SHIP TRAFFIC IN CONTAINER PORT: MODELLING METHODOLOGY AND PERFORMANCE EVALUATION Assoiate Professor Branislav DRAGOVIĆ 1 1) Maritime Faulty, University of Montenegro, Maritime Transport & Traffi Division Dobrota 36, 85330 Kotor, Montenegro, branod@g.a.yu, bdragovi@g.yu www.users.g.yu/bdragovi Professor Nam Kyu PARK 2 2) Department of Distribution Management, Tongmyong University of Information Tehnology, Korea Assoiate Professor Dong-Keun RYOO 3 3) College of International Studies, Division of Shipping Management, Korea Maritime University, Korea Assoiate Professor Romeo MEŠTROVIĆ 4 4) Maritime Faulty, University of Montenegro, Mathematis Division
1. Introdution This paper gives modeling methodology of ship traffi in ontainer port and performane evaluation. The basi approah used mathematial and simulation models. These models are developed for impat analysis of the ship traffi and patterns of arrival ships at terminal performane. The results, analysis and onlusions given in this paper also addresses issues suh as the performane riteria and the models parameters to propose an operational method that redues average ost per ship served and inreases the terminal effiieny. We present effet on apaity performane with numerial results and omputational experiments whih are reported to evaluate the effiieny of Pusan East Container Terminal (PECT). This paper desribes the riteria for the ombined evaluation of important parameters of the total port ost funtion suh as: ship servie and waiting time, the number of berths and related average ontainer ship ost in port and the optimal ombination of berths/terminal and quay ranes/berth. These parameters are the basis of simulation and analytial approahes used in this paper.
The rest of this paper is organized as follows: - In the next setion we provide an overview of the literature related to port simulation and analytial modeling. - The following setion presents a brief desription of shipberth-yard link modeling proedure. Also, this setion is onerned with the evaluation of funtional estimation models in ontainer port. - This is followed by the next setion whih gives model validation and simulation and analytial results for PECT. - Finally, we onlude by summarizing the results and ontributions of this paper.
2. Related literature Most studies and papers fous their attention on the strategi and tatial problems in the appliations of the simulation and analytial models. The determination of optimum number and apaity of berths have been treated both theoretially and pratially in many studies. Considered problems Berth planning Berth alloations and sheduling Approahes Queueing theory: Essentials basi methods of probability theory in port systems. Disrete distributions and ontinuous distributions for desription port operation proesses. Stohasti proesses in port systems. Markov-proesses. Birth-death proesses. Poisson proesses. Little s results. Queuing systems. Priority queues. Queueing network. Heuristi algorithm for BAPD. Heuristi algorithm (HA) for SBAP. Graphs; Heuristi.Geneti algorithm(ga). Lagrangian relaxation (LR) - based HA; Subgradient method (SM). LR; GA. HA for BAPD and BAPC. Tabu searh (TS) heuristis. Mixed integer programming; Simulated annealing. Tree searh proedure. Plumle (1966); Niolaou (1967, 1969); Mettam (1967); Jones and Blunden (1968), Miller (1971); Wanhill (1974); Edmond (1975); Noritake and Kimura (1983, 1989); Noritake (1985); Shonfeld and Sharafeldien (1985); Sabria and Daganzo (1989); Radmilović (1992); Berg-Andreassen and Prokopowiz (1992); Huang et al. (1995, 1997); Zrnić et al. (1999); Chu and Huang (2002); Shabayek and Yeung (2001); Radmilović et al. (2005). Lai and Shih (1992); Imai et al. (1997); Lim (1998); Nishimura et al. (2001); Referenes Imai et al. (2001); Imai et al. (2003); Imai et al. (2005); Zhou Xu (2002); Cordeau et al. (2003); Kim and Moon (2003); Guan and Cheung (2004);
Continue Berth and ranes sheduling SM; Dynami programming Simulated annealing Park and Kim (2003); Dai et al. (2004); Crane sheduling Simulation of ontainer terminals (CT) and ports Heuristi method Branh & Bound (B&B). B&B; Simulated annealing. Dynami programming, TS and squeaky wheel heuristi. B&B; GRASP. Modsim III Objet oriented programming (ORP), C ++. ARENA. ARENA, SLX. Visual SLAM. AweSim. Witness software. Taylor II. GPSS/H. Extend-version 3.2.2. Senario generator. ORP, Java. Daganzo (1989); Peterkofsky and Daganzo (1990); Zhu and Lim (2004); Lim et al. (2004); Kim and Park (2004); Gambradella et al.(1998,2001); Yun and Choi (1999); Tahar and Hussain (2000); Merkuryeva et al. (2000); Legato and Mazza (2001); Nam et al. (2002); Demiri (2003); Shabayek and Yeung (2002); Kia et al. (2002); Pahakis and Kiremidjian (2003); Dragović et al. (2005a,2005b,2005); Sgouridis et al. (2003); Hartmann (2004); Bielli et al. (2005); Overview onept Quantitative models for various deision problems in CT. Logistis proesses and operations in CT optimization methods. Operations researh at ontainer terminals: a literature update Vis and Koster (2003); Steenken, et al. (2004); Stahlbok, and Voß (2008).
3. Problem desription and modeling proedure Container port system is omplex owing to the different interarrival times of ships, different dimensions of ships, multiple quays and berths, different apabilities of QCs and QCs produtivity and so on. Therefore, simulation and analytial models are used to desribe this system. The analytial modeling of ontainer terminal onsists of setting up mathematial models and equations whih desribe ertain stages in the funtioning of the system. Speifially, the probabilisti models are, often, used to desribe the evolution of these systems in the proess of their modeling. Simulation modeling is better than analytial one in representing random and omplex environment of ontainer terminal. In the simulation and analytial models, ustomers and servers are designated to ontainer ships and terminal operators, respetively. The basi struture of the models is shown in next Figure.
Port operation with ship movement in port and proess flow diagram of the terminal transport operations
3.1 Simulation Model Struture Most ontainer terminal systems are suffiiently omplex to warrant simulation analysis to determine systems performane. The GPSS/H simulation language, speifially designed for the simulation of manufaturing and queueing systems, has been used in this paper (Shriber, 1991). In order to present the ship-berth link proesses as aurate as possible the following phases need to be inluded into simulation model (Dragović et al. 2005a,b; 2006a,b): Model struture: Ship-berth-yard link is omplex due to different interarrival times of ships, different dimensions of ships, multiple quays and berths, different apabilities of QCs and so on. The modeling of these systems must be divided into several segments, eah of whih has its own speifi input parameters. These segments are losely onneted with the stages of ship servie.
Data olletion: All input values of parameters within eah segment are based on data olleted in the ontext of this researh. The main input data onsists of ship interarrival times, lifts per ship, number of alloated QCs per ship all, and QC produtivity. Existing input data are subsequently aggregated and analyzed so that an aurate simulation algorithm is reated in order to evaluate ship-berth-yard link parameters. Inter-arrival times of ships: The inter-arrival time distribution is a basi input parameter that has to be assumed or inferred from observed data. The most ommonly assumed distributions in literature are the exponential distribution (Demiri 2003; Pahakis and Kiremidjian 2003; Dragović et al. 2006a,b); the negative exponential distribution (Shabayek and Yeung 2002) or the Weibull distribution (Tahar and Hussain 2000; Dragović et al. 2005a,b). Loading and unloading stage: Aurate representation of number of lifts per ship all is one of the basi tasks of ship-berth link modeling proedure. It means that, in aordane with the division of ships in different lasses, the distribution orresponding to those lasses has to be determined.
Flowhart: Upon arrival, a ship needs to be assigned a berth along the quay. The objetive of berth alloation is to assign the ship to an optimum position, while minimizing osts, suh as berth resoures (Frankel 1987). After the input parameter is read, simulation starts by generating ship arrivals aording to the stipulated distribution. Next, the ship size is determined from an empirial distribution. Then, the priority of the ship is assigned depending on its size. The ship size is important for making the ship servie priority strategies. For the assumed number of lifts per ship to be proessed, the number of QCs to be requested is hosen from empirial distribution. If there is no ship in the queue, the available berths are alloated to eah arriving ship. In other ases ships are put in queue. The first ome first served priniple is employed for the ships without priority and ships from the same lass with priority. After berthing, a ship is assigned the requested number of QCs. In ase all QCs are busy, the ship is put in queue for QCs. Finally, after ompletion of the loading and unloading proess, the ship leaves the port. This proedure is presented in the algorithm shown in next Figure.
Figure 3. Flowhart for a ship arrival/departure
Seond ome First lass prioritiy Higher First ome Seond lass prioritiy LOGIC OF ALGORITHM FOR SIMULATION MODEL Berths are not available! Wait in queue! Compare priorities Berth 4 available!!! Berths are not available! Wait in queue! Cranes are available!!! There is Servie no rane ompleted available! Servie ompleted Wait for rane! Servie ompleted Berth 1 Berth 2 Berth 3 Berth 4
Number of QCs per ship: The data available on the use of QCs in shipberth link operations have to be onsidered too, as this is another signifiant issue in the servie of ships. This is espeially important as total ship servie time depends not only on the number of lifts but also on the number of QCs alloated per ship. Different rules and relationships an be used in order to determinate adequate number of QCs per ship. On the other hand, in simulation models, it is enough to determine the probability distribution of various numbers of QCs assigned per ship. In order to alulate the ship-berth-yard performane, it is essential to have a through understanding of the most important elements in a port system inluding ship berthing/unberthing, rane alloation per ship, yard trator alloation to a ontainer and rane alloation in staking area. As desribed in next Figure - proess flow diagram of the terminal transport operations, the sope of simulation, strategy and initial value and performane measure will have to be defined. In addition, the operational aspet suh as mahine failures having a diret impat on ship, rane and vehile will have to be onsidered. To move ontainers from apron to staking area, four trators are provided for eah ontainer rane.
Flowhart of the terminal transport operations
3.2. Analytial Model Struture Queueing theory (QT) models for analyzing movements of ships in port is proposed and shown in previous Figs. In the analysis of various aspets of average time that ships spend in port, t ws, inluding n s, n b, λ, μ, n and ρ, (e.g., [Plumlee (1966), Niolaou (1967, 1969), Wanhill (1974), Noritake (1985), Noritake and Kimura (1983,1990), Shabauek and Yeung (2001), Taniguhi et al. (1999)) defined t ws as the sum of the average waiting time and average servie time. The average servie time, t = 1/ μ ( ) where μ t + 1 t s = du inludes ships loading/unloading time in hours per ontainership, t, expressed as It follows that t ( n r ) / k on on ( ) k n = (1) ( ln( n r ) ln( t ))/ ln( n ) on on = (2) n λnonr = θ λt on du 1/ k (3)
Further, it an be shown that where ( θ ) = for the (M/M/n b ) model. t w t = t + t (4) ws w b s 2 n ( ) μ( θ ) b n 1! n + θ ( n θ )μ b b s nb θ n 1 n θ n = n s 0 s! In this study, formulae due to Lee and Longton (1959) and Cosmetatos (1975, 1976) have been adapted onerning the average port waiting time of ships (Noritake 1985, Radmilović 1992). Aordingly with it, when the ships servie time has an Erlang distribution with k phases, the following equations are obtained t = t V + t (6) V t ws 1 1 = + 1 2 k ws w the oeffiient of variation of ships servie time distribution and k = the number of phases of an Erlang distribution 1 1 1 1 θ 4 5 2 2 + 1 1 1 1 2 n + + k k nb s ( n 1) ( ) b + 32θ μ b = tw for the (M/Ek/nb) model. b (5) (7)
3.3. Ship traffi
3.3. Modeling of ship loading/unloading operations In general, this model integrates main atual operations of the ontainer terminal by simplifying omplex ativities, and these operations are defined aording to ship lass. In this setion, various objets were observed in the real terminal and model elements. Model elements of the ontainer terminal an be separated into follow group: - berth ost in $ per hour, - QCs ost in $ per hour, - storage yards ost in $ per hour, - transportation ost by yard transport equipment between quayside and storage yard in $ per hour - labor ost for QC gangs in $ per hour, - ships ost in port in $ per hour, - ontainers ost and its ontents in $ per hour 1 = n b nb 2 = nbn = θμn 3 = θμn 4 n on t t t n 5 = θμntl 6 = θμt ws s = θμt The total ost funtion, would be onerned with TC = the ombined terminals and ontainerships ost as = 7 ws n r on on l y a w on t y y 7 i 1 i
It is neessary to know that only the total port ost funtion omputes the number of berths/terminal and QCs/berth that would satisfy the basi premise that the servie port ost plus the ost of ships in port should be at a minimum. This funtion was introdued by Shonfeld and Sharafeldien (1985). We point out that their solutions may not be as good as ours beause we have simulation approah to determine key parameters t w, t s, λ, μ, ρ and espeially k. Therefore, to find the optimal solution, their funtion an be obtained in the following form TC = + θμ f ( θ ) = n ( ) b n + nn + b t a + n t ( + n ) + t ( θ )( + n ) ( n ) on t on on y y l l y t ws s r on w (18) where TC - total port system osts in $/hour. By substituting the Eq. (3) into Eq. (18) yields TC = f ( θ ) ( n + λt ( + n ) + λt ( θ )( + n ) b n l = l n b n b y + λn t on t t on ws a on y s y λnonr + θ λt r on w on du 1/ k (19) where t ws (θ) is defined by the Eq. (6) or the Eq. (7) or or by a result of simulation modeling.
From the total port ost funtion per average arrival rate, we an obtain f AC = = λ ( θ ) f ( θ ) θμ (20) Eq. (20) shows the average ontainer ship ost in $/ship, AC. In this study, the trade-off will be simulative and analytially resolved by minimizing the sum of the relevant ost omponents assoiated with the number of berths/terminal and QCs/berth, and average arrival rate. These three parameters are key to the analysis of faility utilization and ahieving major improvements in ontainer port effiieny, inreasing terminal throughput, minimizing terminal traffi ongestion and reduing re-handling time. A redution in operating ost an be ahieved by jointly optimizing these parameters. In solving the berths/terminal and QCs/berth, analysts and planners are onerned primarily with the average time that ships spend in port and the average ost per ship servied.
4. Computational results This setion gives a ship-berth-yard link modeling methodology based on statistial analysis of ontainer ship traffi data obtained from the PECT. The effiieny of operations and proesses on the ship-berth link has been analyzed through the basi operating parameters suh as traffi intensity, average number of ships in waiting line, average time that ships spend in waiting line, average servie time, average total time in port, average QC produtivity and average number of QCs per ship. 4.1. Parameters Involved An important part of the model implementation is the orret hoie of the values of the simulation parameters. The input data for the both simulation and analytial models are based on the atual ship arrivals at the PECT for the ten months period from January 1, 2005 to Otober 31, 2005 (Fig. 3) and January 1, 2006 to Otober 31, 2006 (Fig. 4), respetively (PECT website, PECT Management reports). This involved approximately 1,225 ship alls in 2005 and 1,285 in 2006. The ship arrival rate was 0.168 ships/hour in 2005 and 0.176 in 2006. Total throughput during the onsidering period was 1,704,173 TEU in 2005 and 1,703,662 TEU in 2006. Also, the berthing/unberthing time of ships was assumed to be 1 hour.
Fig. 4. PECT layout, 2006 Fig. 3. PECT layout, 2005
Table 1. Atual ship arrivals at the PECT in 2005 and 2006 Number of ships Average lifts per ship Total lifts Class of ships 2005 2006 2005 2006 2005 2006 < 500 lifts 292 384 313 305 91,394 117,405 501 1000 lifts 500 485 782 741 364,100 359,401 > 1000 lifts 433 416 1,444 1,413 625,371 587,983 All lasses 1,225 1,285 882 829 1,080,865 1,064,789
The interarrival time distribution (IATD) is plotted in the Figures 5a and 6a. Interestingly, even though ship arrivals of the ships are sheduled and not random, the distribution of interarrival times fitted very well the exponential distribution. Servie times were alulated by using the Erlang distribution with different phases. To obtain aurate data, we have first fitted the empirial distribution of servie times of ships to the appropriate theoretial distribution. Servie time distributions are given in Figure 5b-e for 2005 and in Figure 6b-e for 2006. Goodness-of-fit was evaluated, for all tested data, by both hi-square and Kolmogorov-Smirnov tests at a 5 % signifiane level. We have arried out extensive numerial work for high/low values of the PECT model harateristis. Our numerial experiments are based on different parameters of various PECT harateristis suh as: number of ontainers loading/unloading from ontainer ship, the QC move time, hourly berth ost, average yard ontainer dwell time, transportation ost by yard transport equipment between quayside and storage yard, number of m 2 of storage yard per ontainer, storage yard ost, paid labor time, labor ost, ship ost in port and average payload of ontainers, presented in next Table.
4.2. Model Validation For purposes of validation of simulation model and verifiation of simulation omputer program, the results of simulation model were ompared with the atual measurement. Three statistis were used as a omparison between simulation output and real data: traffi intensity, average servie time and average number of servied ships. The simulation model was run for 44 statistially independent repliations. The average results were reorded and used in omparisons. After analysis of the port data, it was determined that traffi intensity is about 2.55 in 2005 and 2.25 in 2006, while the simulation output shows the value of 2.61 in 2005 and 2.28 in 2006, respetively. Average servie time shows very little differene between the simulation results and atual data, that is, 14.07 h and 14.35 h in 2005 and 12.60 h and 12.88 in 2006, respetively. The simulation results of the number of servied ships ompletely orrespond with the real data (i.e. the simulation result of the total number of ships are 1224.1 in 2005 and 1285.88 in 2006, and the real data are 1225 and 1285; the first lass of ships: 291.11 in 2005 and 383.3 in 2006, and 291 and 384; the seond lass: 502.16 in 2005 and 486,01 in 2006, and 501 and 485; and third lass: 434,17 in 2005 and 415.02 in 2006, and 433 and 416). All the above shows that simulation results are in agreement with real data.
4.3.1. Simulation and Analytial Results for PECT The impat of the different models is determined by omparing the key performane measures of simulation and analytial approahes to those of the real data of PECT. Table 3 presents average servie time of ships (all lasses, I lass, II lass and III lass), while Table 4 shows average average waiting time of ships (all lasses, I lass, II lass and III lass). In addition, Table 5 gives average time that ships spend in port. Aording to this, judging from the omputational results for some numerial examples of the (M/Ek/nb) using average waiting time, from Eq. (6) (for brevity analytial model I (AM I)) and (M/Ek/nb) using average waiting time, from Eq. (7) (for brevity analytial model II (AM II)) models, it an be onfirmed that Eq. (6) is inlined to estimate the values of average time that ontainer ships spend in port, i.e. average waiting time of ships. The average time that ships spend in port for simulation model (SM) is 15.036 h for all lasses of ships in 2006. This is about 15% shorter than that of SM, 17.799 h in 2005 and about 1.5% shorter than that of AM II, 15.245 h in 2006. For first lass of ships, the average time that ships spend in port is 10.380 h for AM II in 2006, about 0.6% shorter than SM, 10.441. This time is 15.232 h for seond lass of ships (AM II) in 2006, about 12% shorter than AM II in 2005. Finally, the average time that ships spend in port for third lass of ships is 19.818 h (SM) in 2006, about 16% shorter than SM in 2005 or 2% shorter than AM II, 20.270 h in 2006.
The results presented here support the argument that average ost per ship or ontainer served, an be easily obtained by the use of the average ost urves in funtion of traffi intensity and QCs/berth. The desribed and tested numerial experiments ontain more segments in relation to the input variables. All numerial results presented in Figure 7 are obtained by using the input data from Table 2. Simulation testing (Simulation model (SM)) was than arried out by using the GPSS/H. The solution proedure for AM I and AM II models was programmed using the MATLAB program. Figure 7 ompares the average ship osts of different ship lasses taken by SM, AM I and AM II models at a PECT in 2005 and 2006. They graphially show the sensitivity of the average ship osts to the various values of θ. In urve SM for all lasses of ships in 2006, the minimum ost per ship served dereases by about 3.3% in 2006 with respet to 2005. However, the average osts per first lass of ships served derease in 2006 by about 7% than the minimum ost in 2005, see urve AM II. This derease for seond lass of ships is about 2% in 2006 with respet to the minimum ost in 2005 for urve AM II. Finally, in urve SM for third lass of ships, the minimum ost per ship served dereases by about 2.6% ($138,019) than the minimum ost in 2005 ($141,697).
5. Conlusions A simulation model employing the GPSS/H has been developed to ship-berth-yard link performane evaluation of PECT. It is shown to provide good results in prediting the atual ship-berth-yard link operations system of the PECT. The attained agreement of the results obtained by using simulation model with real parameters has been also used for validation and verifiation of applied analytial model. In aordane with that, the orrespondene between simulation and analytial results gives, in full, the validity to the applied analytial model to be used for optimization of proesses of serviing ships at PECT. Finally, these models also address the issues suh as the performane riteria and the model parameters to propose an operational method that redues average ost per ship served and inreases the terminal effiieny. However, presented simulation and analytial methodology and results are onvenient for different analyses, planning and development of port system, for example, inreasing the number of berths or traffi intensity depending on the optimum berth apaity and average ship ost.
Container terminals in Busan Port, espeially PECT, are trying to expand apaity and inrease performane at a maximum of investments. Often the ontainer terminal operations are hanging to meet inreased ustomer demands as well as to adapt to new tehnologies. Reasons for the derease of the average ost per ship served with the introdution of new ontainer berth, QCs, ontainer yard area and automated staking ranes (ASC) inlude that waiting time of ships and the average time that ships spend in port derease with the advaned handling systems improving the operations proedures. We develop simulation and analytial models, whih provides solutions to large-sized problems usually enountered in pratie in reasonable omputational times, and analyze its effetiveness. In addition, omputational analysis shows that these models are quite effetive in realisti settings, when the OCs are assigned loser related to the apron area, and when the number of ontainers to be unloaded from/loaded onto eah ship is in the hundreds. Thus, these models an be used to obtain a good solution to the real problem.
--- THANK YOU ---