Download Pedro Pérez Villanueva

Course: Discrete Even Simulation Course
Teacher: Dr. Ernesto Gutierrez Miravete
Womework 2 suplement

Labs 6
Present:
Pedro Pérez Villanueva
November 20 2003
1. Visitors arrive at Kid´s World entertainment park according to an exponential
interrarival time distribution with mean 2.5 minutes. The travel time for the
entrance to the ticket window is normally distributed with mean of three minutes
and standard deviation of 0.5 minute. At the ticket window, visitors wait in a
single line until one of six cashiers is available to serve them. The time for the
purchase of tickets is normally distributed with mean of five minutes and standard
deviation of one minute. After purchase ticket, the visitors go their respective
gates to enter the park,
Create a simulation model, with animation, of this system. Run the simulation
model for 200 hours to determine:
a. The average and maximum length of the ticketing queue
b. The average number of customers completing ticketing per hour.
c. The average utilization of the cashier
d. Do you recommend that management add more cashiers?
R= Is no necesary to put more cashier some cashiers a lot of time was idle
2. A consultant recommended that six individual queues be formed at athe ticket
window (one for each cashiers) instead of one common queue. Create a
simulation model, with animation of this system. Run the simulation model for
200 hours to determine:
a. The average and maximum length of the ticketing queues.
b. The average number of customers completing ticketing per hour.
c. The average utilization of cashiers.
d. Do you agree with the consultant’s decision? Would you recommend a
raise for the consultant?
3.
At the Southern California Airline’s traveler check in facility, three types of customers arrive:
passengers with e-ticket (Tipe e), passengers with paper ticket (Type t), and passengers that need
to purchase ticket (Type P),
The interarrival distribution and the service times for these passenger are given in the table .
Create a simulation model, with animation, of this system. Run the simulation model for 2000
hours. If each type of passenger is served by separate gate agents, determine the following:
a. The average and maximum length of the three queues.
b. The average number of customers of each type completing check-in procedures per hour.
c. The average utilization of the gate agents.
d. Would you recommend one single line for check-in for all three types of travelers?
Diuscuss the pros and cos for such a change.
Types of
Interarrival Distribution
Service time distribution
traveler
Type E
Exponential (mean 5.5 min)
Normal (mean 3 min.std. dev. 1 min.)
Type T
Exponential (mean10.5 min)
Normal (mean 8 min.std. dev. 3 min.)
Type P
Exponential (mean 15.5 min)
Normal(mean 12 min.std. dev. 3 min.)
4
Raja & Rani, a fancy restaurant in Santa Clara, holds a maximum of 100 dinners.
Customers arrive according to an exponential distribution with a mean of 35.
Customers stay in the restaurant according to a triangular distribution with a
minimum of 30 minutes, a maximum of 60 minutes, and a mode of 45 minutes.
Create a simulation model, with animation of this system.
a. Beginning empty, how long is it before the restaurant fills?
b. What is the total dinner number entering the restaurant before it fills?.
c. What is the utilization of the restaurant?.
5.
United Electronics manufactures small custom electronic assemblies. There are
four station through which the parts must be processed: assembly, soldering ,
painting, and inspection. Orders arrive with an exponential interarrival distribution (mean 20
minutes). The process time distribution are shown in the table.
Assembly
Uniform (12,15) minutes
Soldering
Normal
(36,10) minutes
Painting
Uniform (40,70) minutes
Inspection
Exponential (8) minutes
The soldering operation can be perfomed on three jobs at a time. Painting can be done on four jobs
at a time . Assembly and inspection are perfomed on one job at time. Create a simulation model.
With animation, of this system. Simulate this manufacturing system for 100 days, eight hours each
day. Collect and print statiscs on the utilization of each station, associated queues. And the total
number of jobs manufactured during each eigh-hour shift (average).
6. Consider the exercise 5 with the following enhancements. Ten percent of all
finished assemblies are sent back to soldering for rework after inspection. Five
percent are sent back to assembly for rework after inspection, and one percent of
all assemblies fail to pass and are scrapped.
Create a simulation model, with animation, of this system. Simulate this
manufacturing system for 100 days, eight hours each day. Collect and print
statistics on the utilization of each station, associated queues, total number of jobs
assembled, number of assemblies sent for rework to assembly and soldering, and
the number of assemblies scrapped during each eight-hour shift (average).
7. Small appliances are assembled in four stages (Centers 1,2 and 3 and Inspection)
at Pomona Assembly Shop. After each assembly step, the appliance is inspected
or tested and if a defect is found, it must be corrected and then checked again. The
assemblies arrive at a constant rate of one assembly per minute. The times to
assemble, test, and correct defects are normally distributed. The mean and
standard deviation of the times to assemble, inspect, and correct defects, as well
as the likelihood of an assembly error, are shown in the following table. If an
assembly is found defective, the defect is corrected and it is inspected again. After
a defect is corrected, the likelihoof of another defect being found is the same is
during the first inspection. We assume in this model that an assembly defect is
eventually corrected and then it is passed on the next station.
Assembly Time
Inspect Time
Center
Mean
Standard
Deviation
Mean
1
2
3
0.7
0.75
0.8
0.2
0.25
0.15
0.2
0.25
0.15
Correct Time
Standard
.P (error)
Deviation
0.05
0.05
0.03
0.1
0.05
0.03
Mean
Standard
Deviation
0.2
0.15
0.1
0.05
0.04
0.02
Simulate for one year (2000 hours) and determine the number of good appliances
shipped in year.
8. Salt Lake City Electronics manufactures small custom communication equipment.
Two different job types are to be processed within the following manufacturing
cell. The necessary data are given in the table.
Job Number of
Number of
Type Batches Jobs per Batch
Assembly
Time
Soldering
Time
Normal
(36,10)
1
15
5
Triat (5,7,10)
2
25
3
Triat
(7,10,15)
Painting Time
Uniform
(40,70)
Uniform
(30,40)
Inspection
Time
Time between
Batch Arrivals
Exponential (8)
Exp (14)
Exponential (8)
Exp (10)
Simulate the system for 100 days, eight hors each day, to determine the average
number of jobs waiting for different operations, number of jobs of each type
finished each day, average cycle time for each type of job, and the average cycle
time for all jobs.
10. At the Pilot Pen Company, a modeling machine produces pen barrels go to a
filling machine where ink of appropiate color is filled at the rate of 20 pens per
hour (exponentially distributed). Another modeling machine makes caps of three
different colors-red,blue, and green-in the ratio of 3:2:1. The molding time is
triangular (2,3,4) minutes per capo. At the next station, caps and filled barrels of
matching colors are joined together. Simulate for 300 hours. Find the average
number of pens produced per hour. Collect statistics on the utilization of the
molding machines and the joining equipment.