Transcript l6.11 exercises

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DSES - 6620 Simulation Modeling And Analysis
L6.11 Exercises
Kevin Lewelling
March 13, 2002
1. Visitors arrive at Kid’s 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 consultant’s 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 wouldn’t 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
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 Airline’s 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, halfdozen 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%.
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
Average Cycle Time for each type of job
Type 1 - 122.89 minutes
Type 2 - 86.52 minutes
Average Cycle Time for all jobs
=(122.89+86.52)/2=104.71 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, firstserved 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 3:2:1. 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 3:2:1. 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.
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.