1. MGS 3100 Business Analysis Simulation Apr 21, 2016

2. Agenda
Simulation
Problems

3. 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

4. Types of Simulations

5. Types of Simulations 2-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

6. Types of Simulations Multi-Valued
Suppose we put 100 colored balls in a bag and randomly pull them out.
Color # Probability Cumulative
Red %
Blue %
Yellow %
Red
Blue
Yellow
=if(f7<=c$7,“Red”,if(f7<=c$8,“Blue”,“Yellow”))

7. Types of Simulations Multi-Valued
Using vlookup, where does Red start?
Grades example.
Equal distribution of grades A through F:
=randbetween(50,100) F D C B A

8. Agenda
Problems
Simulations

9. 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 19 20 21 12 22 23 24 25 26
Total
100

10. 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

11. 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

12. 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?