People arrive at a self-service cafeteria at the rate of one every 30 ± 20 sec.Forty % go to the sandwich counter, where one worker makes a sandwich in 60 ± 30 sec. The rest go to the main counter, where one server spoons the prepared meal on to a plate in 45 ± 30 sec.All customers must pay a single cashier, which takes 25 ± 10 sec. For all customers eating takes 20 ± 10 min.
After eating, 10% of the people go back for dessert, spending an additional 10 ± 2 min.
altogether in the cafeteria. Simulate until 100 people have left the cafeteria. How many people are left in the cafeteria, and what are they doing, at the time simulation stops?
SOLUTION:
Arrival Record ver-1 Record ver-2 Manager
TRIA (7, 10, 13) ie, 10 3 min
TRIA (6, 10, 14) Ie, 10 4 min
NORM (3.1)
10%
Counter 1-Record ver-1 Counter 2- Record ver-2 Counter 3-Manager
Dept. of IE&M, DSCE, Bangalore Page 21
Dept. of IE&M, DSCE, Bangalore Page 22
Dept. of IE&M, DSCE, Bangalore Page 23
Dept. of IE&M, DSCE, Bangalore Page 24 13. Building simulation models for Post office animation.
Customers arrive at the post office according to an exponential inter-arrival time distribution with mean 3 mins.There are two counters 1 is letter weighing with triangular distribution (7,10,13) and stamping counter with triangular distribution (6,10,14).The customers who comes to post his letters has to check his letters at the inspection counters. The inspection time follows triangular distribution (12,15,20) and 10% of the letters gets rejected and sent back to counter 1 and others go to deposit and are free to travel to their exit. The deposit counter has triangular distribution (6,10,14). Run the simulation for 20 customers to determine the avg.
time in system.
SOLUTION:
Dept. of IE&M, DSCE, Bangalore Page 25 14. Building simulation models for manufacturing operations (Multi arrivals)
Simulate a simple processing system which consists of a drilling machine and the processing tie varies according to Triangular distribution of minimum 1, value 3 and maximum 6. The Part enters the system with a random exponential value of 5 minutes, and then leaves the system. All time units are in minutes. Animate the resource and queue. Simulate the process for 20 minutes. Plot the number waiting at the drill center queue and number busy at the drill press. Report the simulation run statistics.
Add a second machine to which all the parts go immediately after exiting the first machine for a separate kind of processing (Rewash). Processing ties at the second machine are the same as for the first machine. Gather all the statistics as before, plus the time in queue, queue length and utilization at the second machine.
Dept. of IE&M, DSCE, Bangalore Page 26 Immediately after the second machine, there is a pass/fail inspection that takes a constant 5 minutes to carry out and has an 80% chance of passing result; Queuing is possible at inspection, and the queue is first in and first out. All parts exit the system regardless of whether they pass the test. Count the number that fail and the number that pass, and gather statistics on the time in queue, queue length and utilization at the inspection center. Run the simulation for 480 minutes.
In the above exercise, suppose that parts that fail inspection after being washed are sent back ad rewashed, instead of leaving, such rewashed parts must then undergo the same inspection and the same probability of failing. There is no limit on how many times a given part might have to loop back through the waster. Run this model under the same conditions and compare the results for the time in queue length and utilization at the inspection center.
SOLUTION:
Dept. of IE&M, DSCE, Bangalore Page 27 15. Statistical Analysis of Simulation models ( input analysis)
Generate 50 random numbers using RAND function in MS Excel and using them , further generate exponential variates using inverse transform technique. Test the goodness of fit.
SOLUTION:
Random No.
Random Variates (mean=0.5)
Random Variates (mean=1)
Random Variates (mean=2)
0.34942426 2.102936922 1.051468461 0.525734231
Dept. of IE&M, DSCE, Bangalore Page 28
0.75398787 0.564757999 0.282379 0.1411895
0.83119928 0.369771406 0.184885703 0.092442851
0.19707692 3.248322341 1.624161171 0.812080585
0.95939372 0.082907478 0.041453739 0.02072687
0.19679708 3.251164262 1.625582131 0.812791066
0.67341197 0.790795988 0.395397994 0.197698997
0.01182342 8.875346555 4.437673277 2.218836639
0.69035954 0.741085475 0.370542738 0.185271369
0.5680591 1.13105964 0.56552982 0.28276491
0.20272889 3.191771405 1.595885703 0.797942851
0.12322261 4.187525414 2.093762707 1.046881354
0.9604718 0.080661324 0.040330662 0.020165331
0.61783486 0.963068149 0.481534075 0.240767037
0.54440614 1.216119442 0.608059721 0.304029861
0.42772325 1.69855779 0.849278895 0.424639448
0.93817615 0.127635103 0.063817552 0.031908776
0.07021059 5.312512364 2.656256182 1.328128091
0.20173488 3.2016018 1.6008009 0.80040045
0.51447138 1.329230705 0.664615352 0.332307676
0.73889691 0.605193721 0.30259686 0.15129843
0.1535534 3.747413771 1.873706886 0.936853443
0.11885466 4.259707671 2.129853835 1.064926918
0.92109534 0.164383471 0.082191735 0.041095868
0.74612934 0.585712627 0.292856314 0.146428157
0.11096276 4.397121272 2.198560636 1.099280318
0.14292567 3.890861152 1.945430576 0.972715288
Dept. of IE&M, DSCE, Bangalore Page 29
0.86837213 0.282269881 0.141134941 0.07056747
0.95016848 0.102231933 0.051115966 0.025557983
0.08687523 4.886564662 2.443282331 1.221641166
0.31878421 2.286481707 1.143240853 0.571620427
0.21023089 3.119097724 1.559548862 0.779774431
0.85270564 0.318681759 0.159340879 0.07967044
0.47450091 1.490983497 0.745491749 0.372745874
0.64069869 0.890392003 0.445196002 0.222598001
0.34739541 2.114583301 1.057291651 0.528645825
0.58908043 1.058385094 0.529192547 0.264596273
0.43517295 1.664023461 0.83201173 0.416005865
0.13344206 4.028175789 2.014087894 1.007043947
0.02800066 7.151054503 3.575527251 1.787763626
0.5971271 1.031250586 0.515625293 0.257812647
0.72270844 0.649498795 0.324749398 0.162374699
0.56911198 1.12735612 0.56367806 0.28183903
0.30782299 2.35646074 1.17823037 0.589115185
0.40621095 1.801765359 0.900882679 0.45044134
0.83066526 0.371056753 0.185528377 0.092764188
0.95793161 0.085957773 0.042978887 0.021489443
0.21657064 3.059677024 1.529838512 0.764919256
0.50232396 1.37702007 0.688510035 0.344255018
0.72944748 0.630935811 0.315467906 0.157733953
Dept. of IE&M, DSCE, Bangalore Page 30
Dept. of IE&M, DSCE, Bangalore Page 31 Problems for Practice:
1. Simulate a simple processing system which consists of a drilling machine and the processing time varies according to Triangular distribution of minimum 1, value 3 and maximum 6. The part enters the system with a random exponential value of 5 minutes.
And then leaves the system. All time units are in minutes. Animate the resource and queue. Simulate the process for 20 minutes. Plot number waiting at drilling center queue and number busy at drill press. And report the following data
The average total time in the system (part) and
Utilization of drill press
The last part number which entered the system
Number of parts which leaves the system
Average and maximum number of parts in process (wip)
Make 5 replications of the above simulation. And observe the changes in output.
Tabulate the readings.
2. Simulate a simple processing system which consists of a drilling machine and the processing time varies according to Triangular distribution of minimum 1, value 3 and maximum 6. The part enters the system with a random exponential value of 5 minutes. After exiting the first machine the parts go for a separate kind of processing (rewash). Processing times at the second machine are the same as for the first machine. After processing at 2 machine the part leaves the system. All time units are in minutes. Gather all statistics:
The average total time in the system (part)
Utilization of drill press and utilization at the second machine
The last part number which entered the system
Number of parts which leaves the system
Average and maximum number of parts in process (wip)
Time in queue, queue length.
Animate the resource and queue.
Plot number waiting at drilling center queue and number busy at drill press &
rewash.
Run the simulation for 480 minutes
Dept. of IE&M, DSCE, Bangalore Page 32 3.Simulate a simple processing system in which The part enters the system with a random exponential value of 5 minutes. The part moves to a drilling machine and the processing time varies according to Triangular distribution of minimum 1, value 3 and maximum 6. After exiting the first machine the parts go for a separate kind of processing (rewash). Processing times at the second machine are the same as for the first machine. Immediately after the second machine, there’s a pass fail inspection that takes a constant 5 minutes to carry out and has an 80% chance of passing result; queuing is possible at inspection, and the queue is first in and first out. All parts exit the system regardless of whether they pass the test. All time units are in minutes.
Gather all statistics:
The average total time in the system (part)
Utilization of drill press, at second machine, at inspection center
The last part number which entered the system
Count number that fail and number that pass
Average and maximum number of parts in process (wip)
Time in queue, queue length.
Animate the resource and queue.
Add plots to track the queue length and number busy at all three stations.
Run the simulation for 480 minutes
4. Simulate a simple processing system which consists of a drilling machine and the processing time varies according to Triangular distribution of minimum 1, value 3 and maximum 6. The part enters the system with a random exponential value of 5 minutes. After exiting the first machine the parts go for a separate kind of processing (rewash). Processing times at the second machine are the same as for the first machine. Immediately after the second machine, there’s a pass fail inspection that takes a constant 5 minutes to carry out and has an 80% chance of passing result; queuing is possible at inspection, and the queue is first in and first out. The parts that fail inspection after being washed are sent back and rewashed, instead of leaving; such re-washed parts must then undergo the same inspection, and have the same probability of failing.
There’s no limit on how many times a given part might have to loop back through the washer.
All parts exit the system regardless of whether they pass the test. All time units are in minutes.
Gather all statistics:
Dept. of IE&M, DSCE, Bangalore Page 33
The average total time in the system (part)
Utilization of drill press, at second machine, at inspection center
The last part number which entered the system
Count number that fail and number that pass
Average and maximum number of parts in process (wip)
Time in queue, queue length.
Animate the resource and queue.
Add plots to track the queue length and number busy at all three stations.
Run the simulation for 480 minutes
5. Simulate a simple processing system in which the part enters the system with a random exponential value of 5 minutes. The part moves to the drilling machine and the processing time varies according to Triangular distribution of minimum 1, value 3 and maximum 6. After exiting the first machine the parts go for a separate kind of processing (rewash). Processing times at the second machine are the same as for the first machine. Immediately after the second machine, there’s a pass fail inspection that takes a constant 5 minutes to carry out and queuing is possible at inspection, and the queue is first in and first out. The inspection can result in one of the three outcomes; pass (probability 0.8) fail (probability 0.09) and rewash (probability 0.11). Failures leave immediately, and rewashes loop back to the washer. The above probabilities hold for each part undergoing inspection, regardless of its past history. All time units are in minutes.
Gather all statistics:
The average total time in the system (part)
Utilization of drill press, at second machine, at inspection center
The last part number which entered the system
Count number that fail and number that pass
Average and maximum number of parts in process (wip)
Time in queue, queue length.
Animate the resource and queue.
Add plots to track the queue length and number busy at all three stations.
Run the simulation for 480 minutes
Sample Viva Voce Questions:
Dept. of IE&M, DSCE, Bangalore Page 34 1. Define simulation. When is simulation the appropriate tool?
2. What are the advantages and disadvantages of simulation?
3. List the areas of applications of simulation.
4. What is a system?, and what is a model of a system?
5. Discuss the various types of models with examples.
6. What are the steps in a simulation study?
7. Name several entities, attributes, activities, events and state variables for the following systems: Cafeteria, Automobile assembly line, Grocery store, Hospital emergency room.
8. Differentiate between continuous and discrete systems.
9. What is pmf, pdf and cdf in probability distributions?
10. What are the characteristics of queuing systems?
11. List some simulation packages & briefly explain their applications.
12. What are the various methods of generation of random numbers?
13. What is Monte Carlo Simulation?
14. What are the various tests for random numbers?
15. What are the properties of randomness?
16. What are the four steps in the development of a useful model for input data?
17. What are the ways to obtain information about a process even if data are not available?
18. What are verification and validation of simulation models?
19. What are the various models of manufacturing and material handling systems?
20. How does this Simulation lab help you in your professional career?