Sanjeev Saitia
Sanjeev Saitia
Project Submittal
For Discrete Event Simulation and Modeling
Dr. Gutierrez Miravete Ernesto
1
Sanjeev Saitia
TABLE OF CONTENTS
TOPIC
PAGE NO.
ABSTRACT
3
PROBLEM FORMULATION AND OBJECTIVE
3
DATA COLLECTION
4
STATISTICAL RESULTS OF MEASURED DATA
7
TIME STATISTICS OF INDIVIDUAL COMPONENT
8
COMPONENT-WISE DISTRIBUTION SUMMARY CHART
8
MODULAR STATISTICAL DISTRIBUTION
9
DISCRETE EVENT MODEL OF TIME ANALYSIS
10
VERIFICATION AND VALIDATION OF SIMULATION MODEL
11
OUTPUT RESULTS
13
OPTIMIZATION OF PERFORMANCE COST
16
CONCLUSIONS AND OBSERVATIONS
17
FUTURE IMPLEMENTATION
18
REFERENCES
18
APPENDIX
19
2
Sanjeev Saitia
3
OPTIMIZATION OF THE ANALYSIS TIME AND PERFORMANCE COST ANALYSIS
ABSTRACT:
Simulation is widely used in manufacturing for high level planning. Its
application is rapidly increasing in other fields such as scheduling, detailed
equipment models, and application specific models for use in evaluation,
engineering, sales, and marketing. In 1989, the U.S. Department of Defense and
Department of Energy specified that simulation and modeling technology is one of
the top 22 critical technologies in the Unites States. Another recent focus in
task analysis has been placed on simulation of problem solving and other forms
of cognitive behavior. In regard to different purposes for which simulation
models are used, the following principles are mainly applied:
Modeling Principle 6: A model should be evaluated according to its usefulness.
From an absolute perspective, a model is neither good or bad, nor is it neutral.
Modeling Principle 7: The purpose of simulation modeling is knowledge and
understanding, not models.
Keeping these principles in mind, this paper provides insight into the model
that knowledge the performance of the process and the analyst including time
management. The feasibility of doing the time management analytical studies and
simulation, and evaluating the performance cost, is demonstrated by successful
development of real world problem simulation. The results are verified using
statistical and empirical formulations.
PROBLEM FORMULATION AND OBECTIVE:
In the real world, each project completion takes number of days, hours or
months. The analysis time and computation is becoming expensive and time
consuming. Since ‘Time is the Money”, every attempt is made to reduce the time
of computation. In this project, an application-specific time management problem
is analyzed and simulated. In the aircraft engine industry, each engine is
composed of different modules. Each module is analyzed from the weight point of
view before a best design is achieved. In this paper, the actual time taken
(weight analysis time) by each module of an engine to completion of a project is
measured.
Sanjeev Saitia
4
The objective of this study is to analyze and simulate the actual time taken by
each module and to perform cost analysis to achieve the optimum cost of
computation and performance.
The following figure illustrates the division of an engine into different
modules.
Aircraft Engine
AIRFOIL
L
FAN
AFFA
N
LPC
CORE
LPC
LPT
CORE
TEC
LPTTEC
Nomenclature:
Airfoil: An airfoil is a cross-section of the blade.
LPC :
Low Pressure Compressor ;
LPT :
Low Pressure Turbine
TEC :
Turbine Exhaust Case ;
D/B
HPC :
High Pressure Compressor ;
CORE : HPC + D/B + HPT
HPT :
High Pressure Turbine
:
Diffuser Burner
DATA COLLECTION:
The Data collection is crucial and time-consuming part of the simulation. The
objective of the analysis is halfway achieved based on the quality of data collected.
In this case, actual time measured for weight analysis of different modules, is
measured using a watch. The time of start represents when the analysis is started for
a particular section. The break time is the time taken off for personal or other
reasons. The time end is the module analysis completion time. The initial means the
time of initial analysis run.
Sanjeev Saitia
5
Since time taken by a project is sometimes more and constitutes involvement of other
tasks and meetings, the measured data is independent and represents only the analysis
time. There is also a check phase (when results are compared), which is not considered
as the part of this project. It is only the analysis time recorded for this project as
represented by initial run.
Measured Real Project Data
PW8160-OPC3
Dated
Component
Time of
Break
Start
Time of
Time
End
Taken
Minutes
Remarks
Run #
Minutes
5-Nov
DULC
11.56
0
11.58
0.02
PROJECT C3
Initial
5-Nov
HPC
11.58
0
12.11
0.13
PROJECT C3
Initial
5-Nov
D/B
12.12
0
12.14
0.02
PROJECT C3
Initial
5-Nov
HPT
12.14
0
12.18
0.04
PROJECT C3
Initial
5-Nov
CORE
12.2
0
12.31
0.11
PROJECT C3
Check
5-Nov
CORE
12.32
0
12.41
0.09
PROJECT C3
Check
5-Nov
LPC
1.35
0
1.45
0.1
PROJECT C3
Initial
5-Nov
LPC
1.45
0.3
2.55
0.4
PROJECT C3
Initial
5-Nov
LPT
4.12
0
4.2
0.08
PROJECT C3
Initial
8-Nov
LPT
9.1
0
9.15
0.05
PROJECT C3
Check
8-Nov
LPT
0
0
0
0.15
PROJECT C3
Check-Add
8-Nov
HPT
0
0
0
0.15
PROJECT C3
Check-Add
8-Nov
HPC
0
0
0
0.25
PROJECT C3
Check-Add
8-Nov
LPC
0
0
0
0.15
PROJECT C3
8-Nov
LPC-Parametric
0
0
0
150
PROJECT C3
8-Nov
TEC
3.4
0.05
3.5
0.05
PROJECT C3
Initial
8-Nov
A/F
3.55
0
4
0.05
PROJECT C3
Initial
8-Nov
FAN
4.4
0
5
0.2
PROJECT C3
Initial
Check-Add
2,4,6% Parametric Studies
Sanjeev Saitia
Measured Real Project Data (Contd.):
STF1156CA
Dated
Component
Time of
Break
Start
Time of
Time
End
Taken
Minutes
21-Oct
21-Oct
Remarks
Run #
0.1
0.24
ST56CA
ST56CA
Initial
Initial
Minutes
A/F
FAN
8.35
9.06
0
0.1
8.45
9.4
21-Oct
FAN
9.5
0
10
0.1
ST56CA
Initial
21-Oct
FAN-CH
10
0
10.25
0.25
ST56CA
Check
22-Oct
CORE
2.35
0
3.07
0.32
ST56CA
Initial
22-Oct
CORE-CH(IP)
3.2
0
3.35
0.15
ST56CA
Check -I/p
22-Oct
CORE-CH(OP)
3.35
0
4.25
0.5
ST56CA
Check-O/P
22-Oct
LPC
4.35
0
4.45
0.1
ST56CA
Initial
22-Oct
LPC-CH
4.45
0
5.55
0.1
ST56CA
Check
22-Oct
LPT
8.21
0
8.31
0.1
ST56CA
Initial
22-Oct
LPT
8.32
0
8.35
0.03
ST56CA
Check
22-Oct
TEC
8.54
0
8.57
0.03
ST56CA
Initial
22-Oct
TEC
8.57
0
9
0.03
ST56CA
Check
22-Oct
FAN
9.05
0
9.22
0.17
ST56CA
Initial
22-Oct
A/F-REV
9.3
0
9.35
0.05
ST56CA
Initial
22-Oct
FAN-REV
11
0
11.3
0.3
ST56CA
Initial
22-Oct
FAN-REV
12.5
0
1.15
0.25
ST56CA
Initial
Break
Time of
Time
Remarks
Run #
End
Taken
0.35
0.05
PW8160
PW8160
Initial
Check
Measured Real Project Data:
PW8160
Dated
Component
Time of
Start
Minutes
6-Oct
6-Oct
FAN
FAN-CH
6-Oct
6-Oct
Minutes
12.3
1.05
0
0
1.05
1.1
CORE
2.3
0
4
1.3
PW8160
Initial
LPC
1.15
0
1.36
0.21
PW8160
Initial
6-Oct
LPC-contd
1.4
0
1.5
0.1
PW8160
Initial
6-Oct
LPC-CH
1.5
0
1.55
0.05
PW8160
Check
6-Oct
HPC-CH
8.45
0.05
9.27
0.37
PW8160
Check-I/p
6-Oct
HPC-CH
9.27
0.05
9.5
0.18
PW8160
Check-O/P
7-Oct
LPC-CH
8.35
0.1
8.55
0.1
PW8160
Check
7-Oct
LPC-CH
8.55
0.05
9.55
0.05
PW8160
Check
7-Oct
LPT
10.27
0
10.5
0.23
PW8160
Initial
7-Oct
LPT-CH
10.5
0
11.35
0.45
PW8160
Check
7-Oct
LPT-REV
1.1
0
1.32
0.22
PW8160
Initial
7-Oct
HPC-CH
1.35
0
2.4
1.05
PW8160
Check
7-Oct
HPC-CH
2.4
0
3.15
0.35
PW8160
Check
6
Sanjeev Saitia
7
Measured Analysis Time Data:
Analysis Time for Each Module (Minutes)
TAFF
TLP
TCR
TLTEC
Project
S. No.
AIRFOI
L
FAN
LPC
CORE
LPT
TEC
AFFAN
LPC
CORE
LPTTEC
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
5.0
10.0
4.0
4.2
8.7
5.6
6.8
8.9
8.2
7.8
5.3
5.8
9.6
6.1
8.7
9.4
5.5
8.0
7.9
6.9
5.9
9.0
7.8
8.8
4.7
20.0
34.0
35.0
27.2
24.8
28.1
33.4
26.2
31.2
21.7
33.2
25.9
25.3
35.0
31.6
21.0
33.5
30.4
34.3
27.7
24.1
25.7
26.8
29.6
34.2
50.0
10.0
31.0
10.4
31.6
29.9
19.9
43.1
36.9
46.7
16.1
45.9
34.1
38.5
36.1
22.2
46.5
45.1
30.3
44.5
40.5
12.7
44.3
42.9
16.4
41.0
47.0
90.0
87.3
47.1
66.1
67.7
46.7
54.7
56.7
45.9
57.8
61.2
80.8
82.9
86.8
68.6
89.3
65.4
86.9
88.2
83.5
77.0
46.5
78.5
8.0
10.0
23.0
9.4
9.9
13.3
14.0
9.6
15.0
19.3
12.8
20.9
13.8
8.5
12.3
13.7
19.9
21.7
20.3
16.1
19.2
21.7
22.2
8.7
14.0
5.0
3.0
4.0
3.5
4.7
4.4
4.9
3.3
4.0
3.2
3.1
3.8
4.0
4.3
3.3
4.1
3.7
4.7
3.9
4.6
3.8
4.2
4.8
4.5
3.7
25.0
44.0
39.0
31.4
33.5
33.7
40.2
35.1
39.4
29.5
38.5
31.7
34.9
41.1
40.3
30.4
39.0
38.4
42.2
34.6
30.0
34.7
34.6
38.4
38.9
50.0
10.0
31.0
10.4
31.6
29.9
19.9
43.1
36.9
46.7
16.1
45.9
34.1
38.5
36.1
22.2
46.5
45.1
30.3
44.5
40.5
12.7
44.3
42.9
16.4
41.0
47.0
90.0
87.3
47.1
66.1
67.7
46.7
54.7
56.7
45.9
57.8
61.2
80.8
82.9
86.8
68.6
89.3
65.4
86.9
88.2
83.5
77.0
46.5
78.5
13.0
13.0
27.0
12.9
14.6
17.7
18.9
12.9
19.0
22.5
15.9
24.7
17.8
12.8
15.6
17.8
23.6
26.4
24.2
20.7
23.0
25.9
27.0
13.2
17.7
STATISTICAL RESULTS OF THE MEASURED DATA:
The statistical analysis of the measured data is tabulated below. The five different
distributions are calculated for each module using four different criteria
Chi-square (2), P-Value, Kolmogorov-Smirnov, and Anderson-Darling. The mode of
selection of distribution is prioritized on the basis of Kolmogorov-Smirnov
statistical results.
Sanjeev Saitia
8
TIME STATISTICS OF INDIVIDUAL COMPONENT
(Minutes)
AFFAN
LPC
CORE
LPT
N
MIN
MAX
MEAN
MEDIAN
STDEV
Q1
Q3
25
25
44
35.94
35.1
4.608
32.6
8.75
25
10
50
33.02
36.1
12.7
21.05
44.4
25
41
90
68.14
67.7
16.74
50.9
85.15
25
12.8
27
19.11
17.8
5.03
13.9
23.9
COMPONENT WISE DISTRIBUTION SUMMARY CHART
AFFAN STATISTICAL DISTRIBUTION
S. NO.
DISTRIBUTION
1
Triangular Distr
2
3
PARAMETERS
2
P
Kolmogorov-Smirnov
A-D
Min = 25.0, Max = 44.0
2.4
0.1213
0.1430
0.4757
Beta Distr.
 = 12.96,  = 3.78, Scale = 46.4
6.8
0.009
0.1484
0.3317
Extreme Value Distr.
Mode = 38.11, Scale = 3.88
6.8
0.0334
0.1506
0.3795
4
Weibull Distr.
Loc. = -20.41, Scale = 58.35, Shape = 15.0
6.8
0.009
0.1555
0.3879
5
Logistic Distr.
Scale = 2.67, Mean = 36.14
4.4
0.1108
0.1800
0.4787
LPC STATISTICAL DISTRIBUTION
S. NO.
DISTRIBUTION
PARAMETERS
2
P
Kolmogorov-Smirnov
A-D
1
Triangular Distr
Min = 10.0, Max = 50.0
2.8
0.0943
0.1114
0.3914
2
Beta Distr.
 = 1.64,  = 0.84, Scale = 50.02
0.8
0.371
0.1114
0.3602
3
Logistic Distr.
Scale = 7.6, Mean = 34.04
2.8
0.2466
0.1224
0.7571
4
Weibull Distr.
Loc. = -2.07, Scale = 39.29, Shape = 3.02
4.4
0.0359
0.1374
0.8590
5
Normal Distr.
Mean = 33.02 , Stand Dev. = 12.70
6.8
0.0334
0.1417
0.8254
CORE STATISTICAL DISTRIBUTION
S. NO.
DISTRIBUTION
PARAMETERS
2
P
Kolmogorov-Smirnov
A-D
1
Extreme–Value Distr
Mode = 76.2, Scale = 13.87
5.2
0.0743
0.1264
0.8934
2
Logistic Distr.
Mean = 68.58, Scale = 10.34
1.6
0.4493
0.1331
0.8052
3
Beta Distr.
 = 3.28,  = 1.05, Scale = 90.06
3.2
0.0736
0.1403
0.9222
4
Normal Distr.
Mean = 68.14,  = 16.74
3.2
0.2019
0.1416
0.8301
5
Weibull Distr.
Loc. = 32.41, Scale = 40.34, Shape = 2.26
3.2
0.0736
0.1546
0.8534
LPTTEC STATISTICAL DISTRIBUTION
S. NO.
DISTRIBUTION
PARAMETERS
2
P
Kolmogorov-Smirnov
A-D
1
Logistic Distr.
Mean = 18.93, Scale = 3.07
4.4
0.1108
0.1214
0.7035
2
Normal Distr.
Mean = 19.11,  = 5.03
4.4
0.2019
0.1416
0.8301
3
LogNormal Distr.
Mean = 19.12,  = 5.09
4.4
0.1108
0.1405
0.7489
4
Extreme Value Distr.
Mode = 16.71,  = 4.15
6.4
0.0408
0.1428
0.7728
5
Beta Distr.
 = 3.93,  = 1.84, Scale = 28.08
2.8
0.0943
0.1514
0.8725
Sanjeev Saitia
9
MODULAR STATISTICAL DISTRIBUTIONS:
Module Section: AFFAN
C r y s ta l Ba ll Stu d e n t Ve r s io n
A F FA N
N o t fo r C o m m e r c ia l U s e
Triangular distribution with parameters:
Minimum
25.00
Likeliest
34.50
Maximum
44.00
2 5 .0 0
2 9 .7 5
3 4 .5 0
3 9 .2 5
4 4 .0 0
Selected Range is from 25.00 to 44.00
Module Section: LPC
Triangular distribution with parameters:
Minimum
Likeliest
Maximum
10.00
45.90
50.00
Selected range is from 10.00 to 50.00
Module Section: CORE
C r y s ta l Ba ll Stu d e n t Ve r s io n
C OR E
N o t fo r C o m m e r c ia l U s e
Normal distribution with parameters:
Mean
Standard Deviation
68.14
16.74
1 7 .9 3
4 3 .0 4
6 8 .1 4
9 3 .2 5
1 1 8 .3 5
Selected range is from –infinity to +infinity
Module Section: LPTTEC
Normal distribution with parameters:
Mean
Standard Dev.
19.11
5.03
Selected range is from –infinity to +infinity
MODEL TRANSLATION:
The real world problem is portrayed in Discrete Simulation model using Promodel v4.2.
The components that flow in a discrete system, such as people, equipment, orders, and
raw materials, are called entities.
Sanjeev Saitia
10
The different engine modules are treated as entities. The goal of a discrete
simulation model is to portray the activities in which the entities engage and thereby
learn something about the system’s dynamic behavior. Simulation accomplishes this
objective by defining the states of the system and constructing activities that move
it from state to state. The beginning and ending of each activity are events.
The state of the model remains constant between consecutive event times, and a
complete dynamic portrayal of the state of the model is obtained by advancing
simulated time from one event to the next. This timing event is referred to as the
next-event approach. An analytical queuing
model
is created to produce the steady
state results regarding the total module output and the average resource utilization.
In this way, a number of different runs are made at different simulation times to
assure that the steady state condition is reached.
The empirical model is created using M/G/1 and is tabulated to compare with the
simulated model results.
The logic associated with processing the arrival and analysis events depends on the
state of the system at the time of the event. In the case of the arrival event, the
disposition of the arriving event (file modules) is based on the distribution of each
file at the Performance Office Location. At the Analysis event, the status of the
module analysis time depends on whether a file is waiting. If the file is waiting in
the queue, the analyst status remains busy, and the queue length is reduced by 1. And
a analysis file removed from the queue is scheduled, if, however, the queue is empty,
the status is idle.
At any instant in the simulated time, the model is in a particular state. As events
occur, the state of the model may change as prescribed by the logical-mathematical
relationships associated with the events. Thus, events define potential changes. The
state changes can be viewed from two perspectives:
1) The process that the part encounters as it seeks service or
2) The events that cause the state to change.
DISCRETE EVENT MODEL OF THE TIME ANALYSIS SYSTEM:
The states of the time analysis system are measured by the number of parts in the
system and the status of the analyst.
Sanjeev Saitia
11
The following figure illustrates the system:
Time In System
Create Node
Queue Node
COLCT Node
A simple network model illustrates that entities are inserted into the network at the
CREATE node. There is a zero time for the part entity to travel to the QUEUE node, so
that the parts arrive to it at the same time as they are created. The parts either
wait or are processed. The time spent in the system by a part is then collected at the
COLCT node
VERIFICATION AND VALIDATION OF THE SIMULATION MODEL:
The different approaches of verifying and validating the models are: Conceptual Model
Validity, Model Verification, Operational Validity, and Data Validity. The model
verification and validation, is generally considered to a process and is usually part
of the model development process.
Model validation is usually defined to mean “Substantiation that a computerized model
within its domain of applicability possesses a satisfactory range of accuracy
consistent with the intended application of the model”. The model verification is
often defined as “ ensuring that the computer program of the computerized model and
its implementation are correct” and is the definition adopted in the project. Model
accreditation determines if a model satisfies a specified model accreditation criteria
according to a specified process. The amount of accuracy required is specified in the
beginning of the model development and the data collection process. Since the design
variables are random, the properties and functions of the random variables such as
means and variances are used to determine the validity of the model and the data.
It is often too costly and time consuming to determine that a model is absolutely
valid over the complete domain of its intended applicability.
Sanjeev Saitia
12
The simplified version of the modeling process is drawn below, which includes the data
as well as the operational validity.
Problem Entity
Operational
Validity
Conceptual
Model
Validity
Data Validity
Problem Entity
Problem Entity
Computerized
Model
Validity
The validation of the model is objective (Blaci and Sargent 1984 Bibliography), when
it constitutes some type of statistical test or mathematical procedure. The simulation
animation is another way of determining the validation. Apart from that the following
other validation tests are done:
i)
Face Validity – Validates the logic in the conceptual model by asking
Prof. Ernesto (validation from a knowledgeable person about the system).
ii)
Historical Data Validation.
iii)
Fixed Values – Comparison with Empirical Results.
iv)
Internal Validity – Several runs are made and 20 replications are done
once it is determined that the steady state is reached at 10,000 runs.
v)
Operational Graphics – Animation
vi)
Traces
Sanjeev Saitia
13
OUTPUT RESULTS:
The simulation results and the conceptual results are tabulated for the different
models of the engine below:
SIMULATION RESULTS – AFFAN SECTION
COMPARISON BETWEEN EMPIRICAL AND SIMULATED ANALYSIS TIME TAFF
(Minutes)
Empirical
Results




L
LQ

Q
PO
0.023
0.028
4.608
0.817
2.668
1.851
117.4
81.446
0.183
10
Hours
0.928
1.551
0.623
58.15
43.35
0.072
100
Hours
0.777
2.438
1.661
110.8
87.5
0.223
1000
Hours
0.786
2.135
1.349
95.26
72.2
0.214
Simulation Output
10,000
10,100
10,500
Hours
Hours
Hours
0.795
2.365
1.571
104.2
80.4
0.205
0.795
2.36
1.566
104.0
80.2
0.205
0.794
2.34
1.545
103.2
79.38
0.206
10000 Hours
20 Replications
2.34
1.547
103.2
79.2
0.793
Lave
LQavg
avg
Qavg
avg
Lsd
LQsd
sd
Qsd
sd
0.122
0.115
4.63
4.3
0.0072
SIMULATION RESULTS – LOW PRESSURE COMPRESSOR (LPC)
COMPARISON BETWEEN EMPIRICAL AND SIMULATED ANALYSIS TIME TLP
(Minutes)
Empirical
Results




L
LQ

Q
PO
0.022
0.030
12.70
0.718
1.766
1.046
81.23
48.21
0.282
10
Hours
0.779
1.116
0.337
43.8
34.4
0.221
100
Hours
0.679
1.754
1.075
81.29
64.28
0.321
1000
Hours
0.680
1.391
0.711
63.62
46.41
0.320
Simulation Output
10,000
10,100
10,500
Hours
Hours
Hours
0.675
1.448
0.773
66.36
49.45
0.325
0.675
1.446
0.771
66.27
49.45
0.325
0.676
1.445
0.769
66.15
49.24
0.324
10000 Hours
20 Replications
Lavg
LQavg
avg
Qavg
avg
1.433
0.760
66.01
49.14
0.673
Lsd
LQsd
sd
Qsd
sd
0.045
0.038
1.577
1.262
0.0069
Sanjeev Saitia
14
OUTPUT RESULTS(Contd.):
SIMULATION RESULTS – CORE
COMPARISON BETWEEN EMPIRICAL AND SIMULATED ANALYSIS TIME TCR
(Minutes)
Empirical
Results




L
LQ

Q
PO
0.007
0.015
16.70
0.454
0.655
0.200
98.211
30.071
0.546
10
Hours
0.739
0.828
0.089
68.95
63.23
0.261
100
Hours
0.359
0.443
0.0829
82.94
68.78
0.640
1000
Hours
0.463
0.669
0.206
99.25
77.20
0.537
10,000
Hours
0.439
0.618
0.179
96.02
75.77
0.561
Simulation Output
10,100
10,500
Hours
Hours
0.440
0.620
0.180
96.13
75.82
0.560
10000 Hours
20 Replications
0.656
0.204
98.85
77.35
0.452
Lavg
LQavg
avg
Qavg
avg
0.441
0.622
0.181
96.29
75.88
0.559
Lsd
LQsd
sd
Qsd
sd
0.022
0.013
1.59
0.986
0.0092
SIMULATION RESULTS – LOW PRESSURE TURBINE AND EXHAUST CASE
COMPARISON BETWEEN EMPIRICAL AND SIMULATED ANALYSIS TIME TLTEC
(Minutes)
Empirical
Results




L
LQ

Q
PO
0.029
0.052
5.03
0.546
0.897
0.351
31.397
12.287
0.454
10
Hours
0.546
0.701
0.155
23.38
19.72
0.454
100
Hours
0.509
0.871
0.302
30.27
22.39
0.491
1000
Hours
0.538
0.884
0.346
31.47
23.76
0.462
Simulation Output
10,000
10,100
10,500
Hours
Hours
Hours
0.539
0.888
0.349
31.45
23.98
0.461
0.539
0.888
0.349
31.46
23.98
0.461
0.539
0.888
0.349
31.46
23.99
0.461
10000 Hours
20 Replications
Lavg
LQavg
avg
Qavg
avg
0.916
0.373
32.25
24.54
0.543
Lsd
LQsd
sd
Qsd
sd
0.015
0.010
0.313
0.232
0.0047
Cost estimation is an crucial part of engineering and particularly in the analysis
when the most of the time is spent
in the computation. The cost is estimated based on
the Program Evaluation Review Technique. It involves making a most likely estimate, an
optimistic estimate (lowest cost), and a pessimistic estimate (highest cost).
Sanjeev Saitia
The mean and variance for each cost element is calculated as :
E(Ci)
=
Var(Ci)
=
0.167(L + 4M +H)
(0.167(H-L))**2
E(C1) = Expected cost of the AFFAN module section
E(C2) = Expected cost of the LPC module section
E(C3) = Expected cost of the Core module section
E(C4) = Expected cost of the LPTTEC module section
Var(Ci) = Variance of the cost of each module section
LOWEST
COST
MODAL
COST
HIGHEST
COST
AFFAN
E(C1)
$33.3 /Hr
Var(C1)
LPC
$47.9 /Hr
$ 17.9/Hr
$47.4 /Hr
LOWEST
COST
MODAL
COST
HIGHEST
COST
$58.7 /Hr
$ 54.13
/Hr
$79.2 /Hr
E(C4)
Var(C4)
$ 25.9 /Hr
$ 9.9 /Hr
$ 66.7 /Hr
LPTTEC
E(C3)
Var(C3)
$54.7 /Hr
$101.5/Hr
Var(C2)
$ 61.2 /Hr
CORE
LOWEST
COST
MODAL
COST
HIGHEST
COST
E(C2)
$ 13.3 /Hr
$96.8 /Hr
LOWEST
COST
MODAL
COST
HIGHEST
COST
$ 118.4
/Hr
$120.0 /Hr
$ 17.1 /Hr
$ 25.5 /Hr
$ 36.0 /Hr
Based on the Central Limit Theorem, the total cost is the added cost of the subelements
E(CT)
=
Expected Total Cost in Dollars
E(CT)
=
E(C1)
=
47.4
=
$224.2/Hr
=
$ 1793.6/day
+
E(C2)
+
54.1
+
+
E(C3)
96.8
+
+
E(C4)
25.9
15
Sanjeev Saitia
Var(CT)
= Variance of Total Cost In Dollars
Var(CT) =
Var(C1)
=
17.9
=
$225.4/Hr
+
Var(C2)
+
79.2
+
Var(C3)
+
+
118.4
+
Var(C4)
9.9
OPTIMIZATION OF THE PERFORMANCE COST:
The Optimization of the cost function using Automated Design Synthesis (ADS) results
are tabulated below.
Optimization Function Objective : Minimize COST, C(T) = [ 1+ 1.333*T] ** (0.75 / T)
subject to :
T
= TAFF + TLP + TCR + TLTEC
G(1)
= - T + 88.8
G(2)
=
25.0 – TAFF  0.
G(3)
=
TAFF
G(4)
=
10.0 - TAFF  0.
G(5)
=
TLP – 50.0
G(6)
=
41.0 – TCR  0.
G(7)
=
TCR – 90.0
G(8)
=
12.8 – TLTEC  0.
G(9)
=
TLTEC – 27.0
 0.
- 44.0  0.
 0.
 0.
 0.
All time variables are measured in Minutes.
---------------------OPTIMIZATION RESULTS
---------------------OBJECTIVE FUNCTION VALUE
DESIGN VARIABLES
1.02026E+00
(per minute)
16
Sanjeev Saitia
LOWER
VARIABLE
UPPER
BOUND
VALUE
BOUND
1
2.50000E+01
4.40000E+01
1.00000E+11
2
1.00000E+01
5.00000E+01
1.00000E+11
3
4.10000E+01
9.00000E+01
1.00000E+11
4
1.28000E+01
2.70000E+01
1.00000E+11
DESIGN CONSTRAINTS
1) -1.2220E+02 -1.9000E+01
6) -4.9000E+01
3.8147E-06 -4.0000E+01 -1.9073E-05
1.5259E-05 -1.4200E+01 -4.1962E-05
FUNCTION EVALUATIONS =
31
~/design (33)
Cost = $ 1.0203 * 60 = $61.22/hr
= $489.74/day
CONCLUSIONS AND OBSERVATIONS:
1) There is a good agreement of the simulated and the analytical results.
2)
The large values of cost variance indicates that the greater uncertainty, and
variability and hence more conservatism in the TCR.
3)
The estimated cost of analysis is $224/hour.
4)
It is recommended to perform sensitivity of some projects based on the
existing data.
5)
The optimized cost is found to be one fourth of the Estimated Cost.
17
Sanjeev Saitia
18
AVERAGE UTILIZATION - Roe Avg
0.543
TLTEC
0.452
Utilization
TCR
Series1
0.673
TLP
0.793
TAFF
Module
6) The maximum utilization is in the case of the Fan.
FUTURE IMPLEMENTATION:
1)
To analyze the full model with grouping to complete a single project.
2)
Implementation of the Optimization of the following function using Neural
Network.
Optimization Function Objective : Minimize COST, C(T) = [ 1+ 1.333*T] ** (0.75 / T)
REFERENCES:
1)
Certification and Validation of Simulation Models, Robert G. Sargent
2)
Discrete-Event System Simulation, Jerry Banks, John S. Carson, Barry L. Nelson
3)
Promodel User’s Manual and Software
4)
Operations Research An Introduction, Hamdy A. Taha
5)
Handbook of Industrial Engineering, G. Salvendy
6)
Introduction to Simulation and Risk Analysis, James R. Evans, David L. Olson
7)
Integrating Targeted Cycle-Time Reduction Into The Capital Planning Process,
N.Grewal, Jennifer K.Robinson
Sanjeev Saitia
APPENDIX
19
Sanjeev Saitia
20
********************************************************************************
*
*
*
Formatted Listing of Model:
*
*
A:\Pjnew.mod
*
*
*
********************************************************************************
Time Units:
Distance Units:
Minutes
Feet
********************************************************************************
*
Locations
*
********************************************************************************
Name
---------------Table
Engineer
Performance
Analytical_Group
Aerodynamist
Commun
Program_Manager
LocInt
Cap
-------1
1
1
1
1
INFINITE
1
2
Units
----1
1
1
1
1
1
1
1
Stats
----------Basic
Time Series
Basic
Basic
Time Series
Time Series
Time Series
Time Series
Rules
-------------Oldest, ,
Oldest, ,
Oldest, ,
Oldest, ,
Oldest, ,
Oldest, FIFO,
Oldest, ,
Oldest, ,
Cost
-----------30.0/hr
50.0/hr
********************************************************************************
*
Entities
*
********************************************************************************
Name
---------FAN
LPC
CORE
LPT
FANLPC
Speed (fpm)
-----------150
150
150
150
150
Stats
Cost
----------- -----------Time Series
Time Series
Time Series
Time Series
Time Series
********************************************************************************
*
Path Networks
*
********************************************************************************
Name
Type
T/S
From
-------- ----------- ---------------- -------Net1
Non-Passing Time
N1
N2
N3
N4
To
-------N2
N3
N4
N5
BI
---Uni
Uni
Uni
Uni
Dist/Time
---------98.45
2.57
0.15
0.14
Speed Factor
-----------1
1
1
1
********************************************************************************
*
Interfaces
*
Sanjeev Saitia
21
********************************************************************************
Net
Node
---------- ---------Net1
N1
N3
N4
Location
-----------Aerodynamist
Engineer
LocInt
********************************************************************************
*
Processing
*
********************************************************************************
Process
Entity
Location
Operation
Move Logic
-------- --------------- ----------------------------FAN
Commun
WAIT 1 MIN
Routing
Blk
Output
Engineer
Rule
---- -------- --------------- ------1
MOVE
FAN
Destination
Engineer
FIRST 1
WAIT N(28.63,4.50)
Var1 = GETCOST()
MOVE
LPC
MOVE
LPC
MOVE
ALL
FANLPC
MOVE
FANLPC
Commun
Engineer
LocInt
LocInt
1
FAN
LocInt
FIRST 1
1
LPC
Engineer
FIRST 1
1
LPC
LocInt
FIRST 1
1
FANLPC
Program_Manager FIRST 1
1
FANLPC
EXIT
WAIT 5.0 MIN
WAIT N(33.02,12.70)
LP=LP+1
WAIT 5.0
Accum 1
Group 1
As FANLPC
WAIT 0.1
Program_Manager WAIT 0.1
FIRST 1
********************************************************************************
*
Arrivals
*
********************************************************************************
Entity
-------FAN
LPC
Location
-------Commun
Commun
Qty each
---------1
1
First Time
---------0
0
Occurrences
----------INF
INF
Frequency Logic
---------- -----------E(40)Min
E(40) Min
********************************************************************************
*
Variables (global)
*
********************************************************************************
Sanjeev Saitia
ID
---------LP
Var1
Type
-----------Integer
Real
Initial value
------------0
0
Stats
----------Time Series
Time Series
22