1.7599
Kitchen Waiting in line 1.1083 0.0820 1.2668
Order Receive Counter waiting in line 1.0427 1.0004 1.0444
Table 9. Confidence Interval after 25 Iterations

31. CONCLUSIONS
• We observed the queue formation at every counter due to various type of
customers-direct customers and online or telephonic customers, which
creates problems in efficient working of the current system.
• There are some solutions that can be implemented to improve the
performance of the system.
• The proposed solutions are discussed here as two different cases:
 Case 1: No Queues
 Case 2: Improved Service Times

32. • In Case 1, we want to provide quick service to
customer, so we need to eliminate the waiting
line of customer.
• We need to make this system balanced.
• The arrival rate is 1 every 70 seconds, the
Order Counter rate is 1 every 100 seconds, and
the Kitchen Counter rate is 1 every 100
seconds.
• This is nearly a perfect production line.
• If this was implemented then the time in
system have reduced but we are losing
revenue by 69%.
Case 1: No Queues

33. Case 1: No Queues
Statistics Value Lower limit of
Confidence Interval
Upper limit of
Confidence Interval
Gain Rs. 12,743 Rs. 9,369 Rs. 20,338
Loss Rs. 74177 Rs. 63409 Rs. 89344
Billing Counter Efficiency 0.3998 0.2792 0.9982
Kitchen Efficiency 0.3995 0.3202 0.9988
Order receive counter
Efficiency
0.3994 0.3069 0.9986
Billing Counter waiting in
line
0.00 0.00 0.00
Kitchen Waiting in line 0.00 0.00 0.00
Order Receive Counter
waiting in line
0.00 0.00 0.00

34. Case 2: Improved Service Times
• Due to advancement of e business it is necessary to improve service time
of the system because of some invisible queues at each counter.
• Hence, let us consider a one more strategy which introduces new
technology that will cut the average service time at the billing counter and
the Order Window by 25% from 108 seconds to 80 seconds.
• New technology implementation will take Rs. 1,500,000/-approximately,
at each store and must be paid for by increased Gain at the store.

35. • We find the improvement in the Waiting Time in System will be dropped
to nearly two third of present condition.
• We have virtually eliminated many lost customers, and have increased
Gain by Rs 13595/- per day. We would pay back the 1,500,000/-for the
implementation of the new technology in 115 days or less than 4 months.
• This investment is profitable for the organization easily observed through
Graphical interpretation

36. Case 2: Improved Service Times
Statistics Value Lower limit of
Confidence Interval
Upper limit of
Confidence Interval
Gain Rs. 86,920 Rs. 80,294 Rs. 1,05,850
Loss 0 0 0
Billing Counter Efficiency 0.9981 0.6982 0.9981
Kitchen Efficiency 0.9987 0.8004 0.9987
Order receive counter
Efficiency
0.9985 0.7672 0.9985
Billing Counter waiting in
line
0.1197 0.0682 1.2292
Kitchen Waiting in line 0.1070 0.0071 0.1142
Order Receive Counter
waiting in line
0.0210 0.0177 1.0309

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