1. MGS3100_08.ppt/Dec 8, 2014/Page 1 Georgia State University - Confidential MGS 3100 Business Analysis Simulation Dec 8, 2014

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

3. MGS3100_08.ppt/Dec 8, 2014/Page 3 Georgia State University - Confidential 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. MGS3100_08.ppt/Dec 8, 2014/Page 4 Georgia State University - Confidential Types of Simulations Simulation Discrete 2-Value Multi- Valued Continuous

5. MGS3100_08.ppt/Dec 8, 2014/Page 5 Georgia State University - Confidential 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? HeadsTails 0.0.51.0

6. MGS3100_08.ppt/Dec 8, 2014/Page 6 Georgia State University - Confidential Types of Simulations Multi-Valued Suppose we put 100 colored balls in a bag and randomly pull them out. Color# ProbabilityCumulative Red25 25%.25 Blue42 42%.67 Yellow33 33% 1.0 RedBlueYellow 0.0.25.67 1.0 =if(f7<=c$7,“Red”,if(f7<=c$8,“Blue”,“Yellow”))

7. MGS3100_08.ppt/Dec 8, 2014/Page 7 Georgia State University - Confidential Types of Simulations Multi-Valued Using vlookup, where does Red start? Grades example. –Equal distribution of grades A through F: =randbetween(50,100) FDCBA 50 60 70 80 90 100

8. MGS3100_08.ppt/Dec 8, 2014/Page 8 Georgia State University - Confidential Agenda Simulations Problems

9. MGS3100_08.ppt/Dec 8, 2014/Page 9 Georgia State University - Confidential 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 DemandedNumber of weeks 131 142 154 169 1710 1815 1916 2015 2112 229 234 242 251 260 Total100

10. MGS3100_08.ppt/Dec 8, 2014/Page 10 Georgia State University - Confidential 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. MGS3100_08.ppt/Dec 8, 2014/Page 11 Georgia State University - Confidential Problem 2 – Queuing System SSSQ – simplest SSMQ MSSQ MSMQ Examples of each? Arrive in queue Service begins Service ends Wait time in queueService time Wait time in system

12. MGS3100_08.ppt/Dec 8, 2014/Page 12 Georgia State University - Confidential 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?