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Design and optimization of parking lot in an underground container logistics system
Computers & Industrial Engineering 130 (2019) 327–337
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Design and optimization of parking lot in an underground container logistics system
T
Yinping Gaoa, , Daofang Changa, Ting Fangb, Tian Luob ⁎
a b
Institute of Logistics Science and Engineering, Shanghai Maritime University, 1550 Haigang Avenue in Pudong New Area, Shanghai, China School of Economics & Management, Shanghai Maritime University, 1550 Haigang Avenue in Pudong New Area, Shanghai, China
ARTICLE INFO
ABSTRACT
Keywords: Underground container logistics system Underground parking lot Design Optimization Simulation
To relieve the ground traffic pressure caused by container trucks in a port, an underground container logistics system (UCLS) between Shanghai Waigaoqiao Terminal and Jiading Northwest Logistics Park is proposed. Furthermore, in order to guarantee the connection between the UCLS and the yard behind the ground terminal, a design of an underground parking lot in the system is also proposed. The underground parking lot is a buffer used for the loading and unloading of underground guided vehicles (UGVs). A mixed integer nonlinear programming model (MNIP) for UGVs and yard cranes in the underground system is formulated to minimize the total cost of UGVs waiting and yard cranes. Then, the optimization model is solved via MATLAB software. With sensitivity analysis, the number of loading and unloading points in the underground parking lot is optimized for the purpose of minimizing the total cost. Finally, a simulation experiment is carried out to obtain the optimal configuration of the number of loading and unloading points and the arrival rate in the UCLS.
1. Introduction At present, city logistics systems are faced with the following three problems. First, serious traffic congestion and frequent traffic accidents are caused by growing traffic volume, which seriously constrains the accessibility and quality of urban freight. Second, environmental problems, such as noise and air pollution, caused by the city logistics system are also contrary to the principles of highly efficient, low-cost and environmentally friendly sustainable development. Third, in order to solve the urban congestion problem, expanding the existing transportation infrastructure faces high land costs, limited space resources, and cultural heritage protection. The available space on the ground is rapidly being used up, and the largest danger is that built-up spaces are taking over the public green spaces of cities, thereby threatening live ability and quality of life (Admiraal & Cornaro, 2016). Urban living standards are lower in Russia than those in other developed countries. Gamayunova and Gumerova (2016) attempted to utilize underground spaces to solve urban development challenges, so they analysed underground space utilization and transportation infrastructure. Therefore, some researchers have diverted attention to underground space utilization and proposed some programmes that can achieve underground transportation. An underground transport and supply system named the Cargo Cap by researchers at Ruhr University in Germany, was defined as the future of the fifth category of transportation systems. ⁎
It was the combination of the underground logistics system and urban transport, taking full advantage of the varieties of facilities in the urban underground rail system to carry out underground logistics and distribution (Liu, 1999). Underground logistics, also known as an underground freight system, refers to complete freight transportation with automatic guided vehicles, dual-use trucks, and other carrying tools, through large diameter underground pipelines (Montgomery & Fairfax, 2006). In fact, there have been cases of underground space utilization for many years. For example, in 1853, the urban pipeline postal system was established in London, and it was the earliest underground logistics system in the world (Stein, Stein, Beckmann, & Schoesser, 2005). In 1927, the automatic two-track transportation system, which was the first underground logistics system in the world to connect all places in a city, was established in Britain. Amsterdam had the largest flower supply market in the world. To transport flowers safely and rapidly, a professional underground logistics system was established between the airport and the flower market. Zevgolis, Mavrikos, and Kaliampakos (2004) focused on the design of an underground warehousing-logistics centre (WLC) in the extensive metropolitan area of Athens. The layout, storage capacity and operational issues of underground WLC were thoroughly examined. A new approach regarding municipal waste collection and transport involves the installation of an underground pipe network and storage containers, called automated vacuum waste
Corresponding author. E-mail addresses: [email protected] (Y. Gao), [email protected] (D. Chang).
https://doi.org/10.1016/j.cie.2019.02.043
Available online 26 February 2019 0360-8352/ © 2019 Elsevier Ltd. All rights reserved.
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collection (AVAC). This system can minimize operating costs for waste handling and reduce the number of waste collection trips required, a feature that positively influences traffic congestion and minimizes CO2 emissions while also potentially saving space (Nakou, Benardos, & Kaliampakos, 2014). Qiao and Peng (2016) presented a case study on urban underground space (UUS) use such as Hongqiao Central Business District (CBD) and the Lujiazui Business District in Shanghai, China. At the end of June 2013, there were 60 locations below ground in the Lujiazui Business District, including facilities such as underground transportation, underground public infrastructure and underground municipal infrastructure. For the purpose of relieving urban container truck transportation pressure, this paper proposes an UCLS for container terminals. The UCLS is divided into two parts: the underground transportation subsystem and the terminal subsystem. In this paper, the concept of an underground parking lot located in the terminal subsystem is proposed. The parking lot in this paper is designed to allow underground guided vehicles (UGVs) to wait and handle in a queue as a buffer. The specific operation line of the underground parking lot is designed and optimized. Therefore, the container terminal and its underground system can be connected perfectly to improve efficiency and maximize value. The remainder of this paper is organized as follows. Section 2 gives a brief review of the related literature. The UCLS, consisting of the transportation subsystem and the terminal subsystem, is described in Section 3, and the system operation flow is explained. The underground parking lot, its waiting area, and its loading and unloading area are introduced in Section 4. The mixed integer nonlinear programming model (MINP) is formulated in Section 5 with the goal of minimizing the waiting cost of UGVs and the cost of yard cranes. The case study, including solutions and sensitivity analysis performed via MATLAB and the simulation conducted with Tecnomatix Plant Simulation 13.0 are provided in Section 6. The conclusions are given in Section 7.
infrastructure, Rogers et al. (2012) suggested that the costs of the lifecycle and the contribution to sustainable urban development were to be considered when making comprehensive strategic plans. Kaliampakos, Benardos, and Mavrikos (2016) suggested that efficient urban infrastructure development in modern cities would utilize underground space systems. The economic efficiency of underground space utilization was the key element that decided whether underground infrastructures were better than traditional ones. In general, there have been many papers focusing on underground space utilization, including the prospect and function of underground logistics, feasibility reports and underground space planning in large cities. It is noted that container transportation becomes the main development mode of underground logistics. As integral parts of multimodal transportation systems, UCLSs complete point-to-point transportation from one terminal to another (Jia, 2011). Until now, however, UCLSs are still in the conceptual design stage, and there is no built design prototype or demonstration. Therefore, this paper designs a parking lot in an UCLS to connect underground transportation and ground handling. However, the concept of a parking lot in an UCLS is new. This paper discusses the queuing in the parking lot in order to avoid congestion. Lee, Wong, and Li (2015) developed a real-time estimation approach for lane-based queue lengths. Based on detector information at isolated signalized junctions, the number of queued vehicles in each lane is determined. Giorno, Nobile, and Pirozzi (2018) considered the Markovian single-server queueing model with Poisson arrivals and statedependent service rates, characterized by a logarithmic steady-state distribution. Baumann and Sandmann (2017) provided an exact computational analysis of various steady-state performance measures, such as loss and blocking probabilities, expectations and moments of higher numbers of customers in the queues and in the whole system by modelling the multi-server tandem queue as a level-dependent quasi-birthand-death process and applying suitable matrix-analytic methods. In this paper, the queuing length of each loading and unloading point in the parking lot will be counted to find the optimal solutions. Similarly, in a new design for a bi-directional AGV system, in which two AGVs can exchange their loads, their scheduled transportation tasks, and even their vehicle numbers when they move in opposite directions, Hsueh (2010) proposed an off-line mathematical model and carried out a series of simulation experiments. Furthermore, Hsueh confirmed that the new system performs efficiently and robustly. Legato, Mazza, and Gullì (2014) integrated two separate models into a simulation–optimization framework for the berth allocation problem arising in maritime container terminals, which refers to a mathematical programming model at the tactical level and a simulation model at the operational level. Specifically, the framework uses a beam search heuristic to obtain a weekly plan at the tactical level, followed by a simulated annealingbased search process to adjust allocation decisions at the operational level. The main studies reviewed in this paper are summarized in Table 1. Therefore, with regard to the new concept of a parking lot in UCLS, the area map for the UCLS and the model of UGVs and yard cranes are included. In addition, the mathematical model of MINP and operational simulation are given in this paper.
2. Literature reviews There have been many papers about underground logistics. Underground logistics was divided into three styles according to different modes of transportation, including the pneumatic capsule pipeline (PCP), the hydraulic capsule pipeline (HCP), and the electricitydriven transportation tunnel. The PCP and HCP choose air and water as their respective conveyance medium, and the cabin as a cargo tool to transport goods. The feasibility of the PCP system in New York Harbour and New Jersey was studied by Prof. Henry Liu (2009) in the United States. A linear motor-driven PCP system was able to handle 4.1 million TEUs in the ports of New York and New Jersey. There are three main means of electricity-driven transportation: automated guided vehicles (AGVs) in Holland, Cargocap in Germany and dual mode trucks (DMT) in Japan. In addition, the advantages of underground logistics have been proposed, and underground logistics can be used as a solution to urban traffic problems. The feasibility and problems of urban subway freight transportation have been analysed. Chen, Dong, and Ren (2017) analysed the macro-environment of underground logistics systems in China and identified their unique advantages. The present situation, problems and trends of underground logistics were described in relation to the characteristics of the large-scale and rapid development of underground space in China (Qian, 2016). Four kinds of usage trends of underground space in the future were put forward, the first being the comprehensive planning, construction and management of the underground space in Beijing CBD, Shanghai World Expo and the southern part of Ningbo, the second being an urban underground complex with an integrated transport hub as its centre, as in the cases of the Hongqiao Transport Hub and the Beijing South Railway Station, the third being the development of underground subways, roads and logistics systems, and the fourth being the scientific utilization of underground water storage spaces and aeration to create a “sponge city”. To maximize the efficiency of the underground
3. Problem description The container throughput in ports has great potential. The container throughput in Shanghai Waigaoqiao terminal was 16.2205 million TEU in 2013, 17.1641 million TEU in 2014, and 18.2175 million TEU in 2015. During the 13th Five-Year Plan period, the container throughput in Shanghai port is expected to reach 42 million TEU. Moreover, frequent import and export trade stimulates the international maritime shipping industry. At the same time, port congestion has also increased and has become a global problem. Especially for container trade transportation, freight costs and capacity are increasing. The growing 328
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Table 1 The main studies listed in this paper. Authors (year)
Mathematical model
Methodology
Journal Publisher or Proceeding
Lee et al. (2015)
Discriminant model
Transportation Research Part C
Giorno et al. (2018)
An adaptive single-server queuing model
Data processing method for the real-time estimation of lane-based queue lengths Queuing theory
Baumann and Sandmann (2017) Hsueh (2010) Legato et al. (2014)
Modelling the multi-server tandem queue as a leveldependent quasi-birth-and-death process An off-line mathematical model A mathematical programming model at the tactical level and a simulation model at the operational level
container throughput is bound to cause congestion in the collection and distribution system of Waigaoqiao terminal. To avoid and solve the problem of ground traffic congestion caused by container trucks, various proposals were put forward, including constructing more railway, highway and water transportation lines, and even expanding the dock infrastructure. However, the implementation of these programmes requires more land area, and urban land is very expensive. Expanding public infrastructure is in conflict with the limitations of space resources. In the long term, the increasing container throughput, the limited land resources, the high cost of land, and the pressure of container truck transportation congestion all promotes the utilization of underground resources. Accordingly, an underground logistics system is put forward to relieve ground traffic pressure. The underground logistics system can achieve the goals of relieving traffic pressure, reducing environmental pollutions and improving logistics efficiency. The increasing container throughput in Shanghai Waigaoqiao terminal has generated much traffic pressure, especially because traffic accidents occur frequently on the highway between Waigaoqiao and Jiading. The frequent occurrence of traffic accidents is because a large volume of cargo is transferred to Jiading due to its geographic position. In addition, the possibility and feasibility of developing underground container transportation systems in Shanghai have been studied (Fan, Yu, & You, 2015). Taking Shanghai Waigaoqiao terminal as an example, a UCLS is established to relieve road congestion. Ground diversion is carried out, and the number of ground container trucks is reduced due to underground transportation. The UCLS consists of an underground guided vehicle (UGV), yard crane and container truck. This paper proposes that the system is divided into two parts: the transportation subsystem and terminal subsystem, as shown in Fig. 1. In the transportation subsystem, the underground tunnel is responsible for transporting containers by the UGV between Waigaoqiao terminal and Jiading Northwest Logistics Park. The terminal subsystem has an underground parking lot, which is divided into the waiting area and the loading or unloading area. The waiting area serves as a buffer area for UGVs that are waiting. The loading or unloading area is used to load or unload containers. Each loading or unloading point is provided with a fixed yard crane, which is depicted in Fig. 2. The rear yard and temporary storage area are shown in Fig. 2. The rear yard is set up in Waigaoqiao terminal and is used to store
Applying suitable matrix-analytic methods On-line control rules and simulation A beam search heuristics and a simulated annealing based search process
Journal of Mathematical Analysis and Applications European Journal of Operational Research Computers & Industrial Engineering Computers & Industrial Engineering
containers. The container truck is responsible for the horizontal transportation of containers, and the red equipment, called the yard crane, is responsible for handling containers between the container area and the container truck. The handling area is used to handle the exported containers from the UGV or the imported containers in the temporary storage area. The exported containers from the UGV will be put in the temporary storage area. The UCLS is operated using two-way transportation. The operating process is shown in Fig. 3.The process is explained as follows. (1) Imported containers are transported from various terminals of Waigaoqiao to the rear yard. (2) After the UGV reaches the loading area, the exported container is unloaded by the yard crane to the container truck waiting at the temporary storage area. (3) After the exported container on the UGV from Jiading Northwest Logistics Park is unloaded, the imported container on the container truck in the temporary storage area is loaded onto the UGV by the yard crane. (4) After the loading of the imported container, the UGV runs into the underground logistics tunnel, moving to the underground parking lot in Jiading Northwest Logistics Park. The underground logistics tunnel of the transportation subsystem mainly involves pipeline transportation and equipment self-control technology. The UGV runs at a constant speed in the underground logistics tunnel, so excluding the clogging of the underground logistics tunnel, the arrival time of the UGVs is fixed. As the UGVs arrive one after another in the handling area, the yard crane of the handling area needs to unload the containers on the UGV and put another container on the ground on the same UGV. During handling, more UGVs arrive, which will cause congestion and affect efficiency. Therefore, a parking lot is proposed in this paper. To avoid congestion and improve efficiency, the parking lot in the terminal subsystem needs to be designed; in addition, it is important to coordinate the handling time of yard cranes and the arrival time of UGVs in the UCLS. In this paper, by designing and optimizing the parking lot, a reasonable number of loading and unloading points and the arrival interval of the UGVs are calculated. Accordingly, yard cranes at the loading and unloading points can be operated effectively to reduce the residence time of the UGVs in the
Fig. 1. The composition of the underground container logistics system. 329
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Fig. 2. Schematic diagram of the rear yard of Waigaoqiao terminal.
underground system. The import and export operations of containers can also be completed efficiently and conveniently in place of having many container trucks driving on urban roads.
and unloading point, the second UGV runs into 3rd loading and unloading point, and the (s-1)th UGV runs into the sth loading and unloading point. If there is no spare loading and unloading point, the UGV needs to wait; otherwise, it enters the spare loading and unloading point. In addition, if there is no urgent container in the parking lot, the urgent container point can be used to handle other not urgent containers. However, as long as there are urgent containers, other UGVs with not urgent containers must leave. A twin-lift separated spreader is used in the yard crane. The operation process of the yard crane is shown in Fig. 6 and is explained as follows.
4. Design of the underground parking lot As a buffer, the underground parking lot is divided into two parts, a waiting area and a loading or unloading area, as shown in Fig. 4. The UGVs arrive at the parking lot from the underground logistics tunnel along the yellow arrow. Then, the UGVs come to the waiting area and the loading/unloading area one after another. Lastly, they leave the parking lot along the red arrow, and run into the tunnel. In the parking lot, the loading and unloading points are divided into one urgent container point and other not urgent container points. When an urgent container arrives at the parking lot, it will be handled at the urgent container point. If there is no urgent container in the parking lot, other not urgent containers can be handled at the urgent container point. In other words, the urgent container point is equal to other loading and unloading points under the circumstances that there is no urgent container in the parking lot. Fig. 5 describes the loading or unloading process in the parking lot. After completing the transportation in the underground logistics tunnel, the UGV runs into a waiting area with 12 parking lanes. The first UGV does not need to stay in the waiting area but instead directly runs into the loading or unloading area to unload the exported container, after which the yard crane puts the exported containers onto the ground and then continues to load imported containers. Finally, the UGV leaves the parking lot and returns to the transportation subsystem. The loading and unloading rules are as follows. Any urgent containers in the parking lot are handled at the urgent container point. For other not urgent containers, the first UGV runs directly into 2nd loading
(1) There are unloaded and loaded container trucks waiting on both sides of the yard crane. (2) When the UGV reaches the loading and unloading area, the double spreader descends to the underground. The exported container on the UGV is hoisted to the empty, unloaded container truck waiting on the ground. The container truck leaves after the exported container is loaded. (3) The twin-lift separated spreader hoists the imported container that is on the heavy loaded container truck and puts it onto the UGV in the underground. The UGV with the imported container enters the underground logistics tunnel. (4) The next cycle starts. To ensure that the UGVs in the waiting area do not become congested, it is necessary to minimize the waiting time of the UGVs. The queuing length of UGVs is closely related to the arrival interval of UGVs and the number of loading and unloading points. If the waiting time of UGVs is reduced, then the queuing length can be shortened. In general,
Fig. 3. Operation flow chart of underground container logistics system. 330
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Fig. 4. The layout of the underground parking lot.
the waiting time of UGVs can be reduced by increasing the number of loading and unloading points, but this increase will also add to the cost of the yard crane. Therefore, with the goal of minimizing the waiting cost of UGVs and the cost of yard cranes and achieving the optimal target value of the loading and unloading level, the MINP model is formulated in this paper.
5. Model formulation 5.1. Assumptions For the convenience of analysis, the queuing system is assumed to be in balance after running for a certain time. This paper mainly
Fig. 5. Loading and unloading diagram in the underground parking lot. 331
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Fig. 6. Flow diagram of loading and unloading by the yard crane.
discusses the properties of the balanced queue state, including the distribution of the queue length and waiting time. The following assumptions are made. Some equipment performance assumptions are based on reference to Shanghai Zhenhua Heavy Industries Co., Ltd. (ZPMC).
Table 2 The definitions of notations.
(1) All UGVs have the same capacity and shape and transport two TEUs at a time. (2) The efficiency of the yard crane at the loading and unloading points is consistent. (3) Special types of containers are not considered, such as those carrying dangerous or refrigerated goods. (4) In the handling process, the time before the yard crane releases a container and unloads the next container is neglected. (5) The number of containers transported in the two-way underground system is balanced. (6) The UGVs are in a single grouping. (7) The twin-lift separated spreader is used, and two TEUs are carried out at a time.
s
M D T µ v t d cy cw C
annual throughput of containers in the system total working days in one year total working time in one day average service rate of the yard crane speed of the UGV in the underground system arrival time of the urgent container (uc) maximum safe distance between two UGVs cost of yard cranes waiting cost of each UGV in a cycle total cost of yard cranes and waiting cost of UGVs infinite number
t 1) + znuc · cw · L ( , s )
(b) (c) (d) (e) (f) (g)
(2)
where s 1 n=0
service intensity in the parking lot average number of UGVs in the parking lot average number of UGVs queuing in the waiting area
s
average arrival rate of the UGV in the parking lot number of loading and unloading points in the parking lot
(n
s) n!
t yuc = 1, urgent container (uc) is handled at the
urgent container point at time t
z t = 1, not urgent container (nuc) is handled at the urgent container point at time t z t = 0, otherwise
system. Eq. (1) is the objective function. The UGVs arrive at the parking lot according to a Poisson process with arrival rate . The average arrival rate of UGVs is and is determined by the safe distances of UGVs d and the annual throughput of containers M in the system, which is formulated in Eqs. (2a) and (2b). All urgent containers account for 5 percent of annual container throughput in Eq. (2c). Eq. (2d) represents the fact that urgent containers are handled at the urgent container point; otherwise, the not urgent containers are handled at the urgent container point at time t. When an urgent container is handled at the urgent container point, the average number of UGVs in the parking lot is indicated as L ( , s 1) . If the urgent container point is used to handle a not urgent container, then the average number of UGVs at all loading and unloading points in the parking lot is shown as Eq. (3).
(1)
(a)
L ( , s ) = Lq + s + p0
L Lq
t yuc = 0, otherwise
s. t.
0 Z
Parameters
t znuc
(2) The MINP model
2T
set of integers
t yuc
t min C ( , s ) = c y ·s + yuc ·c w ·L ( , s
T y t = 0.05M t = 0 uc t t yuc + z nuc =1 t t yuc , znuc (0, 1)
Z
Decision variables
The definitions of notations in the mathematical model are shown in Table 2. Some parameters of the queuing theory are from the Operations Research Course (Hu & Guo, 2007).
M D
Set
Other variables
(1) Notation definitions
d
Definition
N
5.2. Model description
v
Notations
n
5.3. Deriving function L( , s )
(3)
In the underground container logistics system, increasing the number of loading and unloading points can reduce the waiting cost of UGVs queuing in the parking lot, but it will also increase the cost of yard cranes. When UGVs queue in the waiting area of the parking lot, they will incur some cost. In this paper, the waiting cost of UGVs is used to control the queuing time of UGVs, and the cost increases as the queuing time become longer. The goal of optimization is to minimize the total cost of yard cranes and the waiting cost of UGVs queuing in the
In addition, the UGVs arrive at the parking lot in batches, and the number of UGVs per batch is a random variable X, the probability distribution of which is P(X = i) = xi (i = 0, 1, 2, …, m), where m is the maximum number of UGVs being handled at one point, and m is a positive integer. The service rate of one loading and unloading point is denoted by µm . The number of loading and unloading points in the parking lot is s, and each point can handle m UGVs at most. That is, (m s) is the total number of UGVs that can be handled at all loading and 332
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unloading points. The handling time at each loading and unloading point in the parking lot is independent. The serving rule is first come first served (FCFS). When a new UGV arrives at the parking lot, and all loading and unloading points are busy, the new UGV waits in the waiting area; otherwise the new UGV runs into the point with the lowest number of UGVs available. The number of UGVs that are serviced in the loading and unloading points is denoted by nj (j = 1, 2, …, s), 0 ≤ nj ≤ m, and the total number of UGVs in the parking lot is n, including the UGVs waiting in the waiting area. The state transition equation of the parking lot system is discussed in three cases. The first one, n ＞ m s, (n is the number of UGVs in the parking lot, and m s is the number of UGVs that can be handled at all points), means there are s loading and unloading points that are busy in the parking lot. Each UGV that arrives runs into the waiting queue. When one point finishes the loading and unloading of containers on one UGV, another UGV waiting in the queue can run into the point to be served. The probability of the steady state is indicated by pn = P(N = n) (n = 0, 1, 2, …), and the state transition equation is formulated as Eq. (4).
pn
n
pn =
p0 =
j=1
1
p (n1, …, nj
1, …, ns ) + j Js Jo
= p (n1, …, n jmin + 1, …, ns ) +
µnj p (n1, …, nj
=
n > ms : pn n = ms : n < ms : +
m ns = 0
…
K p n = ms + 1 n
p(ms)j
j Js Jm
1
(5)
s)
(K
s + 1)
s)
K s+1 s
2 [1
,
)
1
(1
s (K
p0
,
s
1
s
=1
s )(K
s )(K
s + 1)
K
(n
s ) pn =
(9)
s + 1)
K s ], s
,
n=s
K
npn
s 1 n= 0
s
1
s
=1
(10)
K
s n=s
pn =
n=s
s 1
npn
n= 0
npn
s 1
pn = L s 1
L ( , s ) = Lq + s + p0 n= 0
(n
s ) pn
n=0
(n
s) n!
s
(11)
n
(12)
Based on the multi-server queuing optimization model, the average queuing length Lq and average length L ( , s ) are used to assess the congestion in the parking lot. As the number of loading and unloading points increases, the average queuing length will be reduced. Then, it is essential to minimize the total cost of yard cranes and the waiting cost of UGVs queuing in the parking lot. 6. Case study 6.1. Numerical simulation In the underground container transportation system, there are some loading and unloading points for handling containers in the underground parking lot. To minimize the total cost and meet the container throughput requirement, it is essential to calculate the number of loading and unloading points. Of all points, there is one point for handling urgent containers. If the urgent container point is not busy, there are s points for handling other containers. Given different values of s, it is possible to calculate the average number of UGVs in the parking lot. To obtain the smallest number of UGVs in the parking lot, the waiting cost of each UGV is set to one million and waiting costs are calculated. Then, the cost of yard cranes and the waiting costs of UGVs are obtained. If the total cost C is minimized, then the iterative algorithm ends. The flowchart of the algorithm to solve the MNIP model is given in Fig. 7. On the basis of the models described above, the results obtained by MATLAB are shown in Fig. 8 and Table 2. According to the actual situation in Waigaoqiao terminal, its annual throughput of containers was 18.2175 million TEU in 2015. The container throughput in the underground container logistics system assumed by this paper is 4
=1
1, …, ns )
s
s!
s ! (1
s ) pn
s 1
1, …, ns ), n < ms
µnj p (n1, …, nj
s ! (1
n=s
µnj + 1 p (n1, …, nj + 1, …, ns ) j Js Jm
+
1
K s+ 1 ) s
s (1
K
1, …, ns )
= p (n1, …, n jmin + 1, …, ns ) +
s 1 n n=0 n !
(n
Lq =
+ sµm pms + 1 = ( + sµm ) pms
p (n1, …, nj
(8)
To calculate the average length L ( , s ) in the parking lot, the average queuing length Lq is derived in Eqs. (11) and (12).
+ sµm pn + 1 = ( + s ) pn
1 s j=1
j Js Jo
p (n1, …, ns ) +
n
2s !
The maximum capacity of the underground parking lot is K. The average arrival rate must be less than the average service rate µ , that is to say, the service intensity is = ( / µ) < 1. Only in this way can the queuing system in the parking lot remain in balance. When the system reaches equilibrium, the probability distribution of a stable system pn can be computed on the basis of formulation (7). m n2 = 0
(
+
p0 s s
(6)
m n1= 0
ms
s 1 n n=0 n !
n=s
µnj + 1 p (n1, …, nj + 1, …, ns )
j Js Jm
n < ms
K
The third one, n < m s, means there are no UGVs waiting in the parking lot. When a new UGV arrives at the parking lot, it will run into the loading and unloading area that has the fewest UGVs. If there is more than one loading and unloading point with the fewest UGVs, the points with the smaller number of UGVs will be chosen. The number of loading and unloading points with the fewest UGVs is denoted by jmin . The set of points at which the number of UGVs nj = 0 is represented as J0 , the set of points with the number of UGVs (nj = m ) is Jm , and the set of points with the number of UGVs (0 < nj < m ) is Js . If one more UGV arrives at the parking lot, it will be serviced by loading and unloading point jmin , and the system state will be (n1, …, n jmin + 1, …, ns ). If one UGV has been serviced at the point j Js Jm , the system state will be (n1, …, ni 1, …, ns ), where nj 1 = min{n1, …, ni 1, …, ns} . The state transition equation is indicated in Eq. (6). j Js Jm
p , s ! sn s 0
Lq =
s
+ sµm pms + 1 = ( + sµm ) pms , n = ms
0
n
The average queuing length Lq is given in Eq. (10).
The second one, n = m s, means that all loading and unloading points are busy, but there is no queuing in the parking lot. If a new UGV arrives at the parking lot, it will queue in the waiting area. When a UGV has completed service, the number of UGVs at the loading and unloading points will be reduced. The state transition equation is shown in Eq. (5).
p(ms)j
p , n! 0
where the idle probability in the parking lot p0 is represented as Eq. (9). The service rate of all loading and unloading points is denoted as Z. s = /sµm , s
(4)
+ sµm pn + 1 = ( + sµm ) pn , n > ms
1
Taking the three cases described above into consideration, when the parking lot reaches balance, the average numbers of UGVs running into the system is equal to that of UGVs running out the system. Then, the probability distribution of stable system can be obtained in Eq. (8).
(7) 333
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Fig. 7. The flowchart of the algorithm.
million TEU. The speed of UGVs is 13.5 m/s, and their safe distance is at least 70 m, as specified by the Mole Company in the UK. The maximum capacity of the underground parking lot is assumed to be 100 in this case. The probability distribution of service time for yard cranes is close to the logarithmic normal distribution, and the service time of yard cranes changes between 20 and 30 TEU each hour. Additionally, the service time has 10 TEU each hour up and down (Zhang, 2007). The cost of each yard crane is 10 million. For each UGV waiting in the parking lot, it will lose 1 million. When the number of loading and unloading points generated is ranged from 1 to 100, the number of loading and unloading points set in order to achieve the minimum cost and meet the container throughput requirement is 24. As shown in Table 3, the arrival interval of UGVs is approximately 16 s, and the number of loading and unloading points is 24. That is, a UGV arrives at the parking lot every 16 s, and 24 yard cranes are provided in the handling area on the ground, which are used to load or
unload the containers on the UGVs. In this case, the average queue length of the UGVs is 23.8522, and the average waiting length of the UGVs is 0.9006, which means there is almost no queuing in the parking lot. The average stay time of UGVs in the underground parking lot is 375 s. When 24 points are set for 4 million containers in the UCLS, the minimum total cost is 255.5861 million. Without the parking lot, all UGVs will queue in the underground tunnel. This situation would cause congestion in the underground transportation system. Thus, the presence of a parking lot is essential to provide space as a buffer for waiting UGVs. According to the solution, it can be found that in order to meet the requirement of 4 million container throughputs, the arrival interval of the UGVs is 15.6852, which is the maximum capacity. In other words, under the circumstances of 4 million containers, setting 24 loading and unloading points is the optimal solution for the purpose of minimizing yard crane cost and UGV waiting numbers. A metaheuristics approach, such as genetic algorithm (Gen, Cheng, & Lin, 2008) can be considered to solve the MINP model and compare with the computational results in this paper. 6.2. Sensitivity analysis In the above example, the UGV arrival interval is set to 15.6852 s in order to satisfy the container throughput of 4 million. Moreover, the cost of loading and unloading points and the waiting cost of the UGVs are minimized. However, taking the actual data of Waigaoqiao terminal into account, the cost of 24 yard cranes is substantial and difficult to be accepted. In this section, different container throughputs are given to analyse the relationship between the minimum cost and container
Fig. 8. The trend of total cost. 334
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Table 3 Results with 4 million TEU container throughputs in the underground system. Name
Total cost Min C (million)
Number of loading or unloading points s
Average arrival rate of the UGV λ
Average number of UGVs in the parking lot L
Average number of UGVs in the waiting area Lq
Arrival interval t
Value
263.8522
24
0.0637
23.8522
0.9006
15.6852
configuration required in the underground parking lot. As the container throughput changes, the arrival rates of UGVs vary correspondingly. The four average queuing lengths are related to the number of loading and unloading points. To adapt to container terminals of different scales, the different configurations required for the parking lot in the UCLS are found at minimum total cost.
throughputs. Four different values of container throughput in the underground container transportation system are set, and the average arrival rates change accordingly. Under the circumstances, given different values for s, the average number of UGVs in the parking lot and the total cost are calculated. If the total cost is minimized, the iterative algorithm ends. Otherwise, the algorithm continues to use another number of loading and unloading points to calculate the total cost. Then, the minimized total cost and number of points can be obtained for different container throughputs. Four different results solved via MATLAB on the basis of the mathematical model described above are shown in Table 4. Among these four cases, the number of loading and unloading points and average rate of UGVs are the optimal solutions. According to the average number of UGVs in the waiting area, it can be found that there are almost no UGVs waiting in the system. The decrease in container throughputs can decrease the average arrival rate of UGVs. In addition, the total cost and average number of UGVs in the parking lot are obtained. For the purpose of finding the minimum total cost, when there are one million TEU containers in the underground system, the number of loading and unloading points is 7, and the average arrival rate of UGVs is 0.0159. Moreover, the average number of UGVs in the waiting area is 0.5620, which is equivalent to no congestion in the parking lot. Then, the better combination of container throughput and minimized cost can be chosen according to different requirements. It can be seen from Table 4 that the total cost of the UCLS decreases with an increase in the UGV arrival interval. As the UGV arrival interval increases, the container throughput in the system is decreased, and the number of loading and unloading points decreases accordingly. In other words, the container throughput determines the arrival interval of the UGVs, while the number of loading and unloading points determines the strength of loading and unloading. There is no doubt that the service rate of the yard cranes must be larger than the arrival rate of the UGVs. It is essential that the transportation subsystem and terminal subsystem maintain a balance to avoid congestion in the underground parking lot. On the basis of the sensitivity analysis, different container throughputs are assumed in the underground container transportation system. The number of loading and unloading points is calculated by an iterative algorithm for the purpose of finding the minimum total cost. Different container throughputs determine the average arrival rate of UGVs, and the number of loading and unloading points is related to the cost of yard cranes and the waiting cost of UGVs in the parking lot. For each container throughput given, the average arrival rate of UGVs and the number of loading/unloading points in the underground parking lot can be found. Then, the total cost of yard cranes and the waiting cost of UGVs are minimized, and there is no congestion in the underground container transportation system. Four different container throughputs given are to analyse the
6.3. Simulation In this section, a simulation is carried out to analyse the influence of average arrival rate and number of points. The yard cranes and UGVs are chosen as simulation objects, and the operations of UGVs arriving and yard cranes handling containers are simulated in Tecnomatix Plant Simulation 13.0 software. In the simulation, four different numbers of loading and unloading points are given, and the average arrival rate is changed to obtain the lowest average queuing length of UGVs in the parking lot. If the average queuing length has no significant changes, then the average arrival rate is the optimal value. Then, the total cost and container throughputs that can be handled in the UCLS are counted. In the simulation, the efficiency of yard cranes at the loading and unloading points follows the logarithmic normal distribution, with a mean of 145 and a square of variance of 90. The arrival rate λ ranges from 15 s to 30 s, and the number of handling points is set between 7 and 10, according to the results of the sensitivity analysis above. Four experiments are simulated, and the simulation time is 365 days. The results of the experiments are obtained by counting the average queuing length of each loading and unloading point and including the container throughput. The four experiments with different arrival rates and numbers of loading and unloading points are shown in Fig. 9. From the simulation experiments, it can be observed that the average queuing length no longer changes significantly, when the arrival rate reaches a certain value. With 7 loading and unloading points, the arrival rate is set to 0.0345, and the average queuing length in the parking lot is one. In other words, the arrival interval of UGVs is 29 s. The underground transportation system can be considered to be in balance and to have no congestion. Similarly, when there are 8 loading and unloading points, the arrival interval is 26 s and there is nearly no queuing in the parking lot. The number of loading and unloading points is 9, and the arrival interval is 23 s. When the number of loading and unloading points is 10, the arrival interval is 20 s, and the queuing length of each loading and unloading point is one. The container throughputs being handled at different points in the underground container logistics system are listed in Table 5. The experimental results illustrate that the combination of the number of loading and unloading points and the average arrival rate, that lead to the UCLS having no congestion and to the system keeping in balance. With regard to Exp 4, where there are 10 loading and
Table 4 Data for the underground container system with different container throughputs. Number
Container throughputs (million TEU)
Total cost Min c (million)
Number of loading or unloading points s
Average arrival rate of the UGV λ
Average number of UGVs in the parking lot L
Average number of UGVs in the waiting area Lq
1 2 3 4
4 3 2 1
263.8522 198.2654 133.0869 76.2776
24 18 12 7
0.0637 0.0477 0.0318 0.0159
23.8522 18.2654 13.0869 6.2776
0.9006 1.1105 1.6529 0.5620
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Fig. 9. Average queuing length with different arrival rates at different loading and unloading points.
UCLS can handle 1.58 million TEU. In other words, the container transportation system can complete 8.67% of the annual container throughput in Waigaoqiao terminal in 2015 (18.2175 million TEU). Even though the amount of container throughput being diverged is small, the UCLS is helpful in that it relieves the pressure of ground transportation and the environmental problems caused by traffic. However, the arrival rate of UGVs in the simulation is based on unlimited sources in the underground parking lot, and the total number of UGVs is not considered in this paper. It remains to be researched further.
Table 5 Container throughputs of different loading and unloading points with minimum average queuing length.
Exp Exp Exp Exp
1 2 3 4
Number of loading and unloading points s
Container throughput (million TEU)
Average arrival rate λ
Average queuing length Lq
7 8 9 10
1.09 1.2 1.37 1.58
0.0345 0.0385 0.0435 0.0500
1.00 0.88 0.78 0.80
Acknowledgements
unloading points in the underground parking lot, and the average arrival interval of UGVs is set to 20 s, the UCLS can handle 1.58 million containers. Moreover, the average queuing length in the parking lot is one. That is, there is no congestion in the underground system.
This work was supported by the National Natural Science Foundation of China (71602114, 71631007), Shanghai Science & Technology Committee Research Project (16040501500, 17595810300).
7. Conclusions
Appendix A. Supplementary material
To relieve traffic jams caused by container trucks, an UCLS is proposed, and an underground parking lot within this system is designed. Aiming at minimizing the overall cost of loading and unloading points and the waiting cost of UGVs in the cycle, a multi-service queuing optimization model is established. When the annual container throughput is four million TEU, the arrival interval of the UGVs is approximately 15.6 s, the number of loading and unloading points is 24, and the minimum cost is 263.8522 million. However, considering the actual data of Waigaoqiao terminal, the number of loading and unloading points needs to be reduced. By setting different container throughputs, on the precondition of minimizing the overall cost, the number of loading and unloading points varies. When the container throughput is only one million TEU, only 7 loading and unloading points are needed. Finally, the goal of the simulation is to provide a comparison of the average queue lengths in the waiting area upon changing the arrival interval of the UGVs. It can be found that when the interval is 20 s, the average queuing length in the parking lot is 0.80. Therefore, it can be concluded that when there are 10 loading and unloading points and the arrival interval of UGVs is set to 20 s, the
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Design and optimization of parking lot in an underground container logistics system
T
Yinping Gaoa, , Daofang Changa, Ting Fangb, Tian Luob ⁎
a b
Institute of Logistics Science and Engineering, Shanghai Maritime University, 1550 Haigang Avenue in Pudong New Area, Shanghai, China School of Economics & Management, Shanghai Maritime University, 1550 Haigang Avenue in Pudong New Area, Shanghai, China
ARTICLE INFO
ABSTRACT
Keywords: Underground container logistics system Underground parking lot Design Optimization Simulation
To relieve the ground traffic pressure caused by container trucks in a port, an underground container logistics system (UCLS) between Shanghai Waigaoqiao Terminal and Jiading Northwest Logistics Park is proposed. Furthermore, in order to guarantee the connection between the UCLS and the yard behind the ground terminal, a design of an underground parking lot in the system is also proposed. The underground parking lot is a buffer used for the loading and unloading of underground guided vehicles (UGVs). A mixed integer nonlinear programming model (MNIP) for UGVs and yard cranes in the underground system is formulated to minimize the total cost of UGVs waiting and yard cranes. Then, the optimization model is solved via MATLAB software. With sensitivity analysis, the number of loading and unloading points in the underground parking lot is optimized for the purpose of minimizing the total cost. Finally, a simulation experiment is carried out to obtain the optimal configuration of the number of loading and unloading points and the arrival rate in the UCLS.
1. Introduction At present, city logistics systems are faced with the following three problems. First, serious traffic congestion and frequent traffic accidents are caused by growing traffic volume, which seriously constrains the accessibility and quality of urban freight. Second, environmental problems, such as noise and air pollution, caused by the city logistics system are also contrary to the principles of highly efficient, low-cost and environmentally friendly sustainable development. Third, in order to solve the urban congestion problem, expanding the existing transportation infrastructure faces high land costs, limited space resources, and cultural heritage protection. The available space on the ground is rapidly being used up, and the largest danger is that built-up spaces are taking over the public green spaces of cities, thereby threatening live ability and quality of life (Admiraal & Cornaro, 2016). Urban living standards are lower in Russia than those in other developed countries. Gamayunova and Gumerova (2016) attempted to utilize underground spaces to solve urban development challenges, so they analysed underground space utilization and transportation infrastructure. Therefore, some researchers have diverted attention to underground space utilization and proposed some programmes that can achieve underground transportation. An underground transport and supply system named the Cargo Cap by researchers at Ruhr University in Germany, was defined as the future of the fifth category of transportation systems. ⁎
It was the combination of the underground logistics system and urban transport, taking full advantage of the varieties of facilities in the urban underground rail system to carry out underground logistics and distribution (Liu, 1999). Underground logistics, also known as an underground freight system, refers to complete freight transportation with automatic guided vehicles, dual-use trucks, and other carrying tools, through large diameter underground pipelines (Montgomery & Fairfax, 2006). In fact, there have been cases of underground space utilization for many years. For example, in 1853, the urban pipeline postal system was established in London, and it was the earliest underground logistics system in the world (Stein, Stein, Beckmann, & Schoesser, 2005). In 1927, the automatic two-track transportation system, which was the first underground logistics system in the world to connect all places in a city, was established in Britain. Amsterdam had the largest flower supply market in the world. To transport flowers safely and rapidly, a professional underground logistics system was established between the airport and the flower market. Zevgolis, Mavrikos, and Kaliampakos (2004) focused on the design of an underground warehousing-logistics centre (WLC) in the extensive metropolitan area of Athens. The layout, storage capacity and operational issues of underground WLC were thoroughly examined. A new approach regarding municipal waste collection and transport involves the installation of an underground pipe network and storage containers, called automated vacuum waste
Corresponding author. E-mail addresses: [email protected] (Y. Gao), [email protected] (D. Chang).
https://doi.org/10.1016/j.cie.2019.02.043
Available online 26 February 2019 0360-8352/ © 2019 Elsevier Ltd. All rights reserved.
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collection (AVAC). This system can minimize operating costs for waste handling and reduce the number of waste collection trips required, a feature that positively influences traffic congestion and minimizes CO2 emissions while also potentially saving space (Nakou, Benardos, & Kaliampakos, 2014). Qiao and Peng (2016) presented a case study on urban underground space (UUS) use such as Hongqiao Central Business District (CBD) and the Lujiazui Business District in Shanghai, China. At the end of June 2013, there were 60 locations below ground in the Lujiazui Business District, including facilities such as underground transportation, underground public infrastructure and underground municipal infrastructure. For the purpose of relieving urban container truck transportation pressure, this paper proposes an UCLS for container terminals. The UCLS is divided into two parts: the underground transportation subsystem and the terminal subsystem. In this paper, the concept of an underground parking lot located in the terminal subsystem is proposed. The parking lot in this paper is designed to allow underground guided vehicles (UGVs) to wait and handle in a queue as a buffer. The specific operation line of the underground parking lot is designed and optimized. Therefore, the container terminal and its underground system can be connected perfectly to improve efficiency and maximize value. The remainder of this paper is organized as follows. Section 2 gives a brief review of the related literature. The UCLS, consisting of the transportation subsystem and the terminal subsystem, is described in Section 3, and the system operation flow is explained. The underground parking lot, its waiting area, and its loading and unloading area are introduced in Section 4. The mixed integer nonlinear programming model (MINP) is formulated in Section 5 with the goal of minimizing the waiting cost of UGVs and the cost of yard cranes. The case study, including solutions and sensitivity analysis performed via MATLAB and the simulation conducted with Tecnomatix Plant Simulation 13.0 are provided in Section 6. The conclusions are given in Section 7.
infrastructure, Rogers et al. (2012) suggested that the costs of the lifecycle and the contribution to sustainable urban development were to be considered when making comprehensive strategic plans. Kaliampakos, Benardos, and Mavrikos (2016) suggested that efficient urban infrastructure development in modern cities would utilize underground space systems. The economic efficiency of underground space utilization was the key element that decided whether underground infrastructures were better than traditional ones. In general, there have been many papers focusing on underground space utilization, including the prospect and function of underground logistics, feasibility reports and underground space planning in large cities. It is noted that container transportation becomes the main development mode of underground logistics. As integral parts of multimodal transportation systems, UCLSs complete point-to-point transportation from one terminal to another (Jia, 2011). Until now, however, UCLSs are still in the conceptual design stage, and there is no built design prototype or demonstration. Therefore, this paper designs a parking lot in an UCLS to connect underground transportation and ground handling. However, the concept of a parking lot in an UCLS is new. This paper discusses the queuing in the parking lot in order to avoid congestion. Lee, Wong, and Li (2015) developed a real-time estimation approach for lane-based queue lengths. Based on detector information at isolated signalized junctions, the number of queued vehicles in each lane is determined. Giorno, Nobile, and Pirozzi (2018) considered the Markovian single-server queueing model with Poisson arrivals and statedependent service rates, characterized by a logarithmic steady-state distribution. Baumann and Sandmann (2017) provided an exact computational analysis of various steady-state performance measures, such as loss and blocking probabilities, expectations and moments of higher numbers of customers in the queues and in the whole system by modelling the multi-server tandem queue as a level-dependent quasi-birthand-death process and applying suitable matrix-analytic methods. In this paper, the queuing length of each loading and unloading point in the parking lot will be counted to find the optimal solutions. Similarly, in a new design for a bi-directional AGV system, in which two AGVs can exchange their loads, their scheduled transportation tasks, and even their vehicle numbers when they move in opposite directions, Hsueh (2010) proposed an off-line mathematical model and carried out a series of simulation experiments. Furthermore, Hsueh confirmed that the new system performs efficiently and robustly. Legato, Mazza, and Gullì (2014) integrated two separate models into a simulation–optimization framework for the berth allocation problem arising in maritime container terminals, which refers to a mathematical programming model at the tactical level and a simulation model at the operational level. Specifically, the framework uses a beam search heuristic to obtain a weekly plan at the tactical level, followed by a simulated annealingbased search process to adjust allocation decisions at the operational level. The main studies reviewed in this paper are summarized in Table 1. Therefore, with regard to the new concept of a parking lot in UCLS, the area map for the UCLS and the model of UGVs and yard cranes are included. In addition, the mathematical model of MINP and operational simulation are given in this paper.
2. Literature reviews There have been many papers about underground logistics. Underground logistics was divided into three styles according to different modes of transportation, including the pneumatic capsule pipeline (PCP), the hydraulic capsule pipeline (HCP), and the electricitydriven transportation tunnel. The PCP and HCP choose air and water as their respective conveyance medium, and the cabin as a cargo tool to transport goods. The feasibility of the PCP system in New York Harbour and New Jersey was studied by Prof. Henry Liu (2009) in the United States. A linear motor-driven PCP system was able to handle 4.1 million TEUs in the ports of New York and New Jersey. There are three main means of electricity-driven transportation: automated guided vehicles (AGVs) in Holland, Cargocap in Germany and dual mode trucks (DMT) in Japan. In addition, the advantages of underground logistics have been proposed, and underground logistics can be used as a solution to urban traffic problems. The feasibility and problems of urban subway freight transportation have been analysed. Chen, Dong, and Ren (2017) analysed the macro-environment of underground logistics systems in China and identified their unique advantages. The present situation, problems and trends of underground logistics were described in relation to the characteristics of the large-scale and rapid development of underground space in China (Qian, 2016). Four kinds of usage trends of underground space in the future were put forward, the first being the comprehensive planning, construction and management of the underground space in Beijing CBD, Shanghai World Expo and the southern part of Ningbo, the second being an urban underground complex with an integrated transport hub as its centre, as in the cases of the Hongqiao Transport Hub and the Beijing South Railway Station, the third being the development of underground subways, roads and logistics systems, and the fourth being the scientific utilization of underground water storage spaces and aeration to create a “sponge city”. To maximize the efficiency of the underground
3. Problem description The container throughput in ports has great potential. The container throughput in Shanghai Waigaoqiao terminal was 16.2205 million TEU in 2013, 17.1641 million TEU in 2014, and 18.2175 million TEU in 2015. During the 13th Five-Year Plan period, the container throughput in Shanghai port is expected to reach 42 million TEU. Moreover, frequent import and export trade stimulates the international maritime shipping industry. At the same time, port congestion has also increased and has become a global problem. Especially for container trade transportation, freight costs and capacity are increasing. The growing 328
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Table 1 The main studies listed in this paper. Authors (year)
Mathematical model
Methodology
Journal Publisher or Proceeding
Lee et al. (2015)
Discriminant model
Transportation Research Part C
Giorno et al. (2018)
An adaptive single-server queuing model
Data processing method for the real-time estimation of lane-based queue lengths Queuing theory
Baumann and Sandmann (2017) Hsueh (2010) Legato et al. (2014)
Modelling the multi-server tandem queue as a leveldependent quasi-birth-and-death process An off-line mathematical model A mathematical programming model at the tactical level and a simulation model at the operational level
container throughput is bound to cause congestion in the collection and distribution system of Waigaoqiao terminal. To avoid and solve the problem of ground traffic congestion caused by container trucks, various proposals were put forward, including constructing more railway, highway and water transportation lines, and even expanding the dock infrastructure. However, the implementation of these programmes requires more land area, and urban land is very expensive. Expanding public infrastructure is in conflict with the limitations of space resources. In the long term, the increasing container throughput, the limited land resources, the high cost of land, and the pressure of container truck transportation congestion all promotes the utilization of underground resources. Accordingly, an underground logistics system is put forward to relieve ground traffic pressure. The underground logistics system can achieve the goals of relieving traffic pressure, reducing environmental pollutions and improving logistics efficiency. The increasing container throughput in Shanghai Waigaoqiao terminal has generated much traffic pressure, especially because traffic accidents occur frequently on the highway between Waigaoqiao and Jiading. The frequent occurrence of traffic accidents is because a large volume of cargo is transferred to Jiading due to its geographic position. In addition, the possibility and feasibility of developing underground container transportation systems in Shanghai have been studied (Fan, Yu, & You, 2015). Taking Shanghai Waigaoqiao terminal as an example, a UCLS is established to relieve road congestion. Ground diversion is carried out, and the number of ground container trucks is reduced due to underground transportation. The UCLS consists of an underground guided vehicle (UGV), yard crane and container truck. This paper proposes that the system is divided into two parts: the transportation subsystem and terminal subsystem, as shown in Fig. 1. In the transportation subsystem, the underground tunnel is responsible for transporting containers by the UGV between Waigaoqiao terminal and Jiading Northwest Logistics Park. The terminal subsystem has an underground parking lot, which is divided into the waiting area and the loading or unloading area. The waiting area serves as a buffer area for UGVs that are waiting. The loading or unloading area is used to load or unload containers. Each loading or unloading point is provided with a fixed yard crane, which is depicted in Fig. 2. The rear yard and temporary storage area are shown in Fig. 2. The rear yard is set up in Waigaoqiao terminal and is used to store
Applying suitable matrix-analytic methods On-line control rules and simulation A beam search heuristics and a simulated annealing based search process
Journal of Mathematical Analysis and Applications European Journal of Operational Research Computers & Industrial Engineering Computers & Industrial Engineering
containers. The container truck is responsible for the horizontal transportation of containers, and the red equipment, called the yard crane, is responsible for handling containers between the container area and the container truck. The handling area is used to handle the exported containers from the UGV or the imported containers in the temporary storage area. The exported containers from the UGV will be put in the temporary storage area. The UCLS is operated using two-way transportation. The operating process is shown in Fig. 3.The process is explained as follows. (1) Imported containers are transported from various terminals of Waigaoqiao to the rear yard. (2) After the UGV reaches the loading area, the exported container is unloaded by the yard crane to the container truck waiting at the temporary storage area. (3) After the exported container on the UGV from Jiading Northwest Logistics Park is unloaded, the imported container on the container truck in the temporary storage area is loaded onto the UGV by the yard crane. (4) After the loading of the imported container, the UGV runs into the underground logistics tunnel, moving to the underground parking lot in Jiading Northwest Logistics Park. The underground logistics tunnel of the transportation subsystem mainly involves pipeline transportation and equipment self-control technology. The UGV runs at a constant speed in the underground logistics tunnel, so excluding the clogging of the underground logistics tunnel, the arrival time of the UGVs is fixed. As the UGVs arrive one after another in the handling area, the yard crane of the handling area needs to unload the containers on the UGV and put another container on the ground on the same UGV. During handling, more UGVs arrive, which will cause congestion and affect efficiency. Therefore, a parking lot is proposed in this paper. To avoid congestion and improve efficiency, the parking lot in the terminal subsystem needs to be designed; in addition, it is important to coordinate the handling time of yard cranes and the arrival time of UGVs in the UCLS. In this paper, by designing and optimizing the parking lot, a reasonable number of loading and unloading points and the arrival interval of the UGVs are calculated. Accordingly, yard cranes at the loading and unloading points can be operated effectively to reduce the residence time of the UGVs in the
Fig. 1. The composition of the underground container logistics system. 329
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Fig. 2. Schematic diagram of the rear yard of Waigaoqiao terminal.
underground system. The import and export operations of containers can also be completed efficiently and conveniently in place of having many container trucks driving on urban roads.
and unloading point, the second UGV runs into 3rd loading and unloading point, and the (s-1)th UGV runs into the sth loading and unloading point. If there is no spare loading and unloading point, the UGV needs to wait; otherwise, it enters the spare loading and unloading point. In addition, if there is no urgent container in the parking lot, the urgent container point can be used to handle other not urgent containers. However, as long as there are urgent containers, other UGVs with not urgent containers must leave. A twin-lift separated spreader is used in the yard crane. The operation process of the yard crane is shown in Fig. 6 and is explained as follows.
4. Design of the underground parking lot As a buffer, the underground parking lot is divided into two parts, a waiting area and a loading or unloading area, as shown in Fig. 4. The UGVs arrive at the parking lot from the underground logistics tunnel along the yellow arrow. Then, the UGVs come to the waiting area and the loading/unloading area one after another. Lastly, they leave the parking lot along the red arrow, and run into the tunnel. In the parking lot, the loading and unloading points are divided into one urgent container point and other not urgent container points. When an urgent container arrives at the parking lot, it will be handled at the urgent container point. If there is no urgent container in the parking lot, other not urgent containers can be handled at the urgent container point. In other words, the urgent container point is equal to other loading and unloading points under the circumstances that there is no urgent container in the parking lot. Fig. 5 describes the loading or unloading process in the parking lot. After completing the transportation in the underground logistics tunnel, the UGV runs into a waiting area with 12 parking lanes. The first UGV does not need to stay in the waiting area but instead directly runs into the loading or unloading area to unload the exported container, after which the yard crane puts the exported containers onto the ground and then continues to load imported containers. Finally, the UGV leaves the parking lot and returns to the transportation subsystem. The loading and unloading rules are as follows. Any urgent containers in the parking lot are handled at the urgent container point. For other not urgent containers, the first UGV runs directly into 2nd loading
(1) There are unloaded and loaded container trucks waiting on both sides of the yard crane. (2) When the UGV reaches the loading and unloading area, the double spreader descends to the underground. The exported container on the UGV is hoisted to the empty, unloaded container truck waiting on the ground. The container truck leaves after the exported container is loaded. (3) The twin-lift separated spreader hoists the imported container that is on the heavy loaded container truck and puts it onto the UGV in the underground. The UGV with the imported container enters the underground logistics tunnel. (4) The next cycle starts. To ensure that the UGVs in the waiting area do not become congested, it is necessary to minimize the waiting time of the UGVs. The queuing length of UGVs is closely related to the arrival interval of UGVs and the number of loading and unloading points. If the waiting time of UGVs is reduced, then the queuing length can be shortened. In general,
Fig. 3. Operation flow chart of underground container logistics system. 330
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Fig. 4. The layout of the underground parking lot.
the waiting time of UGVs can be reduced by increasing the number of loading and unloading points, but this increase will also add to the cost of the yard crane. Therefore, with the goal of minimizing the waiting cost of UGVs and the cost of yard cranes and achieving the optimal target value of the loading and unloading level, the MINP model is formulated in this paper.
5. Model formulation 5.1. Assumptions For the convenience of analysis, the queuing system is assumed to be in balance after running for a certain time. This paper mainly
Fig. 5. Loading and unloading diagram in the underground parking lot. 331
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Fig. 6. Flow diagram of loading and unloading by the yard crane.
discusses the properties of the balanced queue state, including the distribution of the queue length and waiting time. The following assumptions are made. Some equipment performance assumptions are based on reference to Shanghai Zhenhua Heavy Industries Co., Ltd. (ZPMC).
Table 2 The definitions of notations.
(1) All UGVs have the same capacity and shape and transport two TEUs at a time. (2) The efficiency of the yard crane at the loading and unloading points is consistent. (3) Special types of containers are not considered, such as those carrying dangerous or refrigerated goods. (4) In the handling process, the time before the yard crane releases a container and unloads the next container is neglected. (5) The number of containers transported in the two-way underground system is balanced. (6) The UGVs are in a single grouping. (7) The twin-lift separated spreader is used, and two TEUs are carried out at a time.
s
M D T µ v t d cy cw C
annual throughput of containers in the system total working days in one year total working time in one day average service rate of the yard crane speed of the UGV in the underground system arrival time of the urgent container (uc) maximum safe distance between two UGVs cost of yard cranes waiting cost of each UGV in a cycle total cost of yard cranes and waiting cost of UGVs infinite number
t 1) + znuc · cw · L ( , s )
(b) (c) (d) (e) (f) (g)
(2)
where s 1 n=0
service intensity in the parking lot average number of UGVs in the parking lot average number of UGVs queuing in the waiting area
s
average arrival rate of the UGV in the parking lot number of loading and unloading points in the parking lot
(n
s) n!
t yuc = 1, urgent container (uc) is handled at the
urgent container point at time t
z t = 1, not urgent container (nuc) is handled at the urgent container point at time t z t = 0, otherwise
system. Eq. (1) is the objective function. The UGVs arrive at the parking lot according to a Poisson process with arrival rate . The average arrival rate of UGVs is and is determined by the safe distances of UGVs d and the annual throughput of containers M in the system, which is formulated in Eqs. (2a) and (2b). All urgent containers account for 5 percent of annual container throughput in Eq. (2c). Eq. (2d) represents the fact that urgent containers are handled at the urgent container point; otherwise, the not urgent containers are handled at the urgent container point at time t. When an urgent container is handled at the urgent container point, the average number of UGVs in the parking lot is indicated as L ( , s 1) . If the urgent container point is used to handle a not urgent container, then the average number of UGVs at all loading and unloading points in the parking lot is shown as Eq. (3).
(1)
(a)
L ( , s ) = Lq + s + p0
L Lq
t yuc = 0, otherwise
s. t.
0 Z
Parameters
t znuc
(2) The MINP model
2T
set of integers
t yuc
t min C ( , s ) = c y ·s + yuc ·c w ·L ( , s
T y t = 0.05M t = 0 uc t t yuc + z nuc =1 t t yuc , znuc (0, 1)
Z
Decision variables
The definitions of notations in the mathematical model are shown in Table 2. Some parameters of the queuing theory are from the Operations Research Course (Hu & Guo, 2007).
M D
Set
Other variables
(1) Notation definitions
d
Definition
N
5.2. Model description
v
Notations
n
5.3. Deriving function L( , s )
(3)
In the underground container logistics system, increasing the number of loading and unloading points can reduce the waiting cost of UGVs queuing in the parking lot, but it will also increase the cost of yard cranes. When UGVs queue in the waiting area of the parking lot, they will incur some cost. In this paper, the waiting cost of UGVs is used to control the queuing time of UGVs, and the cost increases as the queuing time become longer. The goal of optimization is to minimize the total cost of yard cranes and the waiting cost of UGVs queuing in the
In addition, the UGVs arrive at the parking lot in batches, and the number of UGVs per batch is a random variable X, the probability distribution of which is P(X = i) = xi (i = 0, 1, 2, …, m), where m is the maximum number of UGVs being handled at one point, and m is a positive integer. The service rate of one loading and unloading point is denoted by µm . The number of loading and unloading points in the parking lot is s, and each point can handle m UGVs at most. That is, (m s) is the total number of UGVs that can be handled at all loading and 332
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unloading points. The handling time at each loading and unloading point in the parking lot is independent. The serving rule is first come first served (FCFS). When a new UGV arrives at the parking lot, and all loading and unloading points are busy, the new UGV waits in the waiting area; otherwise the new UGV runs into the point with the lowest number of UGVs available. The number of UGVs that are serviced in the loading and unloading points is denoted by nj (j = 1, 2, …, s), 0 ≤ nj ≤ m, and the total number of UGVs in the parking lot is n, including the UGVs waiting in the waiting area. The state transition equation of the parking lot system is discussed in three cases. The first one, n ＞ m s, (n is the number of UGVs in the parking lot, and m s is the number of UGVs that can be handled at all points), means there are s loading and unloading points that are busy in the parking lot. Each UGV that arrives runs into the waiting queue. When one point finishes the loading and unloading of containers on one UGV, another UGV waiting in the queue can run into the point to be served. The probability of the steady state is indicated by pn = P(N = n) (n = 0, 1, 2, …), and the state transition equation is formulated as Eq. (4).
pn
n
pn =
p0 =
j=1
1
p (n1, …, nj
1, …, ns ) + j Js Jo
= p (n1, …, n jmin + 1, …, ns ) +
µnj p (n1, …, nj
=
n > ms : pn n = ms : n < ms : +
m ns = 0
…
K p n = ms + 1 n
p(ms)j
j Js Jm
1
(5)
s)
(K
s + 1)
s)
K s+1 s
2 [1
,
)
1
(1
s (K
p0
,
s
1
s
=1
s )(K
s )(K
s + 1)
K
(n
s ) pn =
(9)
s + 1)
K s ], s
,
n=s
K
npn
s 1 n= 0
s
1
s
=1
(10)
K
s n=s
pn =
n=s
s 1
npn
n= 0
npn
s 1
pn = L s 1
L ( , s ) = Lq + s + p0 n= 0
(n
s ) pn
n=0
(n
s) n!
s
(11)
n
(12)
Based on the multi-server queuing optimization model, the average queuing length Lq and average length L ( , s ) are used to assess the congestion in the parking lot. As the number of loading and unloading points increases, the average queuing length will be reduced. Then, it is essential to minimize the total cost of yard cranes and the waiting cost of UGVs queuing in the parking lot. 6. Case study 6.1. Numerical simulation In the underground container transportation system, there are some loading and unloading points for handling containers in the underground parking lot. To minimize the total cost and meet the container throughput requirement, it is essential to calculate the number of loading and unloading points. Of all points, there is one point for handling urgent containers. If the urgent container point is not busy, there are s points for handling other containers. Given different values of s, it is possible to calculate the average number of UGVs in the parking lot. To obtain the smallest number of UGVs in the parking lot, the waiting cost of each UGV is set to one million and waiting costs are calculated. Then, the cost of yard cranes and the waiting costs of UGVs are obtained. If the total cost C is minimized, then the iterative algorithm ends. The flowchart of the algorithm to solve the MNIP model is given in Fig. 7. On the basis of the models described above, the results obtained by MATLAB are shown in Fig. 8 and Table 2. According to the actual situation in Waigaoqiao terminal, its annual throughput of containers was 18.2175 million TEU in 2015. The container throughput in the underground container logistics system assumed by this paper is 4
=1
1, …, ns )
s
s!
s ! (1
s ) pn
s 1
1, …, ns ), n < ms
µnj p (n1, …, nj
s ! (1
n=s
µnj + 1 p (n1, …, nj + 1, …, ns ) j Js Jm
+
1
K s+ 1 ) s
s (1
K
1, …, ns )
= p (n1, …, n jmin + 1, …, ns ) +
s 1 n n=0 n !
(n
Lq =
+ sµm pms + 1 = ( + sµm ) pms
p (n1, …, nj
(8)
To calculate the average length L ( , s ) in the parking lot, the average queuing length Lq is derived in Eqs. (11) and (12).
+ sµm pn + 1 = ( + s ) pn
1 s j=1
j Js Jo
p (n1, …, ns ) +
n
2s !
The maximum capacity of the underground parking lot is K. The average arrival rate must be less than the average service rate µ , that is to say, the service intensity is = ( / µ) < 1. Only in this way can the queuing system in the parking lot remain in balance. When the system reaches equilibrium, the probability distribution of a stable system pn can be computed on the basis of formulation (7). m n2 = 0
(
+
p0 s s
(6)
m n1= 0
ms
s 1 n n=0 n !
n=s
µnj + 1 p (n1, …, nj + 1, …, ns )
j Js Jm
n < ms
K
The third one, n < m s, means there are no UGVs waiting in the parking lot. When a new UGV arrives at the parking lot, it will run into the loading and unloading area that has the fewest UGVs. If there is more than one loading and unloading point with the fewest UGVs, the points with the smaller number of UGVs will be chosen. The number of loading and unloading points with the fewest UGVs is denoted by jmin . The set of points at which the number of UGVs nj = 0 is represented as J0 , the set of points with the number of UGVs (nj = m ) is Jm , and the set of points with the number of UGVs (0 < nj < m ) is Js . If one more UGV arrives at the parking lot, it will be serviced by loading and unloading point jmin , and the system state will be (n1, …, n jmin + 1, …, ns ). If one UGV has been serviced at the point j Js Jm , the system state will be (n1, …, ni 1, …, ns ), where nj 1 = min{n1, …, ni 1, …, ns} . The state transition equation is indicated in Eq. (6). j Js Jm
p , s ! sn s 0
Lq =
s
+ sµm pms + 1 = ( + sµm ) pms , n = ms
0
n
The average queuing length Lq is given in Eq. (10).
The second one, n = m s, means that all loading and unloading points are busy, but there is no queuing in the parking lot. If a new UGV arrives at the parking lot, it will queue in the waiting area. When a UGV has completed service, the number of UGVs at the loading and unloading points will be reduced. The state transition equation is shown in Eq. (5).
p(ms)j
p , n! 0
where the idle probability in the parking lot p0 is represented as Eq. (9). The service rate of all loading and unloading points is denoted as Z. s = /sµm , s
(4)
+ sµm pn + 1 = ( + sµm ) pn , n > ms
1
Taking the three cases described above into consideration, when the parking lot reaches balance, the average numbers of UGVs running into the system is equal to that of UGVs running out the system. Then, the probability distribution of stable system can be obtained in Eq. (8).
(7) 333
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Fig. 7. The flowchart of the algorithm.
million TEU. The speed of UGVs is 13.5 m/s, and their safe distance is at least 70 m, as specified by the Mole Company in the UK. The maximum capacity of the underground parking lot is assumed to be 100 in this case. The probability distribution of service time for yard cranes is close to the logarithmic normal distribution, and the service time of yard cranes changes between 20 and 30 TEU each hour. Additionally, the service time has 10 TEU each hour up and down (Zhang, 2007). The cost of each yard crane is 10 million. For each UGV waiting in the parking lot, it will lose 1 million. When the number of loading and unloading points generated is ranged from 1 to 100, the number of loading and unloading points set in order to achieve the minimum cost and meet the container throughput requirement is 24. As shown in Table 3, the arrival interval of UGVs is approximately 16 s, and the number of loading and unloading points is 24. That is, a UGV arrives at the parking lot every 16 s, and 24 yard cranes are provided in the handling area on the ground, which are used to load or
unload the containers on the UGVs. In this case, the average queue length of the UGVs is 23.8522, and the average waiting length of the UGVs is 0.9006, which means there is almost no queuing in the parking lot. The average stay time of UGVs in the underground parking lot is 375 s. When 24 points are set for 4 million containers in the UCLS, the minimum total cost is 255.5861 million. Without the parking lot, all UGVs will queue in the underground tunnel. This situation would cause congestion in the underground transportation system. Thus, the presence of a parking lot is essential to provide space as a buffer for waiting UGVs. According to the solution, it can be found that in order to meet the requirement of 4 million container throughputs, the arrival interval of the UGVs is 15.6852, which is the maximum capacity. In other words, under the circumstances of 4 million containers, setting 24 loading and unloading points is the optimal solution for the purpose of minimizing yard crane cost and UGV waiting numbers. A metaheuristics approach, such as genetic algorithm (Gen, Cheng, & Lin, 2008) can be considered to solve the MINP model and compare with the computational results in this paper. 6.2. Sensitivity analysis In the above example, the UGV arrival interval is set to 15.6852 s in order to satisfy the container throughput of 4 million. Moreover, the cost of loading and unloading points and the waiting cost of the UGVs are minimized. However, taking the actual data of Waigaoqiao terminal into account, the cost of 24 yard cranes is substantial and difficult to be accepted. In this section, different container throughputs are given to analyse the relationship between the minimum cost and container
Fig. 8. The trend of total cost. 334
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Table 3 Results with 4 million TEU container throughputs in the underground system. Name
Total cost Min C (million)
Number of loading or unloading points s
Average arrival rate of the UGV λ
Average number of UGVs in the parking lot L
Average number of UGVs in the waiting area Lq
Arrival interval t
Value
263.8522
24
0.0637
23.8522
0.9006
15.6852
configuration required in the underground parking lot. As the container throughput changes, the arrival rates of UGVs vary correspondingly. The four average queuing lengths are related to the number of loading and unloading points. To adapt to container terminals of different scales, the different configurations required for the parking lot in the UCLS are found at minimum total cost.
throughputs. Four different values of container throughput in the underground container transportation system are set, and the average arrival rates change accordingly. Under the circumstances, given different values for s, the average number of UGVs in the parking lot and the total cost are calculated. If the total cost is minimized, the iterative algorithm ends. Otherwise, the algorithm continues to use another number of loading and unloading points to calculate the total cost. Then, the minimized total cost and number of points can be obtained for different container throughputs. Four different results solved via MATLAB on the basis of the mathematical model described above are shown in Table 4. Among these four cases, the number of loading and unloading points and average rate of UGVs are the optimal solutions. According to the average number of UGVs in the waiting area, it can be found that there are almost no UGVs waiting in the system. The decrease in container throughputs can decrease the average arrival rate of UGVs. In addition, the total cost and average number of UGVs in the parking lot are obtained. For the purpose of finding the minimum total cost, when there are one million TEU containers in the underground system, the number of loading and unloading points is 7, and the average arrival rate of UGVs is 0.0159. Moreover, the average number of UGVs in the waiting area is 0.5620, which is equivalent to no congestion in the parking lot. Then, the better combination of container throughput and minimized cost can be chosen according to different requirements. It can be seen from Table 4 that the total cost of the UCLS decreases with an increase in the UGV arrival interval. As the UGV arrival interval increases, the container throughput in the system is decreased, and the number of loading and unloading points decreases accordingly. In other words, the container throughput determines the arrival interval of the UGVs, while the number of loading and unloading points determines the strength of loading and unloading. There is no doubt that the service rate of the yard cranes must be larger than the arrival rate of the UGVs. It is essential that the transportation subsystem and terminal subsystem maintain a balance to avoid congestion in the underground parking lot. On the basis of the sensitivity analysis, different container throughputs are assumed in the underground container transportation system. The number of loading and unloading points is calculated by an iterative algorithm for the purpose of finding the minimum total cost. Different container throughputs determine the average arrival rate of UGVs, and the number of loading and unloading points is related to the cost of yard cranes and the waiting cost of UGVs in the parking lot. For each container throughput given, the average arrival rate of UGVs and the number of loading/unloading points in the underground parking lot can be found. Then, the total cost of yard cranes and the waiting cost of UGVs are minimized, and there is no congestion in the underground container transportation system. Four different container throughputs given are to analyse the
6.3. Simulation In this section, a simulation is carried out to analyse the influence of average arrival rate and number of points. The yard cranes and UGVs are chosen as simulation objects, and the operations of UGVs arriving and yard cranes handling containers are simulated in Tecnomatix Plant Simulation 13.0 software. In the simulation, four different numbers of loading and unloading points are given, and the average arrival rate is changed to obtain the lowest average queuing length of UGVs in the parking lot. If the average queuing length has no significant changes, then the average arrival rate is the optimal value. Then, the total cost and container throughputs that can be handled in the UCLS are counted. In the simulation, the efficiency of yard cranes at the loading and unloading points follows the logarithmic normal distribution, with a mean of 145 and a square of variance of 90. The arrival rate λ ranges from 15 s to 30 s, and the number of handling points is set between 7 and 10, according to the results of the sensitivity analysis above. Four experiments are simulated, and the simulation time is 365 days. The results of the experiments are obtained by counting the average queuing length of each loading and unloading point and including the container throughput. The four experiments with different arrival rates and numbers of loading and unloading points are shown in Fig. 9. From the simulation experiments, it can be observed that the average queuing length no longer changes significantly, when the arrival rate reaches a certain value. With 7 loading and unloading points, the arrival rate is set to 0.0345, and the average queuing length in the parking lot is one. In other words, the arrival interval of UGVs is 29 s. The underground transportation system can be considered to be in balance and to have no congestion. Similarly, when there are 8 loading and unloading points, the arrival interval is 26 s and there is nearly no queuing in the parking lot. The number of loading and unloading points is 9, and the arrival interval is 23 s. When the number of loading and unloading points is 10, the arrival interval is 20 s, and the queuing length of each loading and unloading point is one. The container throughputs being handled at different points in the underground container logistics system are listed in Table 5. The experimental results illustrate that the combination of the number of loading and unloading points and the average arrival rate, that lead to the UCLS having no congestion and to the system keeping in balance. With regard to Exp 4, where there are 10 loading and
Table 4 Data for the underground container system with different container throughputs. Number
Container throughputs (million TEU)
Total cost Min c (million)
Number of loading or unloading points s
Average arrival rate of the UGV λ
Average number of UGVs in the parking lot L
Average number of UGVs in the waiting area Lq
1 2 3 4
4 3 2 1
263.8522 198.2654 133.0869 76.2776
24 18 12 7
0.0637 0.0477 0.0318 0.0159
23.8522 18.2654 13.0869 6.2776
0.9006 1.1105 1.6529 0.5620
335
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Fig. 9. Average queuing length with different arrival rates at different loading and unloading points.
UCLS can handle 1.58 million TEU. In other words, the container transportation system can complete 8.67% of the annual container throughput in Waigaoqiao terminal in 2015 (18.2175 million TEU). Even though the amount of container throughput being diverged is small, the UCLS is helpful in that it relieves the pressure of ground transportation and the environmental problems caused by traffic. However, the arrival rate of UGVs in the simulation is based on unlimited sources in the underground parking lot, and the total number of UGVs is not considered in this paper. It remains to be researched further.
Table 5 Container throughputs of different loading and unloading points with minimum average queuing length.
Exp Exp Exp Exp
1 2 3 4
Number of loading and unloading points s
Container throughput (million TEU)
Average arrival rate λ
Average queuing length Lq
7 8 9 10
1.09 1.2 1.37 1.58
0.0345 0.0385 0.0435 0.0500
1.00 0.88 0.78 0.80
Acknowledgements
unloading points in the underground parking lot, and the average arrival interval of UGVs is set to 20 s, the UCLS can handle 1.58 million containers. Moreover, the average queuing length in the parking lot is one. That is, there is no congestion in the underground system.
This work was supported by the National Natural Science Foundation of China (71602114, 71631007), Shanghai Science & Technology Committee Research Project (16040501500, 17595810300).
7. Conclusions
Appendix A. Supplementary material
To relieve traffic jams caused by container trucks, an UCLS is proposed, and an underground parking lot within this system is designed. Aiming at minimizing the overall cost of loading and unloading points and the waiting cost of UGVs in the cycle, a multi-service queuing optimization model is established. When the annual container throughput is four million TEU, the arrival interval of the UGVs is approximately 15.6 s, the number of loading and unloading points is 24, and the minimum cost is 263.8522 million. However, considering the actual data of Waigaoqiao terminal, the number of loading and unloading points needs to be reduced. By setting different container throughputs, on the precondition of minimizing the overall cost, the number of loading and unloading points varies. When the container throughput is only one million TEU, only 7 loading and unloading points are needed. Finally, the goal of the simulation is to provide a comparison of the average queue lengths in the waiting area upon changing the arrival interval of the UGVs. It can be found that when the interval is 20 s, the average queuing length in the parking lot is 0.80. Therefore, it can be concluded that when there are 10 loading and unloading points and the arrival interval of UGVs is set to 20 s, the
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