1. INTERNATIONALMechanical Engineering and Technology (IJMET), ISSN 0976 –
International Journal of JOURNAL OF MECHANICAL ENGINEERING
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME
AND TECHNOLOGY (IJMET)
ISSN 0976 – 6340 (Print)
ISSN 0976 – 6359 (Online)
Volume 4, Issue 2, March - April (2013), pp. 47-52
IJMET
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SIMULATION AND OPTIMIZATION OF UNLOADING POINT OF A
SUGARCANE INDUSTRY – A CASE STUDY
1 2
Mr. Bhupendra Singh , Dr. Vishal Saxena
1
Student, M.Tech, Mechanical Engineering Department, IFTM University, Moradabad, India,
244001.
2
Professor & Head, Mechanical Engineering Department, IFTM University, Moradabad,
India, 244001.
ABSTRACT
The problem of finding the required number of unloading points in the sugarcane
industry can be solved by the application of Queuing theory. This paper deals with the
optimization of unloading time in continuously operating process industry such as sugarcane
industry with the help of a simulation model. In this case study, the company selected,
located in the northern part of India, and was facing the problem of high waiting time of
trolleys. The data were collected for the inter-arrival time of trolleys arriving there and the
service time of trolleys. The data were analyzed to find out the suitable probability
distribution with the help of Minitab software. After fitting the suitable distribution to the
data, a simulation model was developed with the help of extend simulation software keeping
in mind the complexity involved in the system. The idea behind it was to model the existing
system and then compare the performance of this model with the existing system to check
whether it matches with the performance of the existing system or not. If it does so, it means
that the model is fairly representative of the existing system. Then we varied the number of
service points and the corresponding waiting time was found out which resulted in the
computation of waiting cost per trolley. Having found out the waiting cost per trolley, the
service time per trolley was also calculated. The cost model was then applied to get the
optimum number of service points.
KEYWORDS: Waiting time, service time, service points, waiting cost.
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2. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME
INTRODUCTION
The Company was facing the problem of high waiting time of trolleys in the queues
of parking place. The average waiting time of trolleys was 15 hours. The factors responsible
for the trolley detention were as follows: Uncertainty in trolley arrival, Under-utilisation of
cranes or machines, No store at the place of service points, Number of queue, Lower average
output. As no standard model is suitable for such industries and the complexities involved are
high, some specific reliable method is needed.
METHODOLOGY
As the data was in haphazard form, a small program was written to sort out these data
into ascending order, converting them into minute and then finding the inter-arrival time.
Then these data were fed to the Minitab software to find out the suitable probability
distribution. Similarly, the service time data have also been fed to the same software for the
same purpose.
After finding out the distribution of the inter-arrival time and service time, we tried to
find out a suitable multi-server queuing model. Unfortunately, we could not find out the
same, so we decided to simulate it with Extend simulation software. The idea behind it was to
model the existing system, and then allow running for a long period & then compare its
performance with the existing system. If the performance of the simulation model matches
with the existing system, it will mean that our model is valid. Then the strategy would be to
change the number of service points and measure the performance e.g. waiting time
corresponding to these service points.
Having found out the waiting time for different number of service points, we decided
to use the cost model to find out the optimum number of service points. Strategy here is to
find out the waiting cost per trolley and service cost per trolley corresponding to the different
service points, thereby finding out the total cost which in turn will decide the optimum
number of service points. The service points corresponding to the minimum total cost would
be the optimum one.
ANALYSIS
Finding the probability distribution of inter-arrival time
The total number of data points (inter-arrival time) = 493.
By feeding the data to Minitab software, the parameters and A-D value for different possible
distribution are as follows:
Distribution Parameter A-D value
Exponential Mean= 9.03 662.5
Weibull Shape= 0.415; scale= 2.601 28.48
Logistic Location= 3.29; scale= 7.02 72.21
Log logistic Location= 1.20; scale= 2.30 38.92
Table 1. Comparison of probability distributions for inter-arrival time.
This comparison represents that the A-D value is minimum for Weibull Distribution.
So the Weibull Distribution has been selected for inter-arrival time data. In other words data
have been fitted to Weibull Distribution.
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3. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME
Finding the probability distribution of service time
The total number of data points (service time) = 64
By feeding the data to Minitab software, the parameters and A-D value for different possible
distribution are as follows:
Distribution Parameter A-D value
Weibull Shape= 1.775; Scale= 22.025 0.42
Lognormal Location= 2.884; Scale= 0.324 1.113
Normal Mean=20.051; St. Dev =8.670 0.398
Log logistic Location= 4.133; Scale= 0.368 0.708
Logistic Location= 23.015; Scale= 4.55 0.438
Table 2. Comparison of probability distributions for service time.
This comparison represents that the A-D value is minimum for Normal Distribution.
So the Normal Distribution has been selected for service time data. In other words data have
been fitted to Normal Distribution.
MODELING OF THE EXISTING SYSTEM
The model corresponding to the existing system with the help of extends simulation
software i.e. model with 3 service points and its performance measurement is shown below:
Figure 1. Model of the existing system
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4. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME
Performance Measurement of the Existing Model
For smooth running of the simulation model, the inputs of the model are the
characteristics of the distribution i.e. outputs of the Minitab software. After allowing the
model i.e. system to run for 9 years, the outputs of the simulation model obtained is as
follows: Average Queue length= 48 trolleys
Average Waiting time = 14.15 hour
Maximum Waiting time = 42.95 hour
Comparison with the Performance of Existing System:
The average waiting time of trolleys in the sugarcane industry of the existing system
is 15 hour. The performance obtained from the simulation model is more or less similar to the
performance of the existing system i.e. 14.15 hour, which reasonably confirms that our model
is valid or it is true representative of the existing system. Now the strategy would be to
change the number of service points in a simulation model and measure the performance i.e.
waiting time corresponding to these service points.
MODEL WITH 5 SERVICE POINTS
For Model, figure 2 can be referred. After allowing it to run for 9 years, the outputs of
the simulation model obtained is as follows:
Average queue length = 4 trolley
Average waiting time = 132.6 minute = 2.21hour
Maximum waiting time = 12.72 hour
T U S f
STOP Rand STOP a
count down D down down
f
d service point d f
1 2 3 b
V random no. input T U S
F
STOP STOP
start
Rand down combine
L W down
program A D down
queue f d f
T U S
prioritiser #
STOP 1 2 3
STOP STOP Exit
down A D down (4)
down Rand down
shut down f f
T U S d
plotter
a 1 2 3 STOP
? b STOP A D down down
V 1 2 3 Rand d
down a
select
source f T U S f
F selection 1 2 3
STOP b
STOP STOP
L W A D down
down down
down Rand
shut down f d
prioritiser f
1 2 3
F
L W
queue
Figure 2. Model with 5 service points
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5. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME
SUMMARY OF AVERAGE WAITING TIME FOR DIFFERENT SERVICE POINTS
After running the simulation model with different service points, the outputs of the
simulation model obtained is shown below:
3 service point = 849.00 min. = 14.15 hr.
4 service point = 443.21 min. = 7.38 hr.
5 service point = 132.60 min. = 2.21 hr.
6 service point = 78.26 min. = 1.30 hr.
COST MODEL
After finding out the waiting time for different number of service points, we then use
the cost model to find out the optimum number of service points. Strategy here would be to
calculate the waiting cost per trolley and service cost per trolley corresponding to the
tr
different service points. Then the total cost is determined which in turn wi decide the
will
optimum number of service points. The service points corresponding to the minimum total
cost would be the optimum one.
Graphical Analysis
The waiting cost, service cost & the total cost can be represented on the same plot as
shown below:
Cost model
waiting cost
service cost
1200 total cost
1000
cost in Rs.
800
600
400
200
0
No. of service points
Figure 3. Total cost representation
The figure 3. clearly shows that there is a point where waiting cost, service cost and total cost
is minimum. This point gives the optimum number of service points.
It is clear from the above graphical analysis (fig. 3) that the optimum number of service
)
points is 5.
RESULTS
The results based on the simulation model and cost model are shown below:
The optimum number of service points
ptimum =5
Corresponding average waiting time of trolleys = 2.21 hr
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6. International Journal of Mechanical Engineering and Technology (IJMET), ISSN 0976 –
6340(Print), ISSN 0976 – 6359(Online) Volume 4, Issue 2, March - April (2013) © IAEME
CONCLUSION
According to the results obtained and analysis of data, it is concluded that the
optimum number of service points is five, which means that there is a deficiency of two
service points in the existing system of the continuously operating process industry here. To
increase the service points, the selected industry needs to install a new crane machines. The
approach adopted in this work is of collecting the data related to inter-arrival time of trolleys,
service time of arriving trolleys, finding the suitable probability distribution of the data,
developing a simulation model of the existing system, waiting time, computation of waiting
cost per trolley and the resultant cost involved has been found to be useful in modeling a
proposed system which enables to lower the costs involved due to waiting time. The same
approach can be adopted for any such process industry which experiences losses due to
excess waiting time.
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