Engineering 25
Monte Carlo
vs. PERT
Tutorial
Bruce Mayer, PE
Registered Electrical & Mechanical Engineer
BMayer@ChabotCollege.edu
ENGR/MTH/PHYS25: Computational Methods
1
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Catenary_Tutorial_Part-1.ppt
NO Time Machines Allowed
 In the Lecture on Monte Carlo
Methods as used in the PERT Prob we
allowed NEGATIVES in the Simulation
 Someone might point out that
no matter how hard we work
we can not MAKE time
• We can only USE time!
 ReDo the simulation
withOUT negative Times
ENGR/MTH/PHYS25: Computational Methods
2
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Catenary_Tutorial_Part-1.ppt
Recall WhareHouse PERT chart
A
2
B
E
1. Project Start
4
C
3
F
5
G
6
H
7
1. Project End
D
 The Schedule Elements
A. Excavate Foundation
B. Construct Foundation
C. Fabricate PreCast
Components
D. Ship PreCast Parts
to Building Site
ENGR/MTH/PHYS25: Computational Methods
3
E. Install PreCast Parts
on Foundation
F. Build Roof
G. Finish Interior
and Exterior
H. Inspect Result
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Catenary_Tutorial_Part-1.ppt
Possibility of Negative Times
 A Small MeanDuration:StdDev ratio indicates a
higher probability of NEGATIVE durations
Task
ID
Task Description
Mean Duration Std Dev
(days)
(days)
A
Foundation Excavation
3.5
1
B
Pour Foundation
2.5
0.5
C
Fab PreCast Elements
5
1
D
Ship PreCast Parts
0.5
0.5
E
Tilt-Up PreCast Parts
5
1.5
F
Roofing
2
1
G
Finish Work
4
1
Expected Duration = 17 Days
ENGR/MTH/PHYS25: Computational Methods
4
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Catenary_Tutorial_Part-1.ppt
5000-Trials Look for Negatives
Task-A
3.056436
2.52984
1.863874
5.206441
2.5827
1.949553
2.991668
2.814304
2.899662
1.717857
4.772899
3.642672
3.580282
5.186825
3.606338
4.374921
4.500536
5.98265
3.291704
3.012582
2.973899
3.650796
2.122011
Task-B
2.961331
1.818524
2.261628
3.185492
2.744966
2.555277
2.669537
2.955902
2.038455
2.10672
2.937509
2.97833
2.741434
2.52439
2.644464
2.868406
2.672725
3.042048
2.58989
3.036188
2.270489
2.599723
1.891614
Task-C
3.947419
5.700165
6.33204
4.912228
6.773191
4.768627
5.649579
6.515047
5.509873
4.063236
4.56152
5.607318
4.458148
4.275817
6.295698
3.340125
5.286593
5.957864
4.831462
5.1351
5.889376
6.28384
3.245027
Task-D
0.129733
0.707146
0.548261
1.270599
0.405553
0.658296
0.769109
0.861729
0.947595
0.0393
-0.15291
0.690005
0.186039
-0.20955
0.157704
0.889552
0.61676
0.735978
0.618231
0.487848
0.910165
-0.1219
0.290797
Task-E
7.033597
5.433
4.69831
5.910327
4.601242
5.151766
6.116489
5.689127
5.159136
5.278079
4.652642
4.635663
5.428526
4.214853
4.325839
5.382214
6.203332
6.859155
2.904533
6.276146
5.469366
4.742472
6.940307
Task-F
0.5795
2.35778
2.830361
1.708905
1.551149
0.838188
3.063697
2.145403
1.083515
0.270139
0.997027
0.710531
1.43336
2.476978
0.921243
2.370047
0.922175
1.87421
1.493275
2.768654
1.474232
2.360848
2.041024
Task-G
3.274485
4.295592
3.616241
4.320006
4.343192
3.394338
4.995988
4.665907
3.096153
4.420309
3.57045
5.212377
3.325785
4.042575
4.013296
3.917809
4.83254
4.637405
3.915265
3.641933
3.917351
4.122835
4.334514
0
0
0
765
2
94
0
15.30%
0.04%
1.88%
ENGR/MTH/PHYS25: Computational Methods
5
SUM
Run
16.90535
1
18.49368
2
18.02521
3
20.33117
4
17.67433
5
14.81121
6
20.59486
7
19.87721
8
15.79627
4986
14.07106
4987
16.93053
4988
17.17957
4989
16.50939
4990
18.44562
4991
15.71378
4992
18.9134
4993
19.13131
4994
22.39547
4995
14.19467
4996
18.7355
4997
17.66049
4998
17.47667
4999
17.32947
5000
0
<0's
% <0
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Catenary_Tutorial_Part-1.ppt
Expected Standard Deviation (RMS)
 Find the Expected Standard Deviation
by GeoMetric (or Pythagorean or RMS)
Calculation
m
 ex 

k 1
2
k
 In This case take the Std Dev from the
GATING item A+B to find:
 ex  2.1794 days recall tex  17 days
ENGR/MTH/PHYS25: Computational Methods
6
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Catenary_Tutorial_Part-1.ppt
Compare Lack of Time Machine
 Review and Run Files:
• Monte_Carlo_Wharehouse_1604.m
– Can MAKE time
• Monte_Carlo_Wharehouse_Vectorized.m
– NO Loops
• Monte_Carlo_Wharehouse_No_Negatives.m
– Can NOT make time
A “Flux Capacitor”
ENGR/MTH/PHYS25: Computational Methods
7
Bruce Mayer, PE
BMayer@ChabotCollege.edu • ENGR-25_Catenary_Tutorial_Part-1.ppt