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A two-stage model for an urban underground container transportation plan problem
Journal Pre-proofs A two-stage model for an urban underground container transportation plan problem Yang Pan, Chengji Liang, Liang Dong PII: DOI: Reference:
S0360-8352(19)30582-0 https://doi.org/10.1016/j.cie.2019.106113 CAIE 106113
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Computers & Industrial Engineering
Please cite this article as: Pan, Y., Liang, C., Dong, L., A two-stage model for an urban underground container transportation plan problem, Computers & Industrial Engineering (2019), doi: https://doi.org/10.1016/j.cie. 2019.106113
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A two-stage model for an urban underground container transportation plan problem Yang Pan 1, Chengji Liang 2，Liang Dong 2 (1.Shanghai Maritime University, Logistics Engineering College ,Shanghai 201306； 2. Shanghai Maritime University , Logistics Research Center 201306）
Abstract As a new transportation mode, underground logistics system can be used as one of the solutions to alleviate traffic congestion and air pollution on urban roads. In this paper, an underground container transport system is designed to realize the roadunderground-ocean container multimodal transport. This paper first analyzes the multistage decision-making content needed to design the underground container transportation system from the functional point of view of transporting a container. Then a two-phase model is built. The first stage is a 0-1 planning model with the lowest single-container cost to determine the planning layout and the second stage is to construct a simulation model under the current scenario to simulate the volume of transport containers within a specified time. Finally, a case study was carried out to determine the effectiveness of the method. Keywords: Underground logistics; Container transportation; modal transportation; simulation model 1. Introduction Container transportation consists of roads, water, and railways. However, the proportions of those means of transportation are unbalanced, especially the ratio of road transportation is too high. For example, the percentage of containers transported by road in Shanghai is 84%, which leads to increasing traffic congestion and air pollution. The statistics of the Shanghai Research Institute of Environment in 2013 shows that 40% of the NOx emissions were caused by trucks, accounting for only 5.2% of the traffic sector. Container transportation aggravated the contradiction between ports and cities. In such a situation, UCLS could be a choice to ease it. Underground Logistics (UL) also known as the Underground Freight Transport System (UFTS), which is a brand-new concept of a transportation and supply system. Solid goods can be transported in automated guiding vehicles or amphibious trucks through large caliber pipes or tunnels(J. Visser et al., 2008; J. G. Visser, 2018). An Underground logistics system use automatic steering vehicle (AGV) and dual-purpose truck (DMT) as load-bearing tools through the tunnel or large-diameter pipe connecting the main underground cargo transfer station. The earliest underground logistics system perhaps is the London Mailrail system since 1930(Bliss, 2000). The most widely applied underground logistics system is Garbage Pneumatic Conveying system (GPC system) which was developed by a Swedish cooperation installed in a hospital in the suburban area of Stockholm in 1967. As a new mode that may be widely used, underground logistics research concerns include: the type of goods carried by underground logistics, the possibility of underground logistics research, the construction technology of underground logistics, the power technology of underground logistics, the policy or advantages of underground logistics and the network design of underground logistics. This study focuses on the design of underground container transport system in the urban underground space in the form of a link network. The underground logistics system
in this problem is a single type of cargo transported for containers, so the system needs not consider the subcontracting process to complete the transport and transshipment process. The application area of this system is urban underground space, which should relate to road transport and marine transportation, so the network form chosen is link form. In this paper, section 3.1 takes the transport of a container as an example, analyzes the specific processing of containers in road-underground-sea multimodal transport. section 3.2, analysis of the decisions in the plan. Section4 creates a two-stage model for an underground container transport system with the lowest cost per case. Section 5 conducted a case study of the model. 2. Literature review 2.1 Issues in the underground logistics transportation Underground logistics, like other transport modes, requires loading and unloading by crane when connecting with other transport modes. However, its operating space is underground, so in addition to considering the design of the transport area, but also to consider the infrastructure design of the underground operating area. Unlike other modes, once the mode is decided the needed vehicles will be choose, but underground logistics mode can have a variety of transport options. Different vehicle option will correspond to different transshipment operations and infrastructure. The concept of the ULS mainly focus on the basic aspects such as conceptual design of a system, the carrier for holding cargo (CargoCap) and the vehicles (Safe Freight Shuttle), which all are powered by electromagnetism( Stein (2003) ). Liu (2004) recommended that pneumatic capsule pipelines (PCP) be used to construct an underground transportation system for New Jersey Port, New York. The feasibility studies and the technical of ULS have drawn more attention in the flowing years. And many times, these two subjects cannot be completely separated. Henry (2008) summarized the feasibility of New York’s wind tunnel piping technology and provided references for the construction of underground logistics in other cities. (Bobylev, 2009; Canós & De Zulueta, 2004; Fouladgar et al., 2012; Xiaobin et al., 2014) Van Binsbergen & Bovy(2000) proposed two construction methods for underground transportation. Qihu Qian (2004) first proposed that urban underground logistic systems could be new alternatives for solving urban traffic congestion. Systematically explored the underground system in China. As for the design of ULS, the challenge is: the transfer needs to overcome the height difference between the tunnel and surface (Van Binsbergen & Bovy, 2000). Other design issues relate to the tubes which need to be as straight as possible(ASCE Task Committee on Freight Pipelines of the Pipeline Division, 1998) especially building new tunnels may prove challenging. A final design issue is determining capacity as, once built, there is a finite limit to capacity before additional tunnels need to be bored(Egbunike & Potter, 2011).
Fig.1 Alternative underground concepts. Source: Based on (Van Binsbergen & Bovy, 2000)
Concepts involved in the design of underground logistics (in Fig.2): underground objects (cellars, depots); underground sections (tunnels); underground links; underground networks. Over the past ten years, more articles coupled with the network and the optimization of the ULS. Vernimmen et al. (2007) developed an underground tunnel connecting the left and right parts of Antwerp Port. Of all the researched about network design, the most concern is the location problem. ZHOU & ZHOU(2017) use the genetic algorithm to optimize the layout of the distribution route, considering the cost if time and input. Wentao & Yanhong( 2016) used the bi-level planning model to study the location selection of logistics nodes in the construction of underground logistics systems, taking into account both the interests of the logistics planning and decisionmaking departments and those of the customers. The scholars mostly used traditional simulation algorithms to solve the optimization problem of underground logistics networks, but most of them discuss the characteristics of ULS systems out of specific urban characteristics. They do not carry out case studies and design solutions in light of the actual situation of ULS. In the current stage, case studies using ULS are urgently needed. 2.2 strategic level issues of intermodal transportation This paper studies the design of underground logistics container transport multimodal transport system is an intermodal transportation plan. Caris et al. (2008) divided intermodal transportation plan problems into three levels by time horizons: strategic, tactical and operational planning. In the strategic level, decisions are found on a very long term (10–20 years). The location of terminals, the network configurations and the design and layout of a terminal are typically decisions were a large amount of capital is fixed for a long time and that are difficult to change(Macharis & Bontekoning, 2004). The decision makers are distinguished as : intermodal operators, network operators, terminal operators and drayage operators. The terminal operators take care of the transshipment operations from road to rail or barge, or from rail to rail or barge to barge.( Caris et al.,2008).In this paper，we stand for the terminal operator to make a strategic level plan of intermodal transportation. Meyer (1998) faces the design problem of a rail–rail terminal in a hub-and-spoke
system for the exchange of a maximum of six trains at a time. In addition, the terminal should be able to handle a limited volume of rail–road exchanges. Bontekoning (2000)research the terminal evaluation problem. Macharis et al.(2011) focus on the barge terminal location and the impact for the performance of the network. Li et al.(2015)considers both terminals and transport connections as an intermodal freight transport network. Meyer (1998) applied Dynamic computer simulation (SIMPRO) with Petrinet to determine required capacity for cranes and internal transport systems, and the most efficient arrival pattern of trains. Bontekoning (2006) develops a simulation model to perform a systematic comparison between various hub exchange facilities in an intermodal rail network. Li et al.(2015) proposes a receding horizon intermodal container flow control (RIFC) approach to address dynamic transport demands and traffic conditions in the network for intermodal freight transport planning problems 3. Problem description 3.1 A container operation progress in underground transport system What this system describes is the transportation process of an underground logistics system during the road-underground-sea transportation process. The focus is on underground logistics and connections with road and sea. Fig. 2 shows the process of transporting export containers through UCLS. The container is lifted by a gantry crane at the entrance of the tunnel and loaded on a vehicle. After a 30-kilometer trip along the rail in the tunnel, the vehicle slows down close to the buffer area and completely stops at the location exactly below the gantry crane at the exit. Then, the container is lifted by the gantry crane up to ground level and loaded on the truck. After being delivered to the storage area, the export container is finally transferred to the berth. The areas shown in Fig. 4 are the most important locations in the system where the decisions on which equipment or infrastructure to use are made. The decision sequence constitutes the programming of the UCLS.
Fig. 2 Process of transporting export containers through the UCLS. The total time for transporting a set of containers from one terminal subsystem to the berth near the other terminal subsystem is:
ts t 1 t 2 t 3 t 4 t 5 t 6
(1) Where, ts is the total duration of loading/unloading from the entrance of the underground tunnel to container ship; t1 is the loading duration of gantry crane at the entrance of the underground tunnel; t2 is the duration of vehicle travelling in the underground tunnel from the entrance close to the buffering area; t3 is the duration of vehicle slow down to stop in the buffering area; t4 is the unloading duration of gantry crane at the exit of the underground tunnel; t5 is the travelling duration of truck from the exit to the storage area; t6 is the container transship duration from the storage location to ship.
3.2 The decision set of the stages of the underground transport system According to Fig. 2, we divided the transport into several stages, each stage of the decision, constitute it a design for our system. 3.2.1. Loading/unloading area at the entrance of the tunnel The container is picked up by a gantry crane, which is the only option on this site. 3.2.2 Vehicle traveling area along the tunnel There are three types of vehicles that can be selected to carry containers. Automated guided vehicles (AGV), which are widely used in automated terminals, can improve the automation level of the system. A new railed vehicle powered by DC, which can be applied to an underground tunnel, was developed by a Mole Solution. There are two equipment operating modes: single run and group run. The mode of traveling singly is so flexible that it could reduce the pressure of the operation schedule. The transport sequence of the containers can be determined simply according to the ship's loading plan while the necessary safe distance between two vehicles will lower the density of vehicles in the tunnel. Traveling in groups is two linked vehicles traveling synchronously and delivering 4 TEU. 3.2.3. Buffer area in the tunnel This site is the bottleneck of the system. Only the vehicle stops completely, so the gantry container can aim at the container lock to lift the container to ground level. As a result, there is a risk of congestion in the buffer area, which is the bottleneck of the system. There are two alternatives, i.e., exiting directly or through a buffer area. In the former alternative, the safe distance should be long enough to ensure no collision at the exit. The latter is to set a buffer area at the exit extending from two to six lanes or rails. The containers could wait for be loaded/unloaded within the buffer area to avoid congestion. 23.2.4. Loading/unloading area at the exit of the tunnel
To avoid collisions with the wharf infrastructure (such as piles), the underground tunnel should be constructed at least 20 meters deep. There are two ways to exit to ground level: along a sloping tunnel or through a shaft. 3.2.5. Truck waiting area aboveground The last issue of this stage is the equipment operation mode at the exit. Loading/unloading points are set at the exit and the containers are lifted to the horizontal ground by rail gantry cranes. One option is to use the current operation mode, which is a single-trip-dual-spreader, of rail gantry cranes. To accelerate operation speed at the exit, another option is a round-trip-dual-spreader mode. The rail gantry crane lifts the containers from the vehicles in the underground tunnel, loads them on the trucks aboveground, lifts another container from the other trucks aboveground, and loads them on the vehicles in the underground tunnel. In this way, the rail gantry crane completes two loading and unloading cycles within one move while the vehicles in the underground tunnel undergo round-trip heavy traveling. Obviously, the mode improves the transportation efficiency of the system. 3.2.6. Container storage area After being loaded on the trucks aboveground, there are three possible options for the delivery of the containers: the container yard, a special yard behind the terminal yard, or a specialized central station for the UCLS. 4. Modelling Methodology 4.1 Model hypothesis The mode programming of UCLS is a complex process. To turn the abstract real problem into a mathematical model, some assumptions have been made as follows: 1. Standard container size is 20 or 40 feet. Containers to be excluded are 45 and 53 feet, overweight, reefer, and dangerous goods containers. 2. All equipment is operated in a normal situation, ignoring the possibility of failures or accidents. 3. Ensuring safe distances between transportation equipment in the underground tunnel. 4. Ignoring the space limitations of storage containers at the underground tunnel exit. 5. The time count begs from the moment the gantry crane at the entrance of the underground tunnel. 6. Ignoring the effects of the changes in vehicle volume in rails on operation velocity. 7. The system runs for 24 hours a day and 30 days a month. 8. Ignoring equipment depreciation. 4.2 Two-stage model In the first stage, you will need to make a decision-making alternative, build a 0-1
planning model, in order to reflect the dynamics of the model and then build a simulation model, to obtain the number of boxes that the system runs within the simulation period. 4.2.1 0-1 programming model each stage takes the available options at each site as the decision set. Accordingly, the programming of the UCLS is a multistage decision process. The multistage decision network is G=(V,E,T) with node V={vki}. k∈K, where K is the set of key sites. (Yunquan (2003))V= V1∪V2∪V3∪V4∪V5∪V6∪V7, where V1 is the set of equipment options. V1={v11}, where v11 represents the gantry crane. V2 is the set of underground tunnel vehicles and their operation mode options. V2={v21,v22,v23}, where v21 represents the AGV operating singly, which means that the AGV departs as soon as the containers are loaded. v22 represents the rail vehicle shift operating singly. v23 represents the rail vehicle operation in a group, which means that a vehicle group may depart only if all the containers have been loaded. V3 is the set of buffering infrastructure options. V3={v31,v32}, where v31 represents no buffer area and v32 represents a buffer extending from two to six lanes. V4 is the set of exit mode options. V4={v41,v42}, where v41 represents an exit through a shaft while v42 represents an exit along a sloping tunnel. V5 is the set of operating ways at the exit options. V5={v51,v52}, where v51 represents loading/unloading on one side of the gantry crane while v52 represents loading/unloading on both sides of the gantry crane. V6 is the set of storage location options. V6={v61,v62,v63}, where v61 represents the terminal yard, v62 represents establishing a station, and v63 represents establishing a yard behind the terminal. V7 is the set of options on the berth. V7={v71}， where v71 represents the berth. Arc set E={(vki,vk+1,j)} represents the selected Vk+1,j, as long as selecting Vki. The weigh set T={tkij} represents the duration from Vki to Vk+1,j.
Fig. 3 Multistage decision network of UCLS Parameters. tkij: Duration of transporting 4 TEU from vki to vk+1,j, min. fk+1,j: The monthly mean of initial cost of Vk+1,j, which is 1,000 yuan/month. hk+1: The energy consumption cost of Vk+1,j per minute, which is 1,000 yuan/month. Qk+1,j : The amount of Vk+1,j;The lower quantity limit of containers in TEU handled
by the UCLS. K: Set of key sites. V: Set of options at all sites. V+: Set of selected options. V-: Set of options to be selected. T: Set of durations, including stochastic parameters, between two sites. F: Set of monthly means of initial construction costs. H: Set of energy consumption factors. Q: Set of equipment amounts. Decision variables.
1，select vk 1, j xkij 0 ，otherwise For an underground logistic system plan program, the huge initial investment and the following operating costs are the critical factors for the system plan. Therefore, the objective function of this problem should model the cost. Under the limitation of delivering capacity, the UCLS is more efficient as more containers are delivered. Conventional methods for solving such optimization models is multistage programming. The first stage is to set up a program plan and the second stage is to find the optimal solution. As the linear-shaped underground logistic system presented in this paper is the simplest logistic system to program, there is no need to choose a route once the system has settled. Therefore, the objective function of this problem is molded by the converted initial investment and operating cost, which is a 0-1 integer nonlinear formulation, of each container. The volume of containers handled by the UCLS increases as more equipment are deployed, such as vehicles in the underground tunnel, gantry cranes. However, the more equipment used, the more will be the initial investment and energy consumption costs each month. The goal of UCLS programming is to balance the volume of containers and the cost of the whole system including initial investment and the operation cost. Therefore. per container cost is a suitable index to measure the balance. We propose the Lowest Cost per TEU of Initial Investment and Operating Cost (LCTIIOC). As different equipment and infrastructure have different designed life span, only the monthly mean of initial investment could be calculated in the objective function, which is marked as fk+1,j. The energy consumption costs are calculated by product of equipment working duration and its volume. Assume that the UCLS is running for T months without replacing equipment. Cost1 is the initial cost for T months, Cost2 is the energy consumption cost in T months, CT is the volume of containers handled in T months, Cp is per container cost: cost1 T ( f 11 f k 1, j xkij )
(2)
cost2 T (h11 (hk 1, j Qk 1, j ) xkij )
(3)
kK iI jJ
kK iI jJ
172800( Q11jx11j） jJ
CT T
t
(4)
x
kij kij
kK iI jJ
cost1 cost2 CT The formula is: (( f 11 h11) ( f k 1, j hk 1, j Qk 1, j ) xkij ) tkijxkij kK iI jJ kK iI jJ min 172800( Q11jx11j） CP
(5)
(6)
jJ
Subject to: 172800 t11jx11j jJ
Q
x
C j I
(7)
11j 11j
kK iI jI
The objective function (6) contains initial investment and the energy consumption costs per container. Subject to：
k 1 1, xkij xkli 0, k 2,3,,6 jI lI 1, k 7
xkij
1 k K
x
Vi V ,Vj V
i I j I kij
W
kK
xkij 0,1 k K, i I , j I
i I , j I
(8)
(9) (10) (11)
Constraint (8) ensures that there is a route from v11 to v71, which is a classical shortest path constraint. Constraint (9) ensures that only one option can be chosen at each transshipment stage. Constraint (10) ensures that at least one option is chosen at each transshipment stage during the whole transportation process. 4.2.2 The simulation model In order to determine the container volume through the underground tunnel under different hardware configurations, we have constructed a simulation model that brings the data obtained from the simulation experiment into the 0-1 programming model, so that we can make a strategic plan from the perspective of the terminal operator. The simulated equipment: gantry crane at the entrance of underground tunnel, the vehicles in the underground tunnel, gantry crane at the exit of underground tunnel and the trucks on ground. The simulated facilities: the loading position at the entrance of underground tunnel,
the travel section of underground tunnel, the buffer section of underground tunnel and the unloading position at the exit of underground tunnel. Taking exporting a container as an example, the processing rules are as follows: At the entrance of underground tunnel, if the container arrives first and the vehicle below does not arrive, the container will wait below the gantry crane for the vehicle. If the vehicle arrives and the container has not yet arrived, the vehicle waits at the loading point below the bridge for the containers. The container is loaded by the gantry crane onto the vehicle of the underground tunnel and then will be carried towards the exit of the underground tunnel. The constraint of this period is: the acceleration and speed of the vehicle does not exceed the maximum of the system and the minimum safety distance between the two vehicles. When the vehicle close to the buffer section of the tunnel, the speed should be gradually reduced to 0 till at the end of the buffer section. To avoid congestion, the lanes of the buffer zone should be extended. The vehicles enter the buffer lane in accordance with the lane with the smallest serial number. If the number of vehicles in the lane does not reach the maximum, the vehicle run into the buffer lane, or run into the buffer lane in the next order. When the vehicle reaches the end of the buffer end, the status of the front loading point need to be evaluated. If no container is being operated, then the vehicle move directly to the loading point; if there is a vehicle in front of the container being operated, the vehicle wait until the front vehicle departure. Containers are loaded and unloaded on the truck on ground, then placed in the container storage area and finally transported to berths for ship transport.
Fig.4 the flow chart of the simulation model 5. Case study To test the behavior of the methodology, a case study was conducted in a location near Jiading of Shanghai, where a container central station was set up in the suburbs of Shanghai to collect and distribute containers mainly from Jiangsu Province in order ease
downtown traffic congestion and air pollution.
Fig.5 The location of UCLS in this case The distance between the two ends of the tunnel was 35 km. The time to transport 4 TEU was calculated according to the methodology presented in Section 5.1, as well as to Liang Jian et al. (2013), Wang Qingbin (2014), Liang Jian et al. (2009), Li Feng et al. (2016), Zhang Ran (2016) and Shi Jianfeng et al. (2016), as shown in Table 1. 5.1. Time related parameter 5.1.1 Duration of loading/unloading at the entrance area A time window begins from the moment that a ground container carrying equipment arrives at the location below the rail gantry crane at the entrance of the underground tunnel.The expectation of the waiting time during which the loading/unloading is operated can be estimated from the rail gantry crane parameters (https://club.1688.com/article/58832562. htm). The variance is 1 ( Jian et al. (2009) ). 5.1.2 Traveling and buffering time through the underground tunnel In the deterministic case, to present the uncertainty of travel time, a three-point distribution is considered with one possible realization below E(t)x(0
There are no parameters for reference. The expectation of the loading/unloading time can be estimated from the parameters of the round-trip-dual-spreader rail gantry crane (https://club.1688.com/article/58832562.htm). As with the dual-spreader quay crane, after the container truck stops at the exact location below the quay crane, it takes the truck much time to reposition for connecting the container with the spreader. The adjustment lowers the efficiency of the dual-spreader quay crane. The theoretical loading/unloading time of the dual-spreader quay crane should be half of that of the single-spreader quay crane but the actual loading/unloading times of both the dualspreader quay and round-trip-dualspreader rail gantry cranes are 5/7 of that of the singlespreader quay crane ( Ran (2016)). The variance is 1(Tao (Tao) ). table1 The value and instruction of parameter tkij（unite：minute/4TEU） parameter
instruction
value
t111 t112 t113 t211 t212 t221 t222 t231 t232 t311 t312 t321 t322 t411 t412 t421 t422 t511 t512 t513 t521 t522 t523 t611 t621 t631
The duration of loading on the AGV The duration of loading on the single ULV The duration of loading on group ULVs AGV travelling duration AGV travelling duration The single ULV travelling duration The single ULV travelling duration Group ULVs travelling duration Group ULVs travelling duration duration from no lane widening buffer area to shaft exit duration from no lane widening buffer area to slope exit duration from lane widening buffer area to shaft exit duration from lane widening buffer area to slope exit The duration of loading on truck on one side at shaft exit The duration of loading on truck on both side at shaft exit The duration of loading on truck on one side at slop exit The duration of loading on truck on both side at slop exit The duration to terminal yard with one truck The duration to station with one truck The duration to yard behind the terminal with one truck The duration to terminal yard with two trucks The duration to station with two trucks The duration to yard behind the terminal with two trucks The duration from terminal yard to berth The duration from station to berth The duration from yard behind terminal to berth
8 8 11 71 71 38 38 38 38 20 18 11 10 12 7 8 5 30 6 15 30 6 15 5 10 7
t111,t112 and t113 represent the time period from elements of V1 to ones of V2:t111 is the time from v11 to v12, which represents the duration of loading/unloading 4 TEUs on the AGV;t112 is the time from v11 to v22 which represents the duration of loading/unloading 4TEUs on the single ULV; t113 is the time from v11 to v23 which represents the duration of loading/unloading 4TEUs on the group ULVs. t211, t212, t221, t222, t231 and t232 represent the time period from elements of V2 to ones of V3: t211 and t212 represent the duration of the
AGV travelling through the underground tunnel; t221 and t222 represent the duration of the single ULV travelling through the underground tunnel; t231 and t232 represent the duration of the group ULVs travelling through the underground tunnel. t311, t312, t321 and t322, represent the time period from elements of V3 to ones of V4:t311 represents the travelling duration to a shaft exit passing a buffering area without lane widening; t312 represents the travelling duration to a slope exit passing a buffering area without lane widening; t321 represents the travelling duration to a shaft exit passing a buffering area with lane widening; t322 represents the travelling duration to a slope exit passing a buffering area with lane widening. t411, t412, t421 and t422 represent the time period from elements of V4 to ones of V5:t411 represents loading/unloading 4 TEUs duration from vehicles in the underground tunnel to trucks on one side on ground of the shaft exit; t412 represents loading/unloading 4 TEUs duration from vehicles in the underground tunnel to trucks on both sides on ground of the shaft exit; t421 represents loading/unloading 4 TEUs duration from vehicles in the underground tunnel to trucks on one side on ground of the slope exit; t422 represents loading/unloading 4 TEUs duration from vehicles in the underground tunnel to trucks on both sides on ground of the slope exit. t511、t512、t521、 t522，t531 and t532 represent the time period from elements of V5 to ones of V6:t511 and t521 represent the duration of trucks travelling from the exit of the underground tunnel to the yard in a terminal; t512 and t522 represent the duration of trucks travelling from the exit of the underground tunnel to the yard in a special station; t513 and t523 represent the duration of trucks travelling from the exit of the underground tunnel to the yard behind the terminal. As there will be several routs for truck travelling on ground, the t511 and t521 have the same value. t512 and t522 and t513 and t523 are the same situation. t611,t621 and t631 represent the time period from elements of V6 to ones of V7:t611 represents duration of trucks carrying TEUs from the yard to berth in the terminal; t621 represents duration of trucks carrying TEUs from the yard in the special station to the berth of the terminal; t631 represents duration of trucks carrying TEUs from the yard behind the terminal to berth of the terminal. 5.2
Cost related parameters
The value of fk+1,j was calculated with the initial investment, lifespan, and the amount of equipment. There are three scenarios for the amount of equipment, as shown in Table 2. Table 2 Information on parameter hk+1,j and fk+1,j Equipment or
Nodes
infrastructure
hk+1,j Cost each Design High in¥/m In 103¥ ed life in year quantity
fk+1,j
Medium
Low
quantity
quantity
in ¥/Mon.
fk+1,j in ¥/Mon.
fk+1,j in ¥/Mon.
Gantry crane at the entrance v11
6.3
25000
30
5
347222.2
5
347222.2
5
347222.2
AGV
v21
52
5000
15
400
11111111
267
7416667
134
3722222
ULV
v22
26
800
20
614
2046667
409
1363333
205
683333.3
Group ULV
v23
26
1600
20
307
2046667
205
1366667
103
686666.7
No lane widened buffer area v31
0
596000 80
1
620833.3
1
620833.3
1
620833.3
lane widened buffer area
0
7450000 80
1
7760417
1
7760417
1
7760417
Gantry crane at the shaft exit v41
6.3
25000
30
14
1284722
10
1006944
8
868055.6
Gantry crane at the slop exit v42
6.3
25000
30
14
1409722
10
1131944
8
993055.6
Single Truck
v51
15
0
-
-
0
-
0
-
0
Double trucks
v52
20
0
-
-
0
-
0
-
0
Terminal yard
v61
15
0
-
1
0
1
0
1
0
station
v62
15
300000 80
1
312500
1
312500
1
312500
Yard behind terminal
v63
15
250000 80
1
260416.7
1
260416.7
1
260416.7
berth
v71
0
0
1
0
1
0
1
0
v32
-
Inf.: Ignore the quantity of truck according to the assumption that there are enough trucks. The initial investment of the existing infrastructures such as terminal yard and berth are assigned 0.
Detail cost calculation and converting the results to unified unit of measurement are being presented in Table 2, the converting unified unit data are put in the objective function. The objective function is formed by initial investments and operation costs. There are multiple optional nodes for one stage, also corresponding node’s cost are present in Table1 Table2. For v51 and v52, the drayage container truck represents the equipped facilities, no additional fixed asset investment required, therefore marked as fk+1,j=0. v61 as container yard and v71 as the quay berth are existing infrastructure, also marked as fk+1,j=0. v31 and v32 are optional infrastructure, illumination facilities, the both means of energy consumption could be treated as equal, therefore both options’ impact are the same, also marked as hk+1,j=0 in Table 2. The data at v61, v62 and v63 are the power consumed to v71 (berth) from each of mentioned nodes for an empty TEU, for a fully loaded container, a proper weight should be multiplied. Since the differences of design durable lifetime of variable equipment and infrastructure, each option’s initial investment costs are being apportioned to the corresponding design durable lifetime on monthly basis. Taking v62 as an example, the design durable lifetime is 80 years, initial investment cost is 300,000,000 RMB, therefore during the lifecycle, monthly cost is 312,500,000 RMB. Underground logistics vehicles investment could be ranged as low, medium and high by the quantity that deployed. Travelling tunnel cost is put in the data at v31 and v32. Gantry crane construction cost including its exit is put in the data at v41 and v42. Even though the same quantity of gantry cranes is deployed, construction cost could be varied due to the different exit modes. Therefore, fk+1,j data at v41 and v42 are different. Taking shaft exit at v41 as an example, gantry crane unit investment cost is 25000000, design durable lifetime is 30 years. In the high case, required gantry crane is 14 units. 5.3Results Due to the different amount of underground transport equipment, there will be different operating results. Increased delivery, the ability to transport more containers,
but there is also a greater risk of congestion, so different numbers of scenarios for equipment delivery will have different design options.
The Interval Time of Scenarios 308 306 304 302 300 298 296 AGV
ULV high
medium
ULV in group low
Fig.6 The interval Time of Scenarios After simulation, it can be seen that different transportation equipment in different situations, the time interval between the two completed tasks as shown in the figure, in the various scenarios of AGV, with the reduction of the amount of equipment, processing the amount of boxes less, so the interval between the completion of the task becomes larger. However, in the ULV and ULV in group scenarios, the medium scheme is the shortest time interval. Preliminary analysis suggests that uLV travel speed is faster than AGV caused. Table 3 The results of the underground transportation system Scenario High
Medium
Low
volume
TEU
solution
AGV
400
7970.7
v11→v23→v31→v41→v51→v61→v71
ULV
614
8380.2
ULV in group
314
8534.4
AGV
267
7676.4
ULV
409
8271
ULV in group
205
8529
AGV
134
6913.8
ULV
205
8314.2
ULV in group
103
8459.1
v11→v22→v31→v41→v51→v61→v71
v11→v23→v31→v42→v51→v62→v71
The table3 shows the vehicle volume parameters, the simulation of one month’s operation in three case of volume of vehicles and the corresponding solution. In the high scenario, if the AGV is used to delivery container in underground tunnel, the volume of
AGV will be 400, the ULV will be 614 and the ULV in group will be 314. The situation in medium and low cases is the same. From the results of tables 3, the options of AGV, setting buffering area with widening the lanes, loading/unloading containers on both sides are chosen in none of the scenarios. 6. Conclusions This paper investigates a road-underground-ocean container transport planning problem of strategic level for the terminal operator, which could be a potential solution for the urban traffic congestion. The behavior of an urban underground container transportation system is formulated from a container operation process perspective and an underground transportation system configuration decision, such as container carrying vehicles options, vehicles grouped options , buffering area lane . A two-stage model is established with dynamic characteristics. The first stage, a layout decision model is to minimize the cost per TEU. The second stage model is a simulation model. Given to the UCLS further development, the 2 main research fields as 1) Complete the cost calculation range, as the infrastructure and facility maintain cost 2) Set up more complicate system, as network structured UCLS
Acknowledgements This work is sponsored by National Natural Science Foundation of China (71471110), Shanghai Science & Technology Committee Research Project (16DZ1201402, 16040501500). We also thank anonymous referees and the editor-in-chief.
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High lights 1) This paper investigates an underground container transport planning problem for the terminal operation. 2) The process of operating a container with the underground system is analysed. 3) A two-stage model is established for the system design. 4) 0-1 programming and simulation models are applied in the problem.
S0360-8352(19)30582-0 https://doi.org/10.1016/j.cie.2019.106113 CAIE 106113
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Please cite this article as: Pan, Y., Liang, C., Dong, L., A two-stage model for an urban underground container transportation plan problem, Computers & Industrial Engineering (2019), doi: https://doi.org/10.1016/j.cie. 2019.106113
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A two-stage model for an urban underground container transportation plan problem Yang Pan 1, Chengji Liang 2，Liang Dong 2 (1.Shanghai Maritime University, Logistics Engineering College ,Shanghai 201306； 2. Shanghai Maritime University , Logistics Research Center 201306）
Abstract As a new transportation mode, underground logistics system can be used as one of the solutions to alleviate traffic congestion and air pollution on urban roads. In this paper, an underground container transport system is designed to realize the roadunderground-ocean container multimodal transport. This paper first analyzes the multistage decision-making content needed to design the underground container transportation system from the functional point of view of transporting a container. Then a two-phase model is built. The first stage is a 0-1 planning model with the lowest single-container cost to determine the planning layout and the second stage is to construct a simulation model under the current scenario to simulate the volume of transport containers within a specified time. Finally, a case study was carried out to determine the effectiveness of the method. Keywords: Underground logistics; Container transportation; modal transportation; simulation model 1. Introduction Container transportation consists of roads, water, and railways. However, the proportions of those means of transportation are unbalanced, especially the ratio of road transportation is too high. For example, the percentage of containers transported by road in Shanghai is 84%, which leads to increasing traffic congestion and air pollution. The statistics of the Shanghai Research Institute of Environment in 2013 shows that 40% of the NOx emissions were caused by trucks, accounting for only 5.2% of the traffic sector. Container transportation aggravated the contradiction between ports and cities. In such a situation, UCLS could be a choice to ease it. Underground Logistics (UL) also known as the Underground Freight Transport System (UFTS), which is a brand-new concept of a transportation and supply system. Solid goods can be transported in automated guiding vehicles or amphibious trucks through large caliber pipes or tunnels(J. Visser et al., 2008; J. G. Visser, 2018). An Underground logistics system use automatic steering vehicle (AGV) and dual-purpose truck (DMT) as load-bearing tools through the tunnel or large-diameter pipe connecting the main underground cargo transfer station. The earliest underground logistics system perhaps is the London Mailrail system since 1930(Bliss, 2000). The most widely applied underground logistics system is Garbage Pneumatic Conveying system (GPC system) which was developed by a Swedish cooperation installed in a hospital in the suburban area of Stockholm in 1967. As a new mode that may be widely used, underground logistics research concerns include: the type of goods carried by underground logistics, the possibility of underground logistics research, the construction technology of underground logistics, the power technology of underground logistics, the policy or advantages of underground logistics and the network design of underground logistics. This study focuses on the design of underground container transport system in the urban underground space in the form of a link network. The underground logistics system
in this problem is a single type of cargo transported for containers, so the system needs not consider the subcontracting process to complete the transport and transshipment process. The application area of this system is urban underground space, which should relate to road transport and marine transportation, so the network form chosen is link form. In this paper, section 3.1 takes the transport of a container as an example, analyzes the specific processing of containers in road-underground-sea multimodal transport. section 3.2, analysis of the decisions in the plan. Section4 creates a two-stage model for an underground container transport system with the lowest cost per case. Section 5 conducted a case study of the model. 2. Literature review 2.1 Issues in the underground logistics transportation Underground logistics, like other transport modes, requires loading and unloading by crane when connecting with other transport modes. However, its operating space is underground, so in addition to considering the design of the transport area, but also to consider the infrastructure design of the underground operating area. Unlike other modes, once the mode is decided the needed vehicles will be choose, but underground logistics mode can have a variety of transport options. Different vehicle option will correspond to different transshipment operations and infrastructure. The concept of the ULS mainly focus on the basic aspects such as conceptual design of a system, the carrier for holding cargo (CargoCap) and the vehicles (Safe Freight Shuttle), which all are powered by electromagnetism( Stein (2003) ). Liu (2004) recommended that pneumatic capsule pipelines (PCP) be used to construct an underground transportation system for New Jersey Port, New York. The feasibility studies and the technical of ULS have drawn more attention in the flowing years. And many times, these two subjects cannot be completely separated. Henry (2008) summarized the feasibility of New York’s wind tunnel piping technology and provided references for the construction of underground logistics in other cities. (Bobylev, 2009; Canós & De Zulueta, 2004; Fouladgar et al., 2012; Xiaobin et al., 2014) Van Binsbergen & Bovy(2000) proposed two construction methods for underground transportation. Qihu Qian (2004) first proposed that urban underground logistic systems could be new alternatives for solving urban traffic congestion. Systematically explored the underground system in China. As for the design of ULS, the challenge is: the transfer needs to overcome the height difference between the tunnel and surface (Van Binsbergen & Bovy, 2000). Other design issues relate to the tubes which need to be as straight as possible(ASCE Task Committee on Freight Pipelines of the Pipeline Division, 1998) especially building new tunnels may prove challenging. A final design issue is determining capacity as, once built, there is a finite limit to capacity before additional tunnels need to be bored(Egbunike & Potter, 2011).
Fig.1 Alternative underground concepts. Source: Based on (Van Binsbergen & Bovy, 2000)
Concepts involved in the design of underground logistics (in Fig.2): underground objects (cellars, depots); underground sections (tunnels); underground links; underground networks. Over the past ten years, more articles coupled with the network and the optimization of the ULS. Vernimmen et al. (2007) developed an underground tunnel connecting the left and right parts of Antwerp Port. Of all the researched about network design, the most concern is the location problem. ZHOU & ZHOU(2017) use the genetic algorithm to optimize the layout of the distribution route, considering the cost if time and input. Wentao & Yanhong( 2016) used the bi-level planning model to study the location selection of logistics nodes in the construction of underground logistics systems, taking into account both the interests of the logistics planning and decisionmaking departments and those of the customers. The scholars mostly used traditional simulation algorithms to solve the optimization problem of underground logistics networks, but most of them discuss the characteristics of ULS systems out of specific urban characteristics. They do not carry out case studies and design solutions in light of the actual situation of ULS. In the current stage, case studies using ULS are urgently needed. 2.2 strategic level issues of intermodal transportation This paper studies the design of underground logistics container transport multimodal transport system is an intermodal transportation plan. Caris et al. (2008) divided intermodal transportation plan problems into three levels by time horizons: strategic, tactical and operational planning. In the strategic level, decisions are found on a very long term (10–20 years). The location of terminals, the network configurations and the design and layout of a terminal are typically decisions were a large amount of capital is fixed for a long time and that are difficult to change(Macharis & Bontekoning, 2004). The decision makers are distinguished as : intermodal operators, network operators, terminal operators and drayage operators. The terminal operators take care of the transshipment operations from road to rail or barge, or from rail to rail or barge to barge.( Caris et al.,2008).In this paper，we stand for the terminal operator to make a strategic level plan of intermodal transportation. Meyer (1998) faces the design problem of a rail–rail terminal in a hub-and-spoke
system for the exchange of a maximum of six trains at a time. In addition, the terminal should be able to handle a limited volume of rail–road exchanges. Bontekoning (2000)research the terminal evaluation problem. Macharis et al.(2011) focus on the barge terminal location and the impact for the performance of the network. Li et al.(2015)considers both terminals and transport connections as an intermodal freight transport network. Meyer (1998) applied Dynamic computer simulation (SIMPRO) with Petrinet to determine required capacity for cranes and internal transport systems, and the most efficient arrival pattern of trains. Bontekoning (2006) develops a simulation model to perform a systematic comparison between various hub exchange facilities in an intermodal rail network. Li et al.(2015) proposes a receding horizon intermodal container flow control (RIFC) approach to address dynamic transport demands and traffic conditions in the network for intermodal freight transport planning problems 3. Problem description 3.1 A container operation progress in underground transport system What this system describes is the transportation process of an underground logistics system during the road-underground-sea transportation process. The focus is on underground logistics and connections with road and sea. Fig. 2 shows the process of transporting export containers through UCLS. The container is lifted by a gantry crane at the entrance of the tunnel and loaded on a vehicle. After a 30-kilometer trip along the rail in the tunnel, the vehicle slows down close to the buffer area and completely stops at the location exactly below the gantry crane at the exit. Then, the container is lifted by the gantry crane up to ground level and loaded on the truck. After being delivered to the storage area, the export container is finally transferred to the berth. The areas shown in Fig. 4 are the most important locations in the system where the decisions on which equipment or infrastructure to use are made. The decision sequence constitutes the programming of the UCLS.
Fig. 2 Process of transporting export containers through the UCLS. The total time for transporting a set of containers from one terminal subsystem to the berth near the other terminal subsystem is:
ts t 1 t 2 t 3 t 4 t 5 t 6
(1) Where, ts is the total duration of loading/unloading from the entrance of the underground tunnel to container ship; t1 is the loading duration of gantry crane at the entrance of the underground tunnel; t2 is the duration of vehicle travelling in the underground tunnel from the entrance close to the buffering area; t3 is the duration of vehicle slow down to stop in the buffering area; t4 is the unloading duration of gantry crane at the exit of the underground tunnel; t5 is the travelling duration of truck from the exit to the storage area; t6 is the container transship duration from the storage location to ship.
3.2 The decision set of the stages of the underground transport system According to Fig. 2, we divided the transport into several stages, each stage of the decision, constitute it a design for our system. 3.2.1. Loading/unloading area at the entrance of the tunnel The container is picked up by a gantry crane, which is the only option on this site. 3.2.2 Vehicle traveling area along the tunnel There are three types of vehicles that can be selected to carry containers. Automated guided vehicles (AGV), which are widely used in automated terminals, can improve the automation level of the system. A new railed vehicle powered by DC, which can be applied to an underground tunnel, was developed by a Mole Solution. There are two equipment operating modes: single run and group run. The mode of traveling singly is so flexible that it could reduce the pressure of the operation schedule. The transport sequence of the containers can be determined simply according to the ship's loading plan while the necessary safe distance between two vehicles will lower the density of vehicles in the tunnel. Traveling in groups is two linked vehicles traveling synchronously and delivering 4 TEU. 3.2.3. Buffer area in the tunnel This site is the bottleneck of the system. Only the vehicle stops completely, so the gantry container can aim at the container lock to lift the container to ground level. As a result, there is a risk of congestion in the buffer area, which is the bottleneck of the system. There are two alternatives, i.e., exiting directly or through a buffer area. In the former alternative, the safe distance should be long enough to ensure no collision at the exit. The latter is to set a buffer area at the exit extending from two to six lanes or rails. The containers could wait for be loaded/unloaded within the buffer area to avoid congestion. 23.2.4. Loading/unloading area at the exit of the tunnel
To avoid collisions with the wharf infrastructure (such as piles), the underground tunnel should be constructed at least 20 meters deep. There are two ways to exit to ground level: along a sloping tunnel or through a shaft. 3.2.5. Truck waiting area aboveground The last issue of this stage is the equipment operation mode at the exit. Loading/unloading points are set at the exit and the containers are lifted to the horizontal ground by rail gantry cranes. One option is to use the current operation mode, which is a single-trip-dual-spreader, of rail gantry cranes. To accelerate operation speed at the exit, another option is a round-trip-dual-spreader mode. The rail gantry crane lifts the containers from the vehicles in the underground tunnel, loads them on the trucks aboveground, lifts another container from the other trucks aboveground, and loads them on the vehicles in the underground tunnel. In this way, the rail gantry crane completes two loading and unloading cycles within one move while the vehicles in the underground tunnel undergo round-trip heavy traveling. Obviously, the mode improves the transportation efficiency of the system. 3.2.6. Container storage area After being loaded on the trucks aboveground, there are three possible options for the delivery of the containers: the container yard, a special yard behind the terminal yard, or a specialized central station for the UCLS. 4. Modelling Methodology 4.1 Model hypothesis The mode programming of UCLS is a complex process. To turn the abstract real problem into a mathematical model, some assumptions have been made as follows: 1. Standard container size is 20 or 40 feet. Containers to be excluded are 45 and 53 feet, overweight, reefer, and dangerous goods containers. 2. All equipment is operated in a normal situation, ignoring the possibility of failures or accidents. 3. Ensuring safe distances between transportation equipment in the underground tunnel. 4. Ignoring the space limitations of storage containers at the underground tunnel exit. 5. The time count begs from the moment the gantry crane at the entrance of the underground tunnel. 6. Ignoring the effects of the changes in vehicle volume in rails on operation velocity. 7. The system runs for 24 hours a day and 30 days a month. 8. Ignoring equipment depreciation. 4.2 Two-stage model In the first stage, you will need to make a decision-making alternative, build a 0-1
planning model, in order to reflect the dynamics of the model and then build a simulation model, to obtain the number of boxes that the system runs within the simulation period. 4.2.1 0-1 programming model each stage takes the available options at each site as the decision set. Accordingly, the programming of the UCLS is a multistage decision process. The multistage decision network is G=(V,E,T) with node V={vki}. k∈K, where K is the set of key sites. (Yunquan (2003))V= V1∪V2∪V3∪V4∪V5∪V6∪V7, where V1 is the set of equipment options. V1={v11}, where v11 represents the gantry crane. V2 is the set of underground tunnel vehicles and their operation mode options. V2={v21,v22,v23}, where v21 represents the AGV operating singly, which means that the AGV departs as soon as the containers are loaded. v22 represents the rail vehicle shift operating singly. v23 represents the rail vehicle operation in a group, which means that a vehicle group may depart only if all the containers have been loaded. V3 is the set of buffering infrastructure options. V3={v31,v32}, where v31 represents no buffer area and v32 represents a buffer extending from two to six lanes. V4 is the set of exit mode options. V4={v41,v42}, where v41 represents an exit through a shaft while v42 represents an exit along a sloping tunnel. V5 is the set of operating ways at the exit options. V5={v51,v52}, where v51 represents loading/unloading on one side of the gantry crane while v52 represents loading/unloading on both sides of the gantry crane. V6 is the set of storage location options. V6={v61,v62,v63}, where v61 represents the terminal yard, v62 represents establishing a station, and v63 represents establishing a yard behind the terminal. V7 is the set of options on the berth. V7={v71}， where v71 represents the berth. Arc set E={(vki,vk+1,j)} represents the selected Vk+1,j, as long as selecting Vki. The weigh set T={tkij} represents the duration from Vki to Vk+1,j.
Fig. 3 Multistage decision network of UCLS Parameters. tkij: Duration of transporting 4 TEU from vki to vk+1,j, min. fk+1,j: The monthly mean of initial cost of Vk+1,j, which is 1,000 yuan/month. hk+1: The energy consumption cost of Vk+1,j per minute, which is 1,000 yuan/month. Qk+1,j : The amount of Vk+1,j;The lower quantity limit of containers in TEU handled
by the UCLS. K: Set of key sites. V: Set of options at all sites. V+: Set of selected options. V-: Set of options to be selected. T: Set of durations, including stochastic parameters, between two sites. F: Set of monthly means of initial construction costs. H: Set of energy consumption factors. Q: Set of equipment amounts. Decision variables.
1，select vk 1, j xkij 0 ，otherwise For an underground logistic system plan program, the huge initial investment and the following operating costs are the critical factors for the system plan. Therefore, the objective function of this problem should model the cost. Under the limitation of delivering capacity, the UCLS is more efficient as more containers are delivered. Conventional methods for solving such optimization models is multistage programming. The first stage is to set up a program plan and the second stage is to find the optimal solution. As the linear-shaped underground logistic system presented in this paper is the simplest logistic system to program, there is no need to choose a route once the system has settled. Therefore, the objective function of this problem is molded by the converted initial investment and operating cost, which is a 0-1 integer nonlinear formulation, of each container. The volume of containers handled by the UCLS increases as more equipment are deployed, such as vehicles in the underground tunnel, gantry cranes. However, the more equipment used, the more will be the initial investment and energy consumption costs each month. The goal of UCLS programming is to balance the volume of containers and the cost of the whole system including initial investment and the operation cost. Therefore. per container cost is a suitable index to measure the balance. We propose the Lowest Cost per TEU of Initial Investment and Operating Cost (LCTIIOC). As different equipment and infrastructure have different designed life span, only the monthly mean of initial investment could be calculated in the objective function, which is marked as fk+1,j. The energy consumption costs are calculated by product of equipment working duration and its volume. Assume that the UCLS is running for T months without replacing equipment. Cost1 is the initial cost for T months, Cost2 is the energy consumption cost in T months, CT is the volume of containers handled in T months, Cp is per container cost: cost1 T ( f 11 f k 1, j xkij )
(2)
cost2 T (h11 (hk 1, j Qk 1, j ) xkij )
(3)
kK iI jJ
kK iI jJ
172800( Q11jx11j） jJ
CT T
t
(4)
x
kij kij
kK iI jJ
cost1 cost2 CT The formula is: (( f 11 h11) ( f k 1, j hk 1, j Qk 1, j ) xkij ) tkijxkij kK iI jJ kK iI jJ min 172800( Q11jx11j） CP
(5)
(6)
jJ
Subject to: 172800 t11jx11j jJ
Q
x
C j I
(7)
11j 11j
kK iI jI
The objective function (6) contains initial investment and the energy consumption costs per container. Subject to：
k 1 1, xkij xkli 0, k 2,3,,6 jI lI 1, k 7
xkij
1 k K
x
Vi V ,Vj V
i I j I kij
W
kK
xkij 0,1 k K, i I , j I
i I , j I
(8)
(9) (10) (11)
Constraint (8) ensures that there is a route from v11 to v71, which is a classical shortest path constraint. Constraint (9) ensures that only one option can be chosen at each transshipment stage. Constraint (10) ensures that at least one option is chosen at each transshipment stage during the whole transportation process. 4.2.2 The simulation model In order to determine the container volume through the underground tunnel under different hardware configurations, we have constructed a simulation model that brings the data obtained from the simulation experiment into the 0-1 programming model, so that we can make a strategic plan from the perspective of the terminal operator. The simulated equipment: gantry crane at the entrance of underground tunnel, the vehicles in the underground tunnel, gantry crane at the exit of underground tunnel and the trucks on ground. The simulated facilities: the loading position at the entrance of underground tunnel,
the travel section of underground tunnel, the buffer section of underground tunnel and the unloading position at the exit of underground tunnel. Taking exporting a container as an example, the processing rules are as follows: At the entrance of underground tunnel, if the container arrives first and the vehicle below does not arrive, the container will wait below the gantry crane for the vehicle. If the vehicle arrives and the container has not yet arrived, the vehicle waits at the loading point below the bridge for the containers. The container is loaded by the gantry crane onto the vehicle of the underground tunnel and then will be carried towards the exit of the underground tunnel. The constraint of this period is: the acceleration and speed of the vehicle does not exceed the maximum of the system and the minimum safety distance between the two vehicles. When the vehicle close to the buffer section of the tunnel, the speed should be gradually reduced to 0 till at the end of the buffer section. To avoid congestion, the lanes of the buffer zone should be extended. The vehicles enter the buffer lane in accordance with the lane with the smallest serial number. If the number of vehicles in the lane does not reach the maximum, the vehicle run into the buffer lane, or run into the buffer lane in the next order. When the vehicle reaches the end of the buffer end, the status of the front loading point need to be evaluated. If no container is being operated, then the vehicle move directly to the loading point; if there is a vehicle in front of the container being operated, the vehicle wait until the front vehicle departure. Containers are loaded and unloaded on the truck on ground, then placed in the container storage area and finally transported to berths for ship transport.
Fig.4 the flow chart of the simulation model 5. Case study To test the behavior of the methodology, a case study was conducted in a location near Jiading of Shanghai, where a container central station was set up in the suburbs of Shanghai to collect and distribute containers mainly from Jiangsu Province in order ease
downtown traffic congestion and air pollution.
Fig.5 The location of UCLS in this case The distance between the two ends of the tunnel was 35 km. The time to transport 4 TEU was calculated according to the methodology presented in Section 5.1, as well as to Liang Jian et al. (2013), Wang Qingbin (2014), Liang Jian et al. (2009), Li Feng et al. (2016), Zhang Ran (2016) and Shi Jianfeng et al. (2016), as shown in Table 1. 5.1. Time related parameter 5.1.1 Duration of loading/unloading at the entrance area A time window begins from the moment that a ground container carrying equipment arrives at the location below the rail gantry crane at the entrance of the underground tunnel.The expectation of the waiting time during which the loading/unloading is operated can be estimated from the rail gantry crane parameters (https://club.1688.com/article/58832562. htm). The variance is 1 ( Jian et al. (2009) ). 5.1.2 Traveling and buffering time through the underground tunnel In the deterministic case, to present the uncertainty of travel time, a three-point distribution is considered with one possible realization below E(t)x(0
There are no parameters for reference. The expectation of the loading/unloading time can be estimated from the parameters of the round-trip-dual-spreader rail gantry crane (https://club.1688.com/article/58832562.htm). As with the dual-spreader quay crane, after the container truck stops at the exact location below the quay crane, it takes the truck much time to reposition for connecting the container with the spreader. The adjustment lowers the efficiency of the dual-spreader quay crane. The theoretical loading/unloading time of the dual-spreader quay crane should be half of that of the single-spreader quay crane but the actual loading/unloading times of both the dualspreader quay and round-trip-dualspreader rail gantry cranes are 5/7 of that of the singlespreader quay crane ( Ran (2016)). The variance is 1(Tao (Tao) ). table1 The value and instruction of parameter tkij（unite：minute/4TEU） parameter
instruction
value
t111 t112 t113 t211 t212 t221 t222 t231 t232 t311 t312 t321 t322 t411 t412 t421 t422 t511 t512 t513 t521 t522 t523 t611 t621 t631
The duration of loading on the AGV The duration of loading on the single ULV The duration of loading on group ULVs AGV travelling duration AGV travelling duration The single ULV travelling duration The single ULV travelling duration Group ULVs travelling duration Group ULVs travelling duration duration from no lane widening buffer area to shaft exit duration from no lane widening buffer area to slope exit duration from lane widening buffer area to shaft exit duration from lane widening buffer area to slope exit The duration of loading on truck on one side at shaft exit The duration of loading on truck on both side at shaft exit The duration of loading on truck on one side at slop exit The duration of loading on truck on both side at slop exit The duration to terminal yard with one truck The duration to station with one truck The duration to yard behind the terminal with one truck The duration to terminal yard with two trucks The duration to station with two trucks The duration to yard behind the terminal with two trucks The duration from terminal yard to berth The duration from station to berth The duration from yard behind terminal to berth
8 8 11 71 71 38 38 38 38 20 18 11 10 12 7 8 5 30 6 15 30 6 15 5 10 7
t111,t112 and t113 represent the time period from elements of V1 to ones of V2:t111 is the time from v11 to v12, which represents the duration of loading/unloading 4 TEUs on the AGV;t112 is the time from v11 to v22 which represents the duration of loading/unloading 4TEUs on the single ULV; t113 is the time from v11 to v23 which represents the duration of loading/unloading 4TEUs on the group ULVs. t211, t212, t221, t222, t231 and t232 represent the time period from elements of V2 to ones of V3: t211 and t212 represent the duration of the
AGV travelling through the underground tunnel; t221 and t222 represent the duration of the single ULV travelling through the underground tunnel; t231 and t232 represent the duration of the group ULVs travelling through the underground tunnel. t311, t312, t321 and t322, represent the time period from elements of V3 to ones of V4:t311 represents the travelling duration to a shaft exit passing a buffering area without lane widening; t312 represents the travelling duration to a slope exit passing a buffering area without lane widening; t321 represents the travelling duration to a shaft exit passing a buffering area with lane widening; t322 represents the travelling duration to a slope exit passing a buffering area with lane widening. t411, t412, t421 and t422 represent the time period from elements of V4 to ones of V5:t411 represents loading/unloading 4 TEUs duration from vehicles in the underground tunnel to trucks on one side on ground of the shaft exit; t412 represents loading/unloading 4 TEUs duration from vehicles in the underground tunnel to trucks on both sides on ground of the shaft exit; t421 represents loading/unloading 4 TEUs duration from vehicles in the underground tunnel to trucks on one side on ground of the slope exit; t422 represents loading/unloading 4 TEUs duration from vehicles in the underground tunnel to trucks on both sides on ground of the slope exit. t511、t512、t521、 t522，t531 and t532 represent the time period from elements of V5 to ones of V6:t511 and t521 represent the duration of trucks travelling from the exit of the underground tunnel to the yard in a terminal; t512 and t522 represent the duration of trucks travelling from the exit of the underground tunnel to the yard in a special station; t513 and t523 represent the duration of trucks travelling from the exit of the underground tunnel to the yard behind the terminal. As there will be several routs for truck travelling on ground, the t511 and t521 have the same value. t512 and t522 and t513 and t523 are the same situation. t611,t621 and t631 represent the time period from elements of V6 to ones of V7:t611 represents duration of trucks carrying TEUs from the yard to berth in the terminal; t621 represents duration of trucks carrying TEUs from the yard in the special station to the berth of the terminal; t631 represents duration of trucks carrying TEUs from the yard behind the terminal to berth of the terminal. 5.2
Cost related parameters
The value of fk+1,j was calculated with the initial investment, lifespan, and the amount of equipment. There are three scenarios for the amount of equipment, as shown in Table 2. Table 2 Information on parameter hk+1,j and fk+1,j Equipment or
Nodes
infrastructure
hk+1,j Cost each Design High in¥/m In 103¥ ed life in year quantity
fk+1,j
Medium
Low
quantity
quantity
in ¥/Mon.
fk+1,j in ¥/Mon.
fk+1,j in ¥/Mon.
Gantry crane at the entrance v11
6.3
25000
30
5
347222.2
5
347222.2
5
347222.2
AGV
v21
52
5000
15
400
11111111
267
7416667
134
3722222
ULV
v22
26
800
20
614
2046667
409
1363333
205
683333.3
Group ULV
v23
26
1600
20
307
2046667
205
1366667
103
686666.7
No lane widened buffer area v31
0
596000 80
1
620833.3
1
620833.3
1
620833.3
lane widened buffer area
0
7450000 80
1
7760417
1
7760417
1
7760417
Gantry crane at the shaft exit v41
6.3
25000
30
14
1284722
10
1006944
8
868055.6
Gantry crane at the slop exit v42
6.3
25000
30
14
1409722
10
1131944
8
993055.6
Single Truck
v51
15
0
-
-
0
-
0
-
0
Double trucks
v52
20
0
-
-
0
-
0
-
0
Terminal yard
v61
15
0
-
1
0
1
0
1
0
station
v62
15
300000 80
1
312500
1
312500
1
312500
Yard behind terminal
v63
15
250000 80
1
260416.7
1
260416.7
1
260416.7
berth
v71
0
0
1
0
1
0
1
0
v32
-
Inf.: Ignore the quantity of truck according to the assumption that there are enough trucks. The initial investment of the existing infrastructures such as terminal yard and berth are assigned 0.
Detail cost calculation and converting the results to unified unit of measurement are being presented in Table 2, the converting unified unit data are put in the objective function. The objective function is formed by initial investments and operation costs. There are multiple optional nodes for one stage, also corresponding node’s cost are present in Table1 Table2. For v51 and v52, the drayage container truck represents the equipped facilities, no additional fixed asset investment required, therefore marked as fk+1,j=0. v61 as container yard and v71 as the quay berth are existing infrastructure, also marked as fk+1,j=0. v31 and v32 are optional infrastructure, illumination facilities, the both means of energy consumption could be treated as equal, therefore both options’ impact are the same, also marked as hk+1,j=0 in Table 2. The data at v61, v62 and v63 are the power consumed to v71 (berth) from each of mentioned nodes for an empty TEU, for a fully loaded container, a proper weight should be multiplied. Since the differences of design durable lifetime of variable equipment and infrastructure, each option’s initial investment costs are being apportioned to the corresponding design durable lifetime on monthly basis. Taking v62 as an example, the design durable lifetime is 80 years, initial investment cost is 300,000,000 RMB, therefore during the lifecycle, monthly cost is 312,500,000 RMB. Underground logistics vehicles investment could be ranged as low, medium and high by the quantity that deployed. Travelling tunnel cost is put in the data at v31 and v32. Gantry crane construction cost including its exit is put in the data at v41 and v42. Even though the same quantity of gantry cranes is deployed, construction cost could be varied due to the different exit modes. Therefore, fk+1,j data at v41 and v42 are different. Taking shaft exit at v41 as an example, gantry crane unit investment cost is 25000000, design durable lifetime is 30 years. In the high case, required gantry crane is 14 units. 5.3Results Due to the different amount of underground transport equipment, there will be different operating results. Increased delivery, the ability to transport more containers,
but there is also a greater risk of congestion, so different numbers of scenarios for equipment delivery will have different design options.
The Interval Time of Scenarios 308 306 304 302 300 298 296 AGV
ULV high
medium
ULV in group low
Fig.6 The interval Time of Scenarios After simulation, it can be seen that different transportation equipment in different situations, the time interval between the two completed tasks as shown in the figure, in the various scenarios of AGV, with the reduction of the amount of equipment, processing the amount of boxes less, so the interval between the completion of the task becomes larger. However, in the ULV and ULV in group scenarios, the medium scheme is the shortest time interval. Preliminary analysis suggests that uLV travel speed is faster than AGV caused. Table 3 The results of the underground transportation system Scenario High
Medium
Low
volume
TEU
solution
AGV
400
7970.7
v11→v23→v31→v41→v51→v61→v71
ULV
614
8380.2
ULV in group
314
8534.4
AGV
267
7676.4
ULV
409
8271
ULV in group
205
8529
AGV
134
6913.8
ULV
205
8314.2
ULV in group
103
8459.1
v11→v22→v31→v41→v51→v61→v71
v11→v23→v31→v42→v51→v62→v71
The table3 shows the vehicle volume parameters, the simulation of one month’s operation in three case of volume of vehicles and the corresponding solution. In the high scenario, if the AGV is used to delivery container in underground tunnel, the volume of
AGV will be 400, the ULV will be 614 and the ULV in group will be 314. The situation in medium and low cases is the same. From the results of tables 3, the options of AGV, setting buffering area with widening the lanes, loading/unloading containers on both sides are chosen in none of the scenarios. 6. Conclusions This paper investigates a road-underground-ocean container transport planning problem of strategic level for the terminal operator, which could be a potential solution for the urban traffic congestion. The behavior of an urban underground container transportation system is formulated from a container operation process perspective and an underground transportation system configuration decision, such as container carrying vehicles options, vehicles grouped options , buffering area lane . A two-stage model is established with dynamic characteristics. The first stage, a layout decision model is to minimize the cost per TEU. The second stage model is a simulation model. Given to the UCLS further development, the 2 main research fields as 1) Complete the cost calculation range, as the infrastructure and facility maintain cost 2) Set up more complicate system, as network structured UCLS
Acknowledgements This work is sponsored by National Natural Science Foundation of China (71471110), Shanghai Science & Technology Committee Research Project (16DZ1201402, 16040501500). We also thank anonymous referees and the editor-in-chief.
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High lights 1) This paper investigates an underground container transport planning problem for the terminal operation. 2) The process of operating a container with the underground system is analysed. 3) A two-stage model is established for the system design. 4) 0-1 programming and simulation models are applied in the problem.