Class:DSES 6620 Simulation Modeling And Analysis

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Class DSES - 6620 Simulation Modeling And
Analysis Homework L6.11 Exercises Name Kevin
Lewelling Date March 13, 2002 1. Visitors
arrive at Kids World engertainment par according
to an exponential interarrival time distribution
with mean 2.5 minutes. The travel time from the
entrance to the ticket window is normally
distributed with a mean of three minutes and
standard deviation of 0.5 minutes. 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 minutesand standard
deviation of one minute. After purchasing
tickets, the visitors go to their respective
gates to enter the park. Creat a simulation
model, with animation, of this system. Run the
simulation 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 cashiers. D. Do you recommend that
management add more cashiers? Answers A. Average
time in queue - 0.0051 visitors Maximum time in
queue - 3 visitors b. Average 4714/200hrs
23.57 visitors/hr c. Average cashier utilization
32.775 d. No. 2. A consultant recommended that
six individual queues be formed at the ticket
window (one for each cashier) 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. Th
average number of customers completing ticketing
per hour. C. The average utlization of the
cashiers. D. Do you agree with the consultants
decision? Would you recomment a raise for the
consultant? Answers Assuming that customers
coninued to arrive in each queue at the same rate
as they arrived in the single queue
before... A. Average 1210.12 Maximum
2460 B. Per hour average 14,437/200hrs
72.185 C. 100 D. If the arrivals were indeed as
described in the assumption, then the consultant
was doomed to fail since visitors were just
arriving at a higher rate. I wouldnt fire him
because this is a different problem. Rerunning
the same model but multiplying the mean
interarrival times by 6 to account for the
arrival times that each cashier would normally
see. A. Average 0.08541 Visitors Maximum 4
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B. Average per hour 4831/200 24.16 C. Cashier
utlization 33.56 D. No. There was no huge
improvement to be had no raise for the
consultant.. Just pay him his money. 3. At the
Southern California Airlines traveler check-in
facility, three types of customers arrive
passengers with e-ticket (Type E), passengers
with paper ticket (Type T), and passengers that
need to purchase ticket (Type P). Ther
interarrival distribution and the service times
for these passengers 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? Discuss the pros and cons for such a
change. Answers A. Average length 0.698
passengers Maximum length 5 B. Average Type E
21224/2000 10.61 passengers/hr Average Type
T 10929/2000 5.46 passengers/hr Average Type
P 7301/2000 3.65 passengers/hr C. Average
Gate Agent Utilization Type E 53.09 Type T
72.74 Type P 73.0 D. No. With one line,
there may be some additional delay in getting
passengers to the correct lines. The current
utilization is good, however any more of a
drop-off would minimize the agents utilization.
The argument could be made that one line would
minimize confusion, but that would also have to
assume that each agent was capable of processing
all 3 ticket types. Six to one, half-dozen to
another. 4. Raja Rani, a fancy restaurant in
Sant Clara, holds a maximum of 100 diners.
Customers arrive according to an exponential
distribution with a mean of 35 minutes.
Customers stay in the restaurant according to a
triangular distribution with a minimum of 30
minutes, a maximumof 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 number of diners
entering the restaurant before it fills? C. What
is the utilization of the restaurant? Answers A.
Infinity.. It never fills. B. Who knows It
never fills. C. After 8 hours of running,
utilization is 7.57.
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5. United Electronics manufactures small custom
electronic assemblies. There are four stations
through which the parts must be processed
assembly, soldering, painting, and inspection.
Orders arrive with an exponential interarrival
distibution (mean 20 minutes). The process time
distributions are shown in the table. The
soldering operation can be performed on three
jobs at a time. Painting can be done on fours
jobs at a time. Assembly and inspection are
performed on one job at a time. Creat 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, and the total number of jobs
manufactured during each eight-hour shift
(average). 6. Consider the Exercise 5 with 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 distibuted. 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 likelihood of another
defect being found is the same as during the
first inspection. We assume in this model that
an assembly defect is eventually corrected and
then passed on to the next station. Simulate for
one year (2000 hours) and determine the number of
good applianced shipped in a year. Answer 602
units 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. Simulate the system
for 100 days, eight hours 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, ant the average cycle time for all
jobs. Anaswers Average Number of Jobs Waiting
for operation Type 1 - 1.79 Type 2 -
10.39 Average Number of Jobs Finished eaach
day Type 1 - 25.94 Type 2 - 38.52
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Average Cycle Time for each type of job Type 1 -
122.89 minutes Type 2 - 86.52 minutes Average
Cycle Time for all jobs (122.8986.52)/2104.71
minutes 9. Six dump trucks at the DumpOnMe
facility in Riverside are used to haul coal from
the entrance of a small mine to the railroad.
Figure L6.39 provides a schematic of the dump
truck operation. Each truck is loaded by one of
two loaders. After loading, a truck immediately
moves to the scale to be wieghted as soon as
possible. Both the loaders and the scale have a
first-come, first-served waiting line (or queue)
for trucks. Travel time from a loader to the
scaled is considered negligible. After being
weighed, a truck begins travel time (during which
time the truck unloads), and then afterward
returns to the loader queue. The distributions
of loading time, wighing time, and travel time
are shown in the table. A. Create a simulation
model, with animation, of this system. Simulate
for 100 days, eight hours each day. B. Collect
statistics to estimate the loader and scale
utilization (percentage of time busy). C. About
how many trucks are loaded each day on
average? Anaswers b. Loader Utilization
Loader 1 - 60.93, Loader 2 - 61.52 Scale
Utilization 51.4 c. Trucks Loaded 103.87 104
Trucks 10. At the Pilot Pen Company, a molding
machine produces pen barrels of three different
colors - red, blue, and green - in the ratio of
321. The molding time is triangular (3, 4, 6)
minutes per barrel. The barrels go to a filling
machine where ink of appropriate color is filled
at a rate of 20 pens per hour (exponentially
distributed). Another molding machine makes caps
of three different colors - red, blue, green - in
the ratio of 321. The molding time is
triangular(2, 3, 4) minutes per cap. At the next
station, caps and filled barrels of matching
colors are joined together. Simulate for 300
hours. Find the average num er of pens produced
per hour. Collect statistics on the utilization
of the molding machines and the joining
equipment.
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11. Customers arrive at the No Wait Burger
hamburger stand with an interarrival time that is
exponentially distributed with a mean of one
minute. Out of 10 customers, five buy a
hamburger and a drink, three buy a hamburger, and
two buy just a drink. One server handles the
hamburger while another handles the drink. A
person buying both items needs to wait in line
for both servers. The time it takes to serve a
customer is normally distributed with a mean of
70 seconds for each item. Simulate for 100 days,
eight hours each day. Collect statistics on the
number of customers served each day, size of
queues, and utilization of the servers. What
changes would you suggest to make the system more
efficient? Average Arrivals per day 425.03
customers Average Length of Hamburger Line 2
customers Average Length of Drink Line 2
customers Average number of Customers
with Hamburger Only 126.58 customers Drink
Only 82.51 customers Hamburger Drink 214.31
customers Total Hamburgers 340.89
customers Total Drinks 295.58 customers Server
Utilization Hamburger Hut 82.96 Drink
Hut 71.94 12. Workers who work at the Detroit
ToolNDie plant must check out tools from a tool
crib. Workers arrive according to an exponential
distribution with a mean time between arrivals of
five minutes. At present, three tool crib clerks
staff the tool crib. The time to serve a worker
is normally distributed with a mean of 10 minutes
and a standard deviation of two minutes. Compare
the following serving methods. Simulate for a
24-hour period and collect data. A. Workers form
a single queue, choosing the next available tool
crib clerk. B. Workers enter the shortest queue
(each clerk has his/her own queue.) c. Workers
choose one of three queues at random.