Optimal design of container terminal gate layout

640 Int. J. Shipping and Transport Logistics, Vol. 9, No. 5, 2017 Optimal design of container terminal gate layout Chu Cong Minh* Department of Bridge and Highway Engineering, Ho Chi Minh City University of Technology, 268 Ly Thuong Kiet Street, District 10, Ho Chi Minh City, Vietnam Email: ccminh@hcmut.edu.vn *Corresponding author Nathan Huynh Department of Civil and Environmental Engineering, University of South Carolina, 300 Main Street, Columbia, SC 29208, USA Email: huynhn@cec.sc.edu Abstract: Over the last 50 years, international trade of goods has grown significantly in the USA, and as a result, US ports have become bottlenecks in the freight supply chain and logistics. A particular issue that most US ports are contending with is gate congestion (i.e., queuing of trucks outside the container terminal gate). This research provides planners and engineers of container terminals a set of methodologies to design an optimal gate layout to reduce gate congestion. The use of the methodologies to determine the optimal number of service gates is illustrated considering various truck arrival rates, gate service rates, and waiting time thresholds. Keywords: queuing model; pooled queues; gate layout; optimisation; queuing time. Reference to this paper should be made as follows: Minh, C.C. and Huynh, N. (2017) ‘Optimal design of container terminal gate layout’, Int. J. Shipping and Transport Logistics, Vol. 9, No. 5, pp.640–650. Biographical notes: Chu Cong Minh is an Associate Professor at the Ho Chi Minh City University of Technology, Vietnam. He received his PhD in Transportation Engineering from the Nagaoka University of Technology, Japan. His research interests include terminal design and operations, and transportation planning and management. Nathan Huynh is an Associate Professor at the University of South Carolina. He received his PhD and MS in Transportation Engineering from the University of Texas at Austin. His research interests include intermodal freight terminal design and operations, intermodal freight transport, and freight transportation planning and logistics. Copyright © 2017 Inderscience Enterprises Ltd. Optimal design of container terminal gate layout 1 641 Introduction Over the last 50 years, international trade of manufactured goods has grown significantly, and as a result, the global supply chains and the underlying support infrastructure, particularly ports, have been strained. Due to the fact that ports have to operate at or near capacity, its ability to withstand ‘shocks’ (in the form of high number of trucks arriving to drop off export containers or pick up import containers) is greatly diminished. The resultant congestion at the terminal gate can have deleterious impacts on air quality due to increased idling from drayage trucks. Also, excessive truck delay leads to a loss of profitability for truckers and can eventually impact consumer prices. Consider the typical gate layout at US marine container terminals (Figure 1), once the trucks arrive at the entry gate they must stop to present transaction information, be inspected, and then be directed to a specific location in the container yard. When the truck arrival rate exceeds that of the service gate, long queues of trucks will begin to form across multiple lanes. Another contributing factor to long queues of trucks is trouble transactions; trouble transactions are generally a result of documentation, container location, or equipment issues and constitute approximately 5% of all transactions. In the typical gate layout (will be referred to as non-pooled queuing strategy), when a truck being serviced has a trouble transaction, all the vehicles in the lane directly behind the ‘trouble’ vehicle must wait for the trouble transaction to clear; trouble transactions take much longer to complete than a normal transaction. Thus, a trouble vehicle will hold up all trucks waiting behind. This phenomenon can lead to situations of ‘socially unjust’ queuing where a truck arriving earlier receive service later because it was stuck behind the trouble vehicle. Figure 1 Satellite image of the entry gate layout of APM Terminal, Port Elizabeth, New Jersey and USA (see online version for colours) Source: https://www.google.com/maps/@40.6695181,74.1602534,209m/ data=!3m1!1e3 Now consider the scenario where all trucks upon arrival are put into a single queue and trucks at the front of the queue are served by the next available gate associates (Figure 2). 642 C.C. Minh and N. Huynh This queuing setup is often employed at places like banks, airports, and theme parks. Using this gate setup, the trouble vehicles no longer prevent vehicles behind it from receiving service. Figure 2 Pooled queuing strategy (see online version for colours) This study seeks to provide a methodology for terminator operators and port planners to design a gate layout that will reduce truck queueing time and gate operation costs. The chief advantage of the developed methodology is that it provides practitioners with a more accurate approach than the state-of-the-practice which assumes deterministic truck arrival rate and gate service rate. The developed methodology can be used for design of a new terminal gate or expansion of an existing terminal gate. Specifically, the developed methodology can be used to: 1 evaluate the performance of different truck queuing strategies (pooled vs. non-pooled) 2 determine the number of gates necessary to achieve average truck waiting time for a given truck arrival rate and gate service rate. The remainder of this paper is organised as follows. The literature review section summarises past studies that are related to this work. The methodology section presents the queuing models and the gate optimisation model. Numerical results and sensitivity analyses are presented in the model application section. Lastly, the conclusion section provides concluding remarks and recommendation for further studies. 2 Literature review A number of studies have addressed the truck queuing problem at the inbound gates of marine container terminals. However, these studies have focused mainly on operational strategies to reduce truck queuing time, such as the use of a truck appointment system, extended gate hours, or truck arrival management (e.g., Giuliano and O’Brien, 2007; Chen et al., 2011, 2013a; Zhang et al., 2013; Chen et al., 2013b). This study deals with the planning and design of gate layout to reduce truck queuing time. The three studies most related to this work are discussed in more detail below. Guan and Liu (2009a, 2009b) developed a model to measure costs of congestion at the gates, provided alternatives to improve gate operation and investigated ways to Optimal design of container terminal gate layout 643 reduce gate congestion at the Port of New York. A multi-server queuing model was used to analyse congestion at the gates and to estimate truck waiting cost. The authors applied the M/Ek/n model given that the truck inter-arrival times followed the exponential distribution and the service times followed the Erlang distribution. The proposed optimisation model was to minimise the total gate system cost, which considered both the cost to trucks (waiting time) and cost to the terminal operator (number of service gates to operate). Fleming et al. (2013) developed an agent-based simulation model to study the terminal gate system with two different queuing strategies, a pooled queue and non-pooled queues. Their simulation model overcomes a key shortcoming of queuing models – vehicle movements within the queue. Using a car-following model, a realistic representation of how trucks move within the queue was captured. The developed simulation model was used to evaluate queuing strategies under various operational conditions. Results indicated that using a pooled queue yielded significantly lower average truck queuing times and variability in queuing times. Minh and Huynh (2014) developed a planning-level tool that can be used by design engineers, terminal operators, port authorities, and transportation planners to assess the effectiveness of different gate layout as well as determine the optimal layout for marine container terminals. Specifically, their analytical tool can be used to determine the average truck queuing time for a given gate configuration or determine how many service gates and queuing lanes are needed to achieve a desired level of service for a given truck arrival rate and truck service rate. This tool accounts for the non-deterministic nature of truck arrivals and service times. Specifically, it accounts for the fact that trucks arrive as a Poisson stream, will be served by one of n gates and that the gate service times are independent and identically distributed random variables. This study expands the work of Guan and Liu (2009a, 2009b) by providing design engineers with a methodology to 1 assess the trade-offs between non-pooled and pooled queuing strategies 2 determine the minimum number of gates needed to ensure that the average queuing time does not exceed a specified threshold. In contrast to the work by Fleming et al. (2013) which used simulation, the developed methodology is analytical and thus much simpler to apply. A key difference between this work and that of Minh and Huynh (2014) is that this work assumes the gate service time of trucks follows the Erlang distribution (Huynh et al., 2011; Guan and Liu, 2009a, 2009b) instead of a general distribution. Thus, this study uses the M/Ek/n queuing model instead of the M/G/n queuing model previously proposed by the authors. The advantage of using the M/Ek/n queuing model is that it provides a simple analytical formula as opposed to the more complicated M/G/n diffusion approximation formulas. 3 Methodology This section describes the queuing models that can be used to analyse the truck queuing situation at container terminal gates. These models assume the following. 1 there is no truck balking after arrival 644 C.C. Minh and N. Huynh 2 there are no obstacles in the queue-to-gate paths 3 arriving trucks will join the shortest queue 4 the utilisation factor (traffic intensity/number of gates) is less than one. 3.1 Non-pooled queues If truck arrivals follow a Poisson process and the gate service times are Erlang distributed (Ek), with k as the shape parameter, the M/Ek/1 model can be used to analyse the non-pooled queuing situation. If is the truck arrival rate (trucks/min) to the terminal and n is the number of gates, then the truck arrival rate for each lane is /n (trucks/min). The average truck queuing time can be calculated using the following equation (Gross et al., 2008): QTM / Ek /1 = 1+ k /n × 2k ( − / n) (1) where, mean of gate service rate of trucks (trucks/min) mean of truck arrival rate (trucks/min) k shape parameter of the Erlang distribution n number of gates. 3.2 Pooled queues In the pooled queuing situation, the gate will have n gates working in parallel to serve a single queue of trucks. Assuming that truck arrivals are Poisson distributed and the gate service times are Erlang distributed, the M/Ek/n model can be used to analyse the pooled queuing situation. The following approximation formula can be used to calculate the average truck queuing time with a relative percentage error less than 2% (Cosmetatos, 1976): ⎡1 + v 2 (1 + v 2 ) (1 − ρ)(r − 1) ( 4 + 5r − 2 ) ⎤ QTM / Ek / n ≈ ⎢ + ⎥ × QTM / M / n 16 ρr ⎣⎢ 2 ⎦⎥ (2) QTM/M/n corresponds to the M/M/n queuing system and can be calculated by using the following formula: QTM / M / n ∑ ⎡ n −1 a i ⎤ an an ≈ × + ⎢ ⎥ 2 (n − 1)!(n − a) ⎢⎣ i = 0 i ! (n − 1)!(n − a) ⎦⎥ −1 where, a = /μ v = var( Ek ) / coefficient of variation of gate service rate, 0 < v < 1. (3) 645 Optimal design of container terminal gate layout ρ = /n < 1 traffic intensity or server utilisation The gate service times of trucks are assumed to follow the Erlang distribution with shape (k) and rate parameters (θ). The mean and the variance of the distribution are k/θ and k/θ2, respectively. The coefficient of variation of gate service times of trucks, v, is: v= var ( Ek ) = k θ × = θ2 k 1 k (4) Finally, the average truck queuing time is calculated as QTM / Ek / n ≈ ∑ ⎡ n −1 a i ⎤ an an × + ⎢ ⎥ 2 (n − 1)!(n − a ) ⎣⎢ i = 0 i ! (n − 1)!(n − a ) ⎦⎥ −1 ⎡ 1 ⎛ 1⎞ ⎤ ⎜ 1 − ⎟ (1 − ρ)(n − 1) ( 4 + 5n − 2 ) ⎥ ⎢1 + k ⎠ ⎥ ×⎢ k + ⎝ 16 ρn ⎢ 2 ⎥ ⎢ ⎥ ⎣ ⎦ (5) 3.3 Gate optimisation model The required number of service gates needed under the pooled queuing situation to meet a specified waiting time threshold (T in minutes) can be determined by solving the following mathematical program (8) minimize n subject to QTM / Ek / n ∑ ⎡ n −1 a i ⎤ an an ≈ × + ⎢ ⎥ 2 (n − 1)!(n − a) ⎢⎣ i = 0 i ! (n − 1)!(n − a) ⎥⎦ −1 ⎡ 1 ⎛ 1⎞ ⎤ ⎜1 − ⎟ (1 − ρ)(n − 1) ( 4 + 5n − 2 ) ⎥ ⎢1 + k⎠ ⎥ ≤T ×⎢ k + ⎝ 2 16 ρn ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ , , a , ρ, T ≥ 0 (9) (10) The stated mathematical program can be solved for by simply evaluating different values of n (from low to high). The optimal value of n is the one that satisfies the expression: n* = arg min{n : QT (n) ≤ T }. n 646 4 C.C. Minh and N. Huynh Model application The models presented above are applied using data collected from one of the container terminals on the US East Coast. Huynh et al. (2011) used the provided terminal webcam to obtain the truck arrival rate and gate service time of trucks. It was found that the truck arrival rate follows the Poisson distribution with mean = 1.4096 trucks/min, and the gate service time of trucks follows the Erlang distribution with shape parameter k = 5 and rate parameter θ = 0.9112. That is, the mean ( ) of gate service rate of trucks at this terminal is 0.18 trucks/min. 4.1 Non-pooled queues vs. pooled queues To assess the performance of non-pooled queuing strategy versus pooled queuing strategy, the terminal layout, truck arrival data, and gate service data collected by Huynh et al. (2010) are used. This particular terminal has 10 service gates, and as stated, the gate service rate follows the Erlang distribution with mean = 0.18 trucks/min. For this analysis, the mean truck arrival rate ( ) is varied from 0.1 to 1.8 trucks/min. As shown in Figure 3, the average truck queuing time of the pooled queuing strategy is always lower than that of non-pooled queuing strategy. This finding is consistent with the results reported in Minh and Huynh (2014). Figure 3 Comparison of average queuing times between pooled and non-pooled queuing strategy Average Waiting time (min) 300 Pooled Non-pooled 250 200 150 100 50 0 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 Arrival Rate (trucks/min) 4.2 Gate optimisation To examine the effect of truck arrival rate and time threshold on the number of service gates and average queuing time, we used a mean gate service rate of 0.18 trucks/min, and the mean truck arrival rate is varied between 0.1 and 2.0 trucks/min. The time threshold, T, is assumed to range between five and 30 min in five-min increments. Table 1 shows the relationships between truck arrival rate, number of service gates, and average truck queuing time. It is clear that the level of n* is dependent on the levels of T and for the pooled queuing system. With a specified time threshold, increasing arrival rate may increase the 647 Optimal design of container terminal gate layout number of gates accordingly, but it is not always true. For example, in case of the time threshold is 15 min, when the truck arrival rate increases from 0.6 to 0.7 trucks/min, the number of gates increases from four to five gates. However, when the truck arrival rate increases from 0.7 to 0.8 trucks/min, the number of gates remains the same (five gates). This is because when the truck arrival rate increases (from 0.7 to 0.8 trucks/min), the queuing time also increases (from 1.55 min to 4.55 min) but it is still less than the waiting time threshold (15 min). When the truck arrival rate reaches 0.9 trucks/min, if the number of gates remains at five, then the server utilisation would reach one ( /(n ) = 0.9/ (5 * 0.18)) and the queue would grow to infinity. Therefore, the number of gates needs to increase by one to six, and therefore reduces the average queuing time to 2.4 minutes. Table 1 Truck arrival rate (trucks/min) 0.1 Effect of truck arrival rate and waiting time threshold on optimal number of service gates and average queuing time Waiting time threshold (min) 5 10 15 20 25 30 No. AQT No. AQT No. AQT No. AQT No. AQT No. AQT 1 4.17 1 4.17 1 4.17 1 4.17 1 4.17 1 4.17 0.2 2 1.57 2 1.57 2 1.57 2 1.57 2 1.57 2 1.57 0.3 3 0.83 2 7.69 2 7.69 2 7.69 2 7.69 2 7.69 0.4 3 2.48 3 2.48 3 2.48 3 2.48 3 2.48 3 2.48 0.5 4 1.16 4 1.16 3 13.09 3 13.09 3 13.09 3 13.09 0.6 4 3.41 4 3.41 4 3.41 4 3.41 4 3.41 4 3.41 0.7 5 1.55 5 1.55 5 1.55 5 1.55 5 1.55 4 28.32 0.8 5 4.55 5 4.55 5 4.55 5 4.55 5 4.55 5 4.55 0.9 6 2.06 6 2.06 6 2.06 6 2.06 6 2.06 6 2.06 1.0 7 1.18 6 6.16 6 6.16 6 6.16 6 6.16 6 6.16 1.1 7 2.55 7 2.55 7 2.55 7 2.55 7 2.55 7 2.55 1.2 8 1.42 7 8.74 7 8.74 7 8.74 7 8.74 7 8.74 1.3 8 3.15 8 3.15 8 3.15 8 3.15 8 3.15 8 3.15 1.4 9 1.62 9 1.62 8 13.81 8 13.81 8 13.81 8 13.81 1.5 9 3.91 9 3.91 9 3.91 9 3.91 9 3.91 9 3.91 1.6 10 1.92 10 1.92 10 1.92 10 1.92 10 1.92 9 28.87 1.7 10 4.96 10 4.96 10 4.96 10 4.96 10 4.96 10 4.96 1.8 11 2.37 11 2.37 11 2.37 11 2.37 11 2.37 11 2.37 1.9 12 1.42 11 6.50 11 6.50 11 6.50 11 6.50 11 6.50 2.0 12 2.82 12 2.82 12 2.82 12 2.82 12 2.82 12 2.82 Notes: No. = number of service gates (n ) and AQT = average queuing time (min) * If a marine terminal provides a vehicle booking system, that is, truck drivers can make appointments by telephone or via the internet before they arrive at the terminal, the gate service time at the terminal can be reduced. On the contrary, if trucks arrive at the terminal without sufficient and appropriate transaction documents, the overall gate service time will be increased. To understand the impacts of these two scenarios, the relationships between gate service rates ( ), number of service gates (n*) and time 648 C.C. Minh and N. Huynh threshold (T) are examined and the results are shown in Table 2. For this analysis, the gate service rate is again assumed to be Erlang distributed, with varied between 0.135 and 0.230 trucks/min, and T is varied between five and 30 minutes, in five-minute increments. The truck arrival rate is assumed to be Poisson distributed with mean = 1.41 trucks/min. Table 2 Gate service rate (trucks/min) Effect of gate service rate and waiting time threshold on optimal number of service gates and average queuing time Waiting time threshold (min) 5 10 15 20 25 30 No. AQT No. AQT No. AQT No. AQT No. AQT No. AQT 0.135 12 11 6.63 11 6.63 11 6.63 11 6.63 11 6.63 0.140 11 3.36 11 3.36 11 3.36 11 3.36 11 3.36 11 3.36 0.145 11 1.98 11 1.98 10 13.53 10 13.53 10 13.53 10 13.53 0.150 11 1.34 10 5.39 10 5.39 10 5.39 10 5.39 10 5.39 0.155 10 3.10 10 3.10 10 3.10 10 3.10 10 3.10 10 3.10 0.160 10 1.95 10 1.95 10 1.95 9 18.47 9 18.47 9 18.47 0.165 10 1.38 9 6.75 9 6.75 9 6.75 9 6.75 9 6.75 0.170 9 3.84 9 3.84 9 3.84 9 3.84 9 3.84 9 3.84 0.175 9 2.54 9 2.54 9 2.54 9 2.54 9 2.54 9 2.54 0.180 9 1.73 9 1.73 9 1.73 8 18.54 8 18.54 8 18.54 0.185 9 1.30 8 7.38 8 7.38 8 7.38 8 7.38 8 7.38 0.190 8 4.34 8 4.34 8 4.34 8 4.34 8 4.34 8 4.34 0.195 8 2.94 8 2.94 8 2.94 8 2.94 8 2.94 8 2.94 0.200 8 2.14 8 2.14 8 2.14 8 2.14 8 2.14 8 2.14 0.205 8 1.56 8 1.56 8 1.56 8 1.56 7 22.50 7 22.50 0.210 8 1.23 7 8.85 7 8.85 7 8.85 7 8.85 7 8.85 0.215 8 0.99 7 5.25 7 5.25 7 5.25 7 5.25 7 5.25 0.220 7 3.59 7 3.59 7 3.59 7 3.59 7 3.59 7 3.59 0.225 7 2.66 7 2.66 7 2.66 7 2.66 7 2.66 7 2.66 0.230 7 2.06 7 2.06 7 2.06 7 2.06 7 2.06 7 2.06 1.61 Notes: No. = number of gates (n ) and AQT = average queuing time (min) * It is clear that the level of n* is dependent on the levels of T and for this system. With a specified waiting time threshold, increasing the gate service rate may decrease the number of gates accordingly, but again, it is not always true. In the case of 15 minutes waiting time threshold, if the gate service rate increases from 0.140 to 0.145 trucks/min, the number of gates reduces from 11 to ten gates. In this instance, the average queuing time increases from 3.36 min to 13.53 min; note that this waiting is acceptable since it is still less than the waiting time threshold of 15 minutes. However, if the gate service rate increases to 0.15 trucks/min, and the number of gates needs to remain at ten gates and not reduce to nine. This is because if the number of gates reduces to nine, the server utilisation would exceed one ( /n = 1.41/(9*0.15) = 1.04), and the queue would grow to 649 Optimal design of container terminal gate layout infinity. The number of gates, therefore, needs to remain the same as before (ten gates), and thus the increase service rate reduces the average queuing time to 5.39 minutes. Figure 4 shows the relationship between the waiting time threshold and the number of gates. When the average truck arrival rate is 1.41 trucks/min and the gate service rate of trucks is 0.18 trucks/min, the number of gates is a function of the waiting time threshold. If the waiting time threshold increases, the number of gates may decrease, so the average queuing time may increase accordingly. However, it is not always true. If the waiting time threshold increases from five to 15 min, the number of gates remains the same, i.e., nine gates. This is because if the number of gates is reduced, the average queuing time will be higher than the specified waiting time threshold. It is noted that if the permitted waiting time increases from 20 to 30 minutes or more, the number of gates would remain the same, i.e., eight gates. This is because for the given truck arrival rate and gate service rate, that is, 1.41 and 0.18 trucks/min, respectively, the minimum number of gates needs to be n = roundup(a) = eight gates to keep the server utilisation less than one. In the other words, the minimum number of gates in this case is eight gates, no matter how high the waiting time threshold is. 10 20 9 18 8 16 7 14 6 12 5 10 4 8 3 6 2 4 1 2 0 0 5 No of Gates Average WT 5 Average Waiting Time (min) The relationship between waiting time threshold and number of gates No of gates Figure 4 10 15 20 25 30 Truck processing time (trucks/min) Truck waiti g ti e threshold trucks/ i Conclusions This paper developed a methodology for terminal operators and port planners to 1 investigate the possible benefit of using a pooled queuing strategy for inbound trucks at maritime terminal gates 2 determine the optimal number of service gates for different truck waiting time thresholds. Numerical results indicated that the pooled queuing strategy yields lower truck queuing time than the non-pooled queuing strategy. This strategy can be implemented by terminal operators and the practice implications are discussed in our previous work (Minh and 650 C.C. Minh and N. Huynh Huynh, 2014). The developed optimisation model provides a methodology for terminal operators to reduce gate operation costs. That is, for a specified truck waiting time threshold, the terminal operators can use the model to determine the minimum number of gates needed to meet this constraint for different truck arrival rates. The developed methodology is limited to situations where the truck inter-arrival times follow the Poisson distribution and the gate service times follow the Erlang distribution. It does not have the capability to analyse complex gate setup that segregates truck transactions by type (e.g., export vs. import, full vs. empty, appointment vs. non-appointment). 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