Assignment on Queuing at Port

7/28/2019 Assignment on Queuing at Port

1/13

Project (Assignment III)

ANALYSIS OF QUEUEING SYSTEMS

THE CASE OF APSEZL WEST PORT COAL TERMINALA report Submitted to

Prof. Girja SharanIn partial fulfillment of the requirements of the course

SYSTEM ANALYSIS AND SIMULATION

1/12/2013

By

Group 1 PGPIM 4

ADANI INSTITUTE OF INFRASTRUCTURE MANAGEMENT - AHMEDABAD


2/13

Introduction:

Queues are a very common occurrence in day to day life. The queues are generally

formed by the variation in the service times and the variations in demand. Analysis of

queues leads to analysis of the financial and operational side of the business.

The below such problem is one such live issue of queue. The study deals with the

queuing of vessels at APSEZL in Mundra.

Problem Description:

APSEZL in Mundra is the largest private port and special economic zone in India.

Various commodities are exported and imported from the APSEZL throughout the

year. West Port is a dedicated coal bulk terminal where coal vessels (ship) fromabroad are unloaded. The terminal caters to an average coal quantity of

14500MT/vessel and an average number of vessels per month of 14 to 16. The vessel

arriving have to wait at the anchorage point before they are scheduled to be

unloaded. After this, the vessels go to the terminal and the coal is unloaded with

help of 2 cranes as shown. The cranes unload the coal and transfer it to the

conveyors leading to the storage area. It takes an average of 3 days with 2 cranes for

the unloading of a vessel. The forecasted demand is to serve an average number of

20 vessels /month. The management is weighing the options of increasing the

number of cranes (unloader) or continues with the existing system.

Visual Diagram of system:

The system at APSEZL West Port, comprises of anchorage area, unloading cranes

and the vessels. The coal carrying vessel approaches directly the unloading cranes

only when there is no queue, otherwise the vessel waits at anchorage till its time of

sequence. At the unloading bay, the cranes (unloaders) unload the coal and then

depart from APSEZL. The visual diagram can be represented as follows:

The queue length will depend on the inter arrival time gap of the vessels and also onthe service time taken for unloading the vessel. From the analysis of the problem, we

can conclude on the waiting times and thus the performance requirement.


3/13

`

Constructing Simulation Model:

The requirement of the process emphasizes on simulation model. The performance

parameters that need to be studied are average waiting time, average utilization and

average waiting vessels. We need to simulate the arrival of the vessels at the APSEZL,

their queuing process, if any and their servicing at the unloading bay with the help of

cranes. From the visual diagram, we can understand that the inter-arrival times andservice times are critical parameters of the system. Thus, the most important step for

developing the simulation model is the modeling of the arrival times and the service

times. Once these parameters are modeled, the other performance attributes can be

easily devised through the simulation model.

The simulation model will simulate the inter-arrival times and service times depicting

a near real-life scenario and the performance parameters like average utilization and

average waiting vessels will be studied. The results will be analyzed to evaluate the

concern put forth by the management. The following section details the modeling of

the inter-arrival times and service times.


4/13

Estimating the parameters for the Model:

The inter arrival times and service times are the critical parameters of the system

and they need to be modeled for developing the simulation model.

Modeling the Inter-arrival times:

Fourteen inter-arrival times were observed and noted down and are given in

appendix 1. These inter-arrival times were analyzed in the following manner. We

need to fit a distribution to this inter-arrival time data. Firstly, as these times are

continuous in nature, the distribution must be a continuous distribution. Secondly,

the inter-arrival times can never take negative values. Thus, the distribution must be

a strictly positive distribution. Thirdly, the inter-arrival times cannot take infinite

values (time between arrivals of two vessels cannot be infinite). The distribution

must conform to this requirement too. The following process was followed toachieve the same.

a) The average inter-arrival time was determined.b) The inter-arrival times were divided into intervals of 20 hrs each and a

histogram of the frequency of occurrence was obtained. (Appendix 2)

c) This histogram was found to closely resemble the exponential distribution.This distribution satisfies our requirements of being a continuous distribution

and of having strictly positive values. For infinite values, the probability of

occurrence becomes nearly equal to zero which satisfies our third criterion.

d) To test whether the exponential distribution, a chi-square goodness of fit test(5% level of significance) was carried out for the observed frequency of

occurrence and expected frequency of occurrence and was found to be

satisfactory

Model for Inter-arrival times is thus,

Mean inter-arrival time = 42:37:30 (hr: min: sec)Mean arrival rate = = 13:30:48 (vessels per hr)


5/13

Modeling the Service times:

Fourteen service times were noted and analyzed in a similar fashion as the inter-

arrival times. The criteria for a good-fit distribution remain the same as that for

the inter-arrival times. The data and the histogram are as shown in Appendix 3

and Appendix 4. Plotting the data it was found to closely resemble normaldistribution. The chi-square goodness of fit test results is as follows

Model for Inter-arrival times is thus,

Mean service time = 68:30:43 (hr: min: sec)

Mean service rate = = 22:38:50 (hr: min: sec)

Using the Inverse CDF function; various replications were derived in excel, using theformula:

F-1(u) = ln(1u) / ..(for exponential function)NORMINV(RAND(),mean, standard deviation)(for normal distribution)

Also to understand the mean number of trucks in queue, mean time in system, mean

time in queue and the server utilization, below modeling is applied:

Mean No. trucks in queue: /(-)

Mean time in system:

1 / (-)

Mean time in queue:

/(-)

Utilization rate (): /


6/13

Simulation Model & Termination:

The simulation model was developed in simple Microsoft Excel. A run length of 20

vessels was employed as the expected average number of vessel arrivals at theAPSEZL is approximately 20 /month. If a vessel arrives and finds the unloading bay is

not free, it waits at anchorage for its turn to arrive. The vessels are served on a first

come first serve basis.

20 Replications were conducted to run this model and below results were found:

Average Service time = 64:30:45 (hr: min: sec)

Average Inter arrival time = 41:15:53 (hr: min: sec)

Average waiting time = 27: 34: 34

Waiting vessels = approx 5

[Refer Appendix 5]

Simulation Model tests:

Average arrival rates and average service rates were changed to understand the

effect of the test.

[1] Reduction in over all service rates (i.e. service rates improved by adding 1 more

crane) keeping Inter arrival rates constant (i.e. capacity of 14 vessels):

Average service rates were reduced accordingly to accommodate 3 working cranesinstead of 2 cranes. The results after replications were as follows:





[Refer Appendix 6]

This reduction in service rates due to addition of 1 more crane benefits the

operations by reducing the waiting time of 5 vessels to 1 vessel. Leading to fast

servicing of 4 vessels and hence an opportunity to serve 18 vessels from current 4vessels.


7/13

[2] Reduction inter-arrival rates (i.e. handling 20 vessels) keeping the service rates

constant (i.e. at 14 vessels handling capacity):

Average inter arrival rates were reduced to 29:50:15 (hr: min: sec) accordingly to

accommodate 20 vessels instead of current handling of 14 vessels. The results after

replications were as follows:Average Service time = 75:18:02 (hr: min: sec)




[Refer Appendix 7]

The reduction in inter arrival rates; will increase the queue as the service capacity is

less to cater more vessels.

[3] Reduction inter-arrival rates (i.e. handling 20 vessels) also reduction in theservice rates (i.e.: service rates improved by adding 1 more crane)

Average inter arrival rates were reduced to 29:50:15 (hr: min: sec) accordingly to

accommodate 20 vessels instead of current handling of 14 vessels. Also the addition

of 3rd

crane reduced the service time. The results after replications were as follows:





[Refer Appendix 8]The reduction in inter arrival rates and the service time; will increase the vessel

handling capacity from 14 to 18 as there is sufficient reduction in waiting time due to

fast operations support.

Recommendations

The increase in expenditure for a 3rd

crane will definitely benefit in handling 4 more

vessels. The decision is up to the management to implement the 3rd

crane.

The other suggestion would be to create another unloading bay which will result in asingle queue multi dock analysis.

The further analysis on this can be opted for as it will achieve economies of scale for

the operations and hence generate higher values.


8/13

Appendix 1:

Inter-arrival time data

Sr.No Vessel Name

Inter Arrival

(hr:min)

1 MV Cape Keystone 00:00

2 MV Aquafaith 184:45

3 MV Tuo Fu 1 07:15

4 MV C. Winner 18:15

5 MV Yue Shan 38:45

6 MV Orient Angel 50:00

7 MV Navios Marco Polo 11:00

8 MV Glyfada I 38:10

9 MV Cape Olive 25:15

10 MV Cape Lilac 49:20

11 MV Aanya 49:30

12 MV Ocean Clarion 24:35

13 MV Atlantic Princess 13:25

14 MV Alameda 86:30

Appendix 2:

0.00

0.05

0.10

0.15

0.20

0.25

0.300.35

0.40

Interarrival time

rel freq

0.00

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

:

:

:

:

:

:

:

:

:

:

:

:

:

:

:

:

rel freq

expo func


9/13

Appendix 3:

Service time data

Sr.No Vessel Name

Service time

(hr:min)

1 MV Cape Keystone 62:00

2 MV Aquafaith 46:40

3 MV Tuo Fu 1 39:35

4 MV C. Winner 57:15

5 MV Yue Shan 83:45

6 MV Orient Angel 109:00

7 MV Navios Marco Polo 28:45

8 MV Glyfada I 34:20

9 MV Cape Olive 92:55

10 MV Cape Lilac 65:30

11 MV Aanya 112:15

12 MV Ocean Clarion 76:15

13 MV Atlantic Princess 63:40

14 MV Alameda 87:15

Appendix 4:

0.00

0.05

0.10

0.15

0.20

0.25

0.30

:

:

:

:

60:00:00

:

:

:

:

:

:

:

:

:

:

:

:

:

:

:

:

Service time

rel freq

0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

:

:

:

:

:

:

:

:

:

:

:

:

:

:

:

:

Rel F(x)

rel freq


10/13

Appendix 5: [Average Service time & Avg Inter arrival time wit h20 replications]


11/13

Appendix 6: [Average Service time reduced & Same Avg Inter arrival time with 20 replications]


12/13

Appendix 7: [Average inter arrival time reduced to meet 20 vessel capacity& service rates are constant]


13/13

Appendix 8: [Average inter arrival time reduced to meet 20 vessel capacity& service rates also reduced]

---X---

Documents

Assignment on Queuing at Port