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Berthing Problem of Ships in Chittagong Port and Proposal for Its Solution

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Berthing Problem of Ships in Chittagong Port and Proposal for Its Solution TECHNICAL BRIEF 66 Berthing Problem of Ships in Chittagong Port and Proposal for its Solution proposals are made to solve the congestion problem of this BERTHING PROBLEM OF SHIPS IN important seaport. CHITTAGONG PORT AND JETTY QUEUING MODEL PROPOSAL FOR ITS SOLUTION The system of operation at the port can be thought as a typical queuing process. Ships come to the port as A. K. M. Solayman Hoque customers to get services and the facilities of the port Additional Chief Engineer, Chittagong Dry Dock Limited, render services to ships as servers. Here, services refer to Patenga, Chittagong, Bnagladesh handling of cargoes and use of facilities of jetties for berthing of ships. A large portion of the solution of waiting S. K. Biswas line problems that may arise in practice in Chittagong port Department of Mechanical Engineering, Chittagong involves making decisions in one or a combination of the University of Engineering & Technology, Bangladesh following: (a) Number of jetties, needed to serve the arriving ships INTRODUCTION (b) Delay of loading/unloading of cargo/container Since 1888, Chittagong port, the main port of (c) Future expansion of the facilities Bangladesh with the shore base facilities, has been playing Considering the future expected marine congestion a vital role in the economic development of the country. It problem at Chittagong port, an attempt is made in the has 15 general purpose jetties beside having a few present paper to provide an appropriate guideline to the additional jetties to handle oil, clinker, food grain, etc. The management of the port authority for the future expansion jetties were built about nine nautical miles inside from the of berthing facilities. shoreline of the Bay of Bengal. The ports of the world have The problem can be modeled as a multi-server changed significantly with the advent of containerization in queuing problem with no system limit; arrival can be from trade in the seventies of the last century. The port of a theoretically infinite source. For simplification, only the Chittagong, despite many constraints, continues to cope first come first serve priority rule is applied. Before solving with the changing patterns of the trade1. However, it has a typical queuing problem, the probability distributions of been suffering from the problems of poor operational arrival and service processes are required. Six years’ efficiency. (1994-2000) field data of arrivals and departures of ships to The traffic through the port is increasing along with and from Chittagong port is considered. During the period the economic development of the country. It is frequently a total of 5726 arrivals took place of which 4832 (84.38% seen that a queue of arriving ships is formed and of the total arrivals) are general cargo ships. The year wise sometimes ships have to wait for a longer time. In addition breakup of the general cargo ship arrivals is shown in to that the lack of adequate inland infrastructure to handle Table 1(a). Table 1(b) shows the actual data of the containers gives rise to the instances of congestion in frequency of ship arrivals and departures. jetties and the delays in the final delivery of goods to the Chi-square test has been applied to determine the importer premises with consequent increase in goodness of fit of the actual data shown in Table 1(b) to transportation and other costs. the standard probability distributions. In an attempt to fit In this paper, the berthing problem of ships in the model to M/M/s(∞), Chi-square test was done for the Chittagong port is analyzed using multi-server queuing arrival process considering Poisson distribution. M/M/s(∞) models. Data of arrivals and departures of ships from 1994 denotes the queuing model for arrival with Poisson to 2000 are collected and statistical techniques are applied distribution and service time with exponential distribution to find out and analyze the probability distributions and considering infinite server and infinite queuing space. The other parameters of the arrival and departure processes. It distribution of arrival of ships is plotted in Fig. 1. It is seen is predicted that the congestion problem at Chittagong port that the arrival process may be fitted nicely with Poisson will take a serious turn after 2015 AD if the present import and export growth rates continue. Therefore, some Table 1(a): Year wise break-up of ship arrival Year 1994-95 1995-96 1996-97 1997-98 1998-99 1999-00 Grand Total General Cargo ship 724 718 830 761 900 899 4832 Table 1(b): Frequency of ship arrival and departure Occurrence of ship arrival in Frequency of the occurrence Occurrence of ship departure Frequency of the occurrence a day of arrival in a day of departure 0 239 0 254 1 529 1 542 2 588 2 557 3 456 3 444 4 218 4 246 5 105 5 100 6 42 6 38 7 13 7 8 8 2 8 3 Journal of Mechanical Engineering, vol. ME37, June. 2007 Transaction of the Mech. Eng. Div., The Institution of Engineers, Bangladesh TECHNICAL BRIEF 67 Berthing Problem of Ships in Chittagong Port and Proposal for its Solution 30 25 Observed Expected 20 15 10 Frequency ( % ) 5 0 012345678 Arrival of ships per day Figure 1: Distributions of arrival of ships per day. 25 Observed 20 Expected 15 10 Frequency (%) 5 0 12345678910111213141516 Service time per ship Figure 2: Distributions of service time. Table 2: Comparison of theoretical results with those obtained by simulation Parameter Theoretical model M/M/s (∞ ) Simulation Mean queue length 1.423 1.504 Mean waiting time 0.646 0.688 Mean system time 6.072 6.213 Mean system length 13.370 13.567 distribution. The distribution of service time per ship is random numbers generated by computer. Actual data of plotted in Fig. 2 and it is clear that the service process does service time per ship collected between 1994 and 2000 are not satisfy the assumed exponential distribution in the used to estimate both relative and cumulative frequencies M/M/s(∞) model. So the berthing problem of the of service times. Using cumulative distribution thus Chittagong port is considered as M/G/s(∞) queuing model. calculated, computer generated random numbers M/G/s(∞), which is same as M/M/s(∞) model except that distributed between 0 and 1 and corresponding to each of the service time distribution is non-exponential. the service time was selected in the simulation. The calculation and simulation were done for the arrival rate, λ SOLUTION OF THE QUEUING MODEL = 2.203 per day, service rate, µ = 5.505 days per ship and Exact solution of the queuing problem is possible only number of servers i.e. jetties, S = 15. Mean arrival rate and in some limited cases. Simulation and approximation mean service time used in the model are obtained from the methods are used when exact theoretical solutions are not actual collected data. Table 2 shows the results obtained available. Here Diffusion Approximation method 2-4 has from the M/M/s(∞) model and simulation. The mean been used to solve the queuing model. At first, a M/M/s system length was also varied by Diffusion Approximation (∞) simulation model is developed with the exact data of method in which diffusion equations are solved using arrival and departure of ships during the period of 1994- MathCAD 2000 professional software and system length, 2000 and the results were verified using the exact results Ls was found to be equal to 13.404. This validates the available in the textbooks5 of queuing theory. Since the developed simulation program. This simulation was later arrival process fits nicely to Poisson probability applied to solve M/G/s(∞) queue model which represents distribution, exponential deviates are determined using the berthing problem of the Chittagong port. Journal of Mechanical Engineering, vol. ME37, June. 2007 Transaction of the Mech. Eng. Div., The Institution of Engineers, Bangladesh TECHNICAL BRIEF 68 Berthing Problem of Ships in Chittagong Port and Proposal for its Solution 1200 Y = 37.771x + 672.8 1000 800 Number of Ships 600 400 1994-95 1995-96 1996-97 1997-98 1998-99 1999-00 2000-01 2001-02 2002-03 2003-04 2004-05 Year Figure 3: Forecast of arrival of ships at Chittagong port. 180000 Import 135000 Linear (Import) 90000 Import 45000 Y = 9511.6x + 14354 0 1985- 1986- 1987- 1988- 1989- 1990- 1991- 1992- 1993- 1994- 1995- 1996- 1997- 86 87 88 89 90 91 92 93 94 95 96 97 98 Year Figure 4: Forecast of import 180000 Observed Linear (export) 135000 90000 Export Y = 8961x - 10101 45000 0 1985-86 1986-87 1987-88 1988-89 1989-90 1990-91 1991-92 1992-93 1993-94 1994-95 1995-96 1996-97 1997-98 1998-99 1999-00 2000-01 2001-02 2002-03 2003-04 2004-05 Year Figure 5: Forecast of export. Journal of Mechanical Engineering, vol. ME37, June. 2007 Transaction of the Mech. Eng. Div., The Institution of Engineers, Bangladesh TECHNICAL BRIEF 69 Berthing Problem of Ships in Chittagong Port and Proposal for its Solution Table 3: Forecast of imports arrival of ships and import and the arrival of ships and Year Imports Arrival of ships export are calculated. The coefficient of correlation in the 2005 204594 998 case of import is 0.64 and in the case of export is 0.63. Due 2010 252154 1131 to the simplified assumptions, coefficient of correlations 2015 299714 1264 has become considerably low. The forecasted values would 2020 347274 1398 have been more accurate had they been above 80 %. Then 2025 394834 1531 based on the forecasted imports and exports, arrival of 2030 442394 1664 ships up to 2030 AD have been forecasted and the results are shown in Tables 3 and 4.
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