MGS3100_08.ppt/Dec 8, 2014/Page 1Georgia State University - Confidential

MGS 3100

Business Analysis

Simulation

Dec 8, 2014

MGS3100_08.ppt/Dec 8, 2014/Page 2Georgia State University - Confidential

Agenda

ProblemsSimulation

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Simulation

• What is a simulation?

• What does random mean?

• Benefits to simulation:– Time can be compressed – Simulations do not disrupt ongoing activities of the real system – Simulations can be used to analyze transient (infrequent) conditions – Developing a simulation model can lead to better understanding of the

real system

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Types of Simulations

Simulation

Discrete Continuous

2-Value Multi-Valued

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Types of Simulations2-Value: Coin Toss

• Create a column of random numbers from 0 to 1• How would you assign a value to heads and tails?

Heads Tails

0.0 .5 1.0

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Types of SimulationsMulti-Valued

• Suppose we put 100 colored balls in a bag and randomly pull them out.

Color # Probability CumulativeRed 25 25% .25Blue 42 42% .67Yellow 33 33% 1.0

Red Blue Yellow

0.0 .25 .67 1.0

=if(f7<=c$7,“Red”,if(f7<=c$8,“Blue”,“Yellow”))

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Types of SimulationsMulti-Valued

• Using vlookup, where does Red start?• Grades example.

– Equal distribution of grades A through F:

=randbetween(50,100)

F D C B A

50 60 70 80 90 100

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Agenda

Simulations Problems

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Problem 1

• Jimmy prints a neighborhood newspaper. He has 10 subscribers. He also sells it to whoever comes by, from his front lawn on Friday afternoons. His mother has kept track of his demand (including requests made after he had sold out) for the past 100 weeks, and observed the following pattern:

• The papers cost 30 cents to print and Jimmy sells them for 50 cents. Assume that he prints 20 copies a week. Mom makes him throw away unsold copies. Simulate his sales for a year and determine his earnings.

• What if the # printed were adjusted?

Papers Demanded Number of weeks

13 1

14 2

15 4

16 9

17 10

18 15

19 16

20 15

21 12

22 9

23 4

24 2

25 1

26 0

Total 100

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Problem 2 – Queuing System

• Trucks arrive at a loading dock on average every 0.6 hours. It takes on average 0.5 hours to unload a truck. Assuming that arrival intervals and service times are exponentially distributed, simulate the queuing system to find the average waiting times and the average number of trucks in the queue/system.

• Suppose you could install an new conveyor belt system to unload trucks faster, so that the average unloading time is cut to 0.25 hours. How much improvement will there be in the average waiting time and average number in queue/system?

• Queuing systems consist of multiple inputs: Number of servers, Number of Queues Arrival rate/Arrival interval Service rate/Service time

• And multiple outputs: Average wait time Average number in queue / system

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Problem 2 – Queuing System

• SSSQ – simplest• SSMQ• MSSQ• MSMQ• Examples of each?

Arrive in queue

Service begins

Service ends

Wait time in queue Service time

Wait time in system

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Exponential Distribution

• Take Random #

• Take the negative logarithm of random #, and multiply by average desired

• After looking at histogram, why can’t we break-down distribution to exact probabilities?