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Modeling and Simulation Lab Queuing Theory for Presentation by :- Rajat Goyal(2014UME1504) Pawan Yadav(2014UME1488) Sagar Kartik Dharmendra(2014UME1456) Presented to: Dr. Gunjan Soni
37

Simulation project on Burger King

Apr 21, 2017

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Kartik Sagar
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Page 1: Simulation project on Burger King

Modeling and Simulation Lab

Queuing Theory for

Presentation by :-

Rajat Goyal(2014UME1504)Pawan Yadav(2014UME1488)

Sagar Kartik Dharmendra(2014UME1456)

Presented to:

Dr. Gunjan Soni

Page 2: Simulation project on Burger King

WHY BURGER KING ????

Huge foot fall in the Peak Hours Proper Utilization of Restaurant’s resources

Location : GT CENTRAL

Rush hours : 6:30 – 8:30 pm

The evening hours experiences almost 1000 customers at the shop

Page 3: Simulation project on Burger King

In the rush hours the average waiting time of the customer reaches up to 15 minutes at the cash counters itself..………!!!!!!!!!!!!

With competition being nearby itself, efficiency must be worked upon

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• There are no breaks for the workers during the time when the model is running. Every counter has a single server.

• Only one customer from each group place an order and even that is only once. No repetition in order is observed.

• Group of 4 customers or exceeding are averaged as group of five based on data.

• There is no intermixing in queue of different cash counters and service counters as observed in minimum cases.

• The time is assumed to be same for both cash counters and also at service counters.

• The ice cream ordered by a person dining is taken at the ice cream counter separately.

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PROBLEM LAYOUT

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Data Collection

Input Analyzer Modelling Simulation Result

Interpretation

Finding the Distribution• Data Entry• Curve fitting

Finding the Distribution• Data Entry• Curve fitting

Multiple iteration on the basis of entered Data

Interpret the data (output) to put in form of Physical Model

ARENA –STUDENT VERSION

Process Followed

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DATA COLLECTION

Time of data collection: 6:30-8:30 pmNo. of visits made: 5

DATA

CO

LLEC

TIO

NRelative arrival time of customers with

group size for both take away counter and dine in counters.

Service time at cash counters for a set of customers.

Service time at food counters for same set of customers.

Sitting time also of same group.

Service time at ice cream counter.

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DATA SAMPLESGroup size Stop watch time(mins) Time in seconds

2 0:00 0

3 0:13 131 1:25 853 2:08 1281 5:15 3181 5:35 3353 7:17 4372 7:25 4452 8:32 512

ORDER START ORDER END ORDER TIMEMIN SEC TIME IN SEC MIN SEC TIME IN SEC SEC

3 40 220 6 16 376 156

18 38 1118 27 51 1671 553

25 40 1540 26 26 1586 46

32 6 1926 39 4 2344 418

33 51 2031 36 32 2192 161

35 58 2158 37 1 2221 63

41 27 2487 44 50 2690 203

Data of Arrival

Sample of Data of Cash Counter (also similar for food counter service and the Take away service)

Page 13: Simulation project on Burger King

DATA FITTING TO DISTRIBUTIONS

Raw data collected was modified as shown below in tabular form:FREQUENCY TABLE FORMATION FOR ARRIVAL OF PEOPLE IN GROUP OF 2

TIME INTERVAL (sec) MEAN VALUE FREQUENCY

0-100 50 23

100-200 150 8

200-300 250 5

300-400 350 0

400-500 450 1

500-600 550 0

600-700 650 1

700-800 750 1

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DATA FITTING TO DISTRIBUTIONS

Frequencies of different interval were arranged in text file and distribution for each data file was plotted to find the required expression.

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DATA FITTING TO DISTRIBUTIONS

• The expression obtained with a least square error is: 20 + EXPO(85.4).

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ARRIVAL OF ONE PERSON 50 + EXPO(158).

ARRIVAL OF THREE PERSON 50 + EXPO (200)

ARRIVAL OF MORE THAN FOUR PERSON

TRIA( 50, 95.8, 1.15e+003).

CASH COUNTER SERVICE RATE TRIA(62,117,238)

FOOD COUNTER SERVICE RATE NORM(264,189).

IDLE TIME IN SITTING TRIA( 50, 200, 1.15e+003).

SITTING TIME FOR MEAL TRIA (450, 582, 2.25e+003).

ICE CREAM COUNTER/ TAKE AWAY ARRIVAL RATE

25 + EXPO(116).

TIME IN TAKE AWAY/ ICE CREAM COUNTER

NORM (71.2, 36.6)

DATA FITTING TO DISTRIBUTIONS

Page 17: Simulation project on Burger King

ARENA MODEL

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RUN SETUP

• Simulation run for 2 hours

• Total no. of

replication were 20 for most appropriate result

Page 19: Simulation project on Burger King

SIMULATION

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RESULTS

BY ENTITY

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RESULTS

BY QUEUE

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ARENA MODEL

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RESULTS

Total average number of seats occupied in a system is 40 while number of person prefers ice cream or take away the order is 53.

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NOW WE PROVIDE THE INTERPRETATION AND POSSIBLE SOLUTION……….

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Increase the customer productivity by decreasing

time at cash counters.

Increase the labor productivity by increasing the

resource utilization factor.

FINALLY….REDUCTION IN QUEUE LENGTH

INTERPRETED SOLUTION

Automated Soda Fountain Machine

TOKEN SYSTEM

USED…..!!!!!

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INTERPRETED SOLUTION

Digital Display Queue Management System for order status

• Decrease the crowd and for instantaneous acknowledgement of order delivery to the customer.

• Decrease the overall service time and queue length at the service counters.

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INTERPRETED SOLUTION

INCREMENT IN BURGER MACHINE

REDUCTION IN SERVICE TIME

Approximate cost : Rs 7,00,000

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INTERPRETED SOLUTION

Get your order here app

No standing

in queue

Direct food

service with

generated token no.

• Will increase the potential of customer• Lead to mass expansion of Burger King

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IMPROVED MODEL

ADDITIONAL DECISION FOR COKE COUNTER

COKE COUNTER

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CHANGES PROPOSED

Expression 20 + EXPO(31).

Resource Self Serviced

Action Seize Delay Release

Customer Preference 70%

Improved Cash Counter Service Expression

NORM(120, 40.5)

Improved Food Counter Service Expression

NORM(180,160)

Self service soda fountain Machine

Digital Display Queue Management System

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PROCESS ANALYZER OUTPUTS

• The number out is increased to 233.• Average customers in system is decreased to 60

BY ENTITY

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CHANGES PROPOSED

BY QUEUE

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STATISTICAL COMPARISION

Cash Counter1

Cash Counter2

Food Counter1

Food Counter

Actual Model 544 438 1466 1378

Proposed Model

259 183 1115 787

Time decrement

4 Minutes 45 Seconds

4 Minutes 15 Seconds

5 Minutes 52 Seconds

9 Minutes 52 Seconds

Cash Counter1

Cash Counter2

Food Counter1

Food Counter

Actual Model 4.6 3.4 10.7 9.4

Proposed Model

2.1 1.4 8.2 5.4

•Waiting Time( in seconds)

•Waiting Queue( in numbers)

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STATISTICAL COMPARISION

RESOURCE UTILIZATION

Resource 1 Resource 2 Resource 3 Resource 4 Resource 50

0.2

0.4

0.6

0.8

1

1.2

Actual ModelProposed Model

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BY USER SPECIFIED

Number of customer occupying a sit is increased by 5 persons.

STATISTICAL COMPARISION

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THANK YOU..!!!

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QUSETIONS AND ANSWERS