OPEN ACCESS
The current dropandpull (DP) transport process has many defects, including but not limited to the insufficient information sharing, the private ownership of vehicles and infrastructure, and the mismatch between vehicles and goods. Moreover, the hardware and software of existing freight stations fall short of the demand for DP transport. To solve these problems, this paper optimizes the design of the DP transport network based on shared freight station and the hubandspoke (HS) network. The freight stations were taken as the hubs, and the routes between supply/demand point and freight station are treated as spokes. On this basis, an optimization model was established to minimize the total cost of freight stations and maximize the force from freight stations on supply/demand points in the HS DP network. In addition, all the supply/demand points in the region are covered by the selected freight stations. The LINGO software was introduced to solve the established model. Taking a region in southern China for example, the proposed shared freight station design was compared with the traditional freight station design. The results show that the singlehub HS DP network obtained by the traditional design could meet the demand when the DP demand was relatively small; however, only the multihub HS DP network obtained by the shared freight station design could fulfil a large DP demand in an efficient manner. The research findings show that the shared freight station is the future of DP transport.
dropandpull (DP) transport, hubandspoke (HS) network, shared freight station, optimization
According to The General Administration of Quality Supervision, Inspection and Quarantine of the People’s Republic of China, dropandpull (DP) transport is defined as a transportation mode that two trailers are pulled in turn by the same tractor to their respective destinations. The DP transport can effectively improve the transport efficiency, reduce the transport cost and shorten the transport time.
This advanced transportation mode provides a desirable way to speed up logistics service and promote energy saving and emissions reduction. The benefits of the DP transport can be maximized if the vehicles, traffic network, and transport industry are mature and standardized. As a result, most large freight enterprises have adopted the DP transport in developed countries like the UK, the US and Japan.
In the DP transport system, the freight station serves as the center for the distribution and organization of goods. The operations of the freight station directly affect the transit, distribution and storage links in the system. Therefore, the site of the station must be selected properly, making the DP transport more organized, rational and comprehensive.
In recent years, the DP transport has made marked progress due to the advancement of the Internet technology, big data and cloud computing. The most prominent progress is the emerging DP transport network, which reflects the concepts of truck pooling, station renting and information sharing.
The efficiency of the DP transport network hinges directly on the planning and construction of the socalled shared freight station. This new type of freight station optimizes the cost and scope of resource transaction by sharing infrastructure, vehicles and information.
The current DP transport process has many defects, including but not limited to the insufficient information sharing, the private ownership of vehicles and infrastructure, and the mismatch between vehicles and goods.
Moreover, the hardware and software of existing freight stations fall short of the demand for DP transport. For example, many freight stations are located in wrong places, which are far from large goods distribution centers and loosely connected with support facilities.
To solve the above problems, this paper optimizes the design of the DP transport network based on shared freight station and the hubandspoke (HS) network.
2.1 Relevant studies on the DP transport
The existing studies on the DP transport mainly focus on three aspects: vehicle safety, route optimization and vehicle performance.
On vehicle safety, Vlk [1] divided driver operations into turning, braking and turningbraking, investigated how these operations affect the safety of the DP vehicle system, and concluded that DP vehicles are prone to accidents in the turning process. Godbole et al. [2] identified the influencing factors of the dynamic load of DP vehicles, including load level, position of mass center, suspension setting and damping of vibration components, and explored their impacts on the vertical motion of the chassis of the tractor. Salati et al. [3] carried out wind tunnel experiments on heavy duty trucks with trailer connectors on both front and rear axles, and studied the aerodynamic drag of European heavy duty trucks.
On route optimization, Wang and Chan [4] developed a multiobjective integer programming model for the DP transport of multiple goods, which optimizes the number of vehicles, finds the most effective routes, and minimizes the energy and operational costs. To satisfy different consumer demands, Villegas et al. [5] obtained multiple optimal routes through partitioned scheduling of DP services. Similarly, Derigs et al. [6] analyzed several vehicle routing problems (VRPs) with load constraint or time window, combined a heuristic algorithm with local search and neighborhood search to solve the problems, and verified the feasibility and accuracy of the combined method through example analysis. Mirmohammadsadeghi and Ahmed [7] probed into a tractor and trailer routing problem (TTRP) with random demand and time window. Galić et al. [8] introduced an informatized vehicle path optimization system to solve the distribution problem of fastmoving consumer goods (FMCGs), which trims the cost, reduces the number of depots, and enhances consumer satisfaction without increasing the number of distribution vehicles.
On vehicle performance, Vlk [9] simulated the response time and operation method of drivers on unbalanced vehicles. Pflug [10] conducted 3D simulations how different combinations of tractor and trailer change in lateral stability, damping performance and vibration frequency, under extreme driving conditions. Kim et al. [11] disclosed the mechanism of drag reduction by analyzing the precursor of the vehicle model, laying the basis for the design of new conditional random field (CRF) models and the improvement of aerodynamic performance of heavy vehicles.
2.2 Relevant studies on freight station design
There are relatively a few studies on the site selection and design of freight stations in the DP network. Based on minmax formulation, Horta et al. [12] designed a mathematical program that returns the optimal design of a crossdocking warehouse for justintime distribution. Rakesh and Adil [13] developed an algorithm that the lane depth, number of storage levels, lateral depth and longitudinal width of a 3D order picking warehouse, aiming to minimize the space occupation and handling cost. Melo et al. [14] put forward a multistage site selection model for freight stations. Zhong et al. [15] established a mathematical model to select the site of freight stations, solved the model with genetic algorithm (GA), and evaluated the optional sites through Arenabased simulation. Using VisSim program, Zhou et al. [16] built a traffic simulation model of DP transport terminal for coastal ports of China, and examined the traffic conditions and functional design of the terminal.
2.3 Relevant studies on vehicle sharing
Sharing is a hot topic in recent years. Numerous shared products have emerged, ranging from shared bicycles to shared power banks. The sharing frenzy has not spread to freight stations, because of the special locations, scale of equipment and difficulty in benefit allocation. Shared trailers are now available in only a few logistics enterprises. The previous research on vehicle sharing mainly focuses on bicycles and cars.
Based on the Petri net, Labadi et al. [17] created a discrete event model to evaluate the performance of public bicycle sharing systems. Yang et al. [18] studied the impact of public bicycle sharing systems on the original public transport network in urban areas. Considering the spatialtemporal variation of carsharing demand, Mohammadi and Shirouyehzad [19] developed a multigoods, multiperiod model based on the travelling salesman problem (TSP), and utilized the model to rebalance the bicycle sharing. Zhu et al. [20] optimized the depot locations with an approach to cover the spatialtemporal demand.
To sum up, there are only a few qualitative studies on the design of freight stations in the DP transport network, not to mention the site selection of shared freight stations. What is worse, the previous research mostly tackles the turnover of goods. In this paper, the research object is changed to the number of trailers, a more representative indicator of the DP transport.
For the above reasons, this paper puts forward a design of shared freight station based on the HS network, according to the TP demand in a region in southern China and in the light of the previous results on freight station design. Under the premise of sharing the infrastructure, a freight station design model was established to cover all supply and demand points with the minimal cost and maximal applied force. The model was solved by the LINGO software. Empirical results show that the shared freight station can be utilized more thoroughly than the traditional freight station.
3.1 TP transport network based on the HS network (HS TP network)
The HS network is a system of multiple nodes and routes. In this network, the goods must arrive at a central location (hub), i.e. the freight station, whether they are transported from different supply points (origins) or the same supply point (origin) to different demand points (destinations). The goods will be directly transported to the demand points from the freight station. The route between each supply/demand point and the freight station is considered as a spoke in the network. The HS network aims to concentrate the traffic flow and realize the economy of scale.
In the HS TP network, most nodes can achieve the transmission of personnel, goods and services through the interaction with one or several freight stations. Depending on the number of freight stations, the HS TP networks can be divided into singlehub HS TP network or multihub HS TP network.
In a singlehub HS TP network (Figure 1), each supply/demand point is connected to only one transfer station. The vehicles from a supply point can only travel to the demand points via the only transfer station. In this network, a transfer station serves several supply points or demand points. The same supply/demand point cannot be served by multiple transfer stations. The transfer station is semishared.
In a multihub HS TP network (Figure 2), each supply/demand point is connected to more than one freight stations. The vehicles from a supply point can travel through any of the freight stations as long as it is idle.
Figure 1. Singlehub HS TP network
Figure 2. Multihub HS TP network
This paper aims to optimize the design of shared transfer station(s), while satisfying the supply and demand of all points in the HS TP network.
3.2 Model of traditional freight station design in the HS TP network
3.2.1 Hypotheses
The following hypotheses were put forward before modelling traditional freight station design in the HS TP network:
(1) The freight station is selected from a limited number of alternatives.
(2) All supply/demand points must be connected to all freight stations, that is, the goods between any pair of supply and demand points must go through a freight station.
(3) The capacity, i.e. the maximum accommodatable number of trailers, of each freight station can satisfy the demand.
(4) The transport fee is the same in the region.
(5) The transfer between freight stations is not considered in the region.
(6) The total DP cost in the region includes the transfer station construction cost, the transfer station management cost and the transport cost.
3.2.2 Symbols and decision variables
The symbols used for the modelling are described below:
U is the total DP cost in the region; r is the transport fee; D_{ij} is the distance from supply point i to the alternative freight station j; D_{jk} is the distance from the alternative freight station j to the demand point k; X_{ij} is the number of trailers from supply point i to the alternative freight station j; Y_{jk} is the number of trailers from the alternative freight station j to the demand point k; g is the monthly management cost per alternative transfer station; S_{j} is the construction cost of alternative freight station j; M_{j} is the capacity of alternative freight station j; A_{i} is the number of trailers in the supply point i; B_{k} is the number of trailers in demand point k. Note that supply point and demand point refer to the origin and destination of goods in trailers, respectively.
The decision variables for the modelling are described: I={1,2,...,m}, J={1,2,...,n} and K={1,2,...,q} are the sets of supply points, alternative freight stations and demand points, respectively.
$P_{j}=\left\{\begin{array}{ll}{1} & {\text { If alternative freight station } j \text { is selected; }} \\ {0} & {\text { otherwis. }}\end{array}\right.$
3.2.3 Model construction
(1) Objective function
Cost minimization is a common objective in many VRPs [21]. The objective to minimize the DP cost in the region can be expressed as:
$\min U=\sum_{i=1}^{m} \sum_{j=1}^{n} r D_{i j} X_{i j}+\sum_{j=1}^{n} \sum_{k=1}^{q} r D_{j k} Y_{j k}+\sum_{i=1}^{m} \sum_{j=1}^{n} g X_{i j}+\sum_{j=1}^{n} P_{j} S_{j}$ (1)
Then, another objective can be established to maximize the force from the selected freight station acting on supply and demand points.
Based on logistics field theory, the field strength $\vec{E}_{\mathrm{ij}}$ of freight station j at supply point i can be described as:
$\vec{E_{i j}}=K_{j} \frac{Q_{j}}{D_{i j}^{2}} \vec{n}$ (2)
where, K_{j} is the logistics factor; Q_{j} is the scale of freight station j; $\vec{n}$ is the unit direction vector. The logsitics factor is an integrated weighted value of the various factors affecting the strength of the logistics field, namely, economic strength, geographic location and traffic conditions [22]. Here, the K_{j} value of each alterantive frieght station is computed by Jin’s method [23], based on the data in the statistical yearbook of the region. The scale of freight station equals the capacity of that station, M_{j}. The value of $\vec{n}$ is one, and the direction of $\vec{n}$ is the logsitics direction.
Then, the force from freight station j acting on supply point i can be calculated as:
$\vec{F}_{i j}=X_{i j} \vec{E}_{i j}=K_{j} \frac{X_{i j} Q_{j}}{D_{i j}^{2}} \vec{n}$ (3)
where, $\vec{n}$ is negligible, because direction is not considered in our research.
Drawing on the breakingpointring theory, the forces F_{1}, F_{2}, …, F_{n} from n freight stations P_{1}, P_{2}, ..., P_{n} in the region acting on supply point i satisfies:
$F=\operatorname{Max}\left\{F_{1}, F_{2}, \ldots, F_{n}\right\}$ (4)
Under ideal conditions, each supply point should select the freight station that exerts the largest force on it for goods transfer. However, this is impossible for all supply points, due to the limited capacity of each freight station per day. Therefore, this expectation was modified as maximizing the overall force F acting on all supply/demand points.
$\operatorname{Max} F=\sum_{i=1}^{m} \sum_{j=1}^{n} F_{i j}+\sum_{j=1}^{n} \sum_{k=1}^{q} F_{j k}$ (5)
where, F_{ij} is the force of freight station j acting on supply point i; F_{jk} is the force of freight station j acting on demand point i.
(2) Constraints
Each freight station should fully cover all supply/demand points. The coverage rate of freight stations was calculated based on the coverage computation for buses.
For a bus station, its coverage is equivalent to the size of the circle centering on the bus station with a suitable walking distance (generally 300 m) as the radius, or the size of the rectangle with the bus route as the horizontal line of symmetry and a suitable walking distance (generally 500 m) as the width. Thus, the coverage rate f of a bus station can be computed by:
$f=\frac{\sum\limits_{i=1}^{n}{{{a}_{i}}}}{E}$ (6)
where, n is the number of bus routes or bus stations; a is the coverage of each bus route or bus station; E is the total area of the region.
Similarly, the coverage of a freight station was considered a circle centering on the station. The coverage H_{j} of freight station j can be computed by:
$H_{j}=K_{j} * \pi C^{2}$ (7)
where, C is the economically feasible transport distance of the freight station (km).
The coverage rate α of a freight station should subjected to the following constraint:
$\frac{\sum_{j=1}^{n} P_{j} K_{j} \pi C^{2}}{E} \geq \alpha$ (8)
The other constraints are as follows:
${{A}_{i}}={{P}_{j}}{{X}_{ij}}\quad (j=1,2,\ldots \ldots n)$ (9)
${{B}_{k}}={{P}_{j}}{{Y}_{jk}}\quad (j=1,2,\ldots \ldots n)$ (10)
${{P}_{j}}{{M}_{j}}{{P}_{j}}\sum\limits_{i=1}^{m}{{{X}_{ij}}}\ge 0\quad (j=1,2,\cdots ,n)$ (11)
$\sum\limits_{j=1}^{n}{{{P}_{j}}}{{Y}_{jk}}{{B}_{k}}\ge 0\quad (k=1,2,\cdots ,q)$ (12)
$\sum\limits_{i=1}^{m}{{{X}_{ij}}}=\sum\limits_{k=1}^{q}{{{Y}_{jk}}\quad }(j=1,2,\cdots ,n)$ (13)
$\begin{align}& {{X}_{ij}}\ge 0,{{Y}_{jk}}\ge 0 \\& (i=1,2,\cdots ,m;j=1,2,\cdots ,n;k=1,2,\cdots ,q) \\\end{align}$ (14)
Formula (9) indicates that the trailers from a supply point can only travel through the same freight station; Formula (10) specifies that the trailers to a demand point should come from the same freight station; Formula (11) regulates that the total quantity of goods on the trailers arriving at freight station j should not surpass the capacity of that station; Formula (12) requires that the number of trailers from freight station j to demand point k must satisfy the demand at that point; Formula (13) means the number of trailers entering a freight station should equal that leaving the station; Formula (14) ensures that the parameters are nonnegative.
3.3 Model of shared freight station design in the HS TP network
In the HS TP network, the objective function of the shared freight station design can be expressed as:
$\begin{array}{l}{\operatorname{Min} U=\sum_{i=1}^{m} \sum_{j=1}^{n} r C_{i j} X_{i j}+\sum_{j=1}^{n} \sum_{k=1}^{q} r D_{i j} Y_{i j}} \\ {+\sum_{i=1}^{m} \sum_{j=1}^{n} a g X_{i j}+\sum_{j=1}^{n} b P_{j} S_{j}}\end{array}$ (15)
$\operatorname{Max}F=\sum\limits_{i=1}^{m}{\sum\limits_{j=1}^{n}{{{F}_{ij}}}}+\sum\limits_{j=1}^{n}{\sum\limits_{k=1}^{q}{{{F}_{jk}}}}$ (16)
where, a and b are the coefficients management cost and construction cost of a shared freight station, respectively.
The constraints of the model are as follows:
$\frac{\sum\limits_{j=1}^{n}{{{P}_{j}}}{{K}_{j}}\pi {{C}^{2}}}{E}\ge \alpha $ (17)
${{P}_{j}}{{M}_{j}}{{P}_{j}}\sum\limits_{i=1}^{m}{{{X}_{ij}}}\ge 0\quad (j=1,2,\cdots ,n)$ (18)
$\sum\limits_{j=1}^{n}{{{P}_{j}}}{{Y}_{jk}}{{B}_{k}}\ge 0\quad (k=1,2,\cdots ,q)$ (19)
$\sum\limits_{i=1}^{m}{{{X}_{ij}}}=\sum\limits_{k=1}^{q}{{{Y}_{jk}}}\quad (j=1,2,\cdots ,n)$ (20)
$\begin{array}{l}{X_{i j} \geq 0, Y_{j k} \geq 0} \\ {(i=1,2, \cdots, m ; j=1,2, \cdots, n ; k=1,2, \cdots, q)}\end{array}$ (21)
$A_{i}\sum_{j=1}^{n} P_{j} X_{i j}=0 \quad(i=1,2, \ldots, m)$ (22)
Formula (22) indicates that the trailers from each supply point must all travel through a shared freight station. The other constraints are the same as those of the model of traditional freight station design in the HS TP network.
3.4 Model solving
The software LINGO was selected to solve the established model. LINGO is a highly specialized package for solving optimization problems. With a complete set of solving programs and dozens of internal functions, the software can solve both linear and nonlinear equations, and support integer programming, including 01 integer programming (i.e. the decision variables can be integers). In addition to convenience and flexibility, LINGO boasts a simple and intuitive input model, timely error prompts and fast execution of commands. The software can exchange data easily with Excel, databases or other software. The model was solved in three steps: Converting the multiobjective problem into a singleobjective problem (transforming objective function (1) into a constraint); converting the model into LINGO language; substituting the parameters to solve the model.
China has the largest highway freight market in the world, which is supported by an extremely complex highway network. However, there is ample room to improve the transport network. Therefore, a region of southern China was selected for empirical analysis.
4.1 Empirical analysis on the model of traditional freight station design in HS TP network
In the selected region, there are 6 supply points, 9 alternative freight stations and 6 demand points. Several alternative freight stations need to be selected for actual transport. The data on all the nodes in the HS TP network are listed in Tables 15 below.
Table 1. Capacity (10,000 vehicles/month), construction cost (RMB 10,000 yuan), logistics factor of each alternative freight station

Station 1 
Station 2 
Station 3 
Station 4 
Station 5 
Station 6 
Station 7 
Station 8 
Station 9 
Capacity 
2.4705 
6.722 
1.5185 
4.4445 
1.1575 
3.3335 
2.148 
2.222 
5.5555 
Construction cost 
2,000 
3,000 
1,500 
2,000 
2,000 
500 
500 
5,000 
600 
Logistics factor 
0.94 
2.04 
0.62 
2.29 
0.81 
1.24 
0.65 
1.99 
1.35 
Table 2. Supply volume of each supply point (10,000 vehicles/month)

Supply point 1 
Supply point 2 
Supply point 3 
Supply point 4 
Supply point 5 
Supply point 6 
Supply volume 
2.000 
1.61 
1.311 
1.421 
0.7 
2.230 
Table 3. Demand volume of each demand point (10,000 vehicles/month)

Demand point 1 
Demand point 2 
Demand point 3 
Demand point 4 
Demand point 5 
Demand point 6 
Demand volume 
1.5305 
0.073 
0.828 
0.709 
0.6335 
1.6775 
Table 4. Distance from supply point to alternative freight station (km)

Station 1 
Station 2 
Station 3 
Station 4 
Station 5 
Station 6 
Station 7 
Station 8 
Station 9 
Supply point 1 
342.4 
99.2 
226 
199.5 
458.9 
149 
271.8 
439 
79 
Supply point 2 
736.8 
534.2 
613 
320.5 
39 
540 
204 
53.4 
483 
Supply point 3 
122 
454 
204 
627.7 
750 
334 
652 
803 
498.1 
Supply point 4 
335 
124 
163.1 
266 
574 
152.5 
300.4 
457 
150 
Supply point 5 
318.2 
103.5 
198 
256 
484 
132 
325 
465 
97.1 
Supply point 6 
582 
321 
451 
395 
651.6 
369 
460 
612 
261 
Table 5. Distance from alternative freight station to demand point (km)

Demand point 1 
Demand point 2 
Demand point 3 
Demand point 4 
Demand point 5 
Demand point 6 
Station 1 
673.6 
454 
330 
622 
390.2 
320 
Station 2 
477.2 
248 
184 
225.2 
163.6 
165 
Station 3 
612 
337 
203.2 
303.1 
272.3 
204.5 
Station 4 
220 
90.4 
344 
201 
134 
243 
Station 5 
134 
274.2 
563 
349 
404 
455 
Station 6 
525 
295 
276 
271.8 
207.3 
220.4 
Station 7 
265 
131 
311 
175.9 
220 
282 
Station 8 
112 
150 
452 
327 
358 
426 
Station 9 
416 
194.7 
199.9 
217 
144 
140 
In light of the above results, alternative freight stations 2, 3, 8 and 9 were selected for the transport services. Because all goods from the supply points only pass through one freight station, the established network is a singlehub HS DP network. Then, the supply and demand volumes of the supply/demand points were increased (Tables 7 and 8) and substituted into the model of traditional freight station design in HS TP network. No feasible solution was obtained. In this case, the singlehub HS DP network can no longer satisfy the demand, and should be replaced with a multihub network.
Table 6. Calculation results of the model of traditional freight station design
Variable 
Value 
Variable 
Value 
P(2) 
1.000000 
X(5,9) 
0.7000000 
P(3) 
1.000000 
X(6,9) 
2.230000 
P(8) 
1.000000 
Y(2,4) 
0.7090000 
P(9) 
1.000000 
Y(2,5) 
0.7120000 
X(1,9) 
2.000000 
Y(3,3) 
1.311000 
X(2,8) 
1.610000 
Y(8,1) 
1.537000 
X(3,3) 
1.311000 
Y(8,2) 
0.7300000E01 
X(4,2) 
1.421000 
Y(9,6) 
4.930000 
Total cost RMB 130.92 million yuan 
Table 7. Supply volume of each supply point (10,000 vehicles/month)

Supply point 1 
Supply point 2 
Supply point 3 
Supply point 4 
Supply point 5 
Supply point 6 
Supply volume 
2.1015 
2.221 
1.5135 
1.706 
0.984 
2.569 
Table 8. Demand volume of each demand point (10,000 vehicles/month)

Demand point 1 
Demand point 2 
Demand point 3 
Demand point 4 
Demand point 5 
Demand point 6 
Demand volume 
1.5305 
1.6295 
0.728 
0.609 
1.3335 
1.3775 
4.2 Empirical analysis on the model of shared freight station design in HS TP network
The model of shared freight station design in HS TP network was applied under the supply and demand volumes in Tables 7 and 8. It is assumed that a and b, the coefficients management cost and construction cost of a shared freight station, are both 1. Then, the following results were obtained through calculation (as shown in Table 9).
Table 9. Calculation results of the model of shared freight station design
Variable 
Value 
P(2) 
1.000000 
P(3) 
1.000000 
P(8) 
1.000000 
P(9) 
1.000000 
X(1,9) 
2.101500 
X(2,8) 
2.221000 
X(3,3) 
1.513500 
X(4,2) 
1.706000 
X(5,2) 
0.099 
X(5,9) 
0.8850000 
X(6,9) 
2.569000 
Y(2,4) 
0.6100000 
Y(2,5) 
1.195000 
Y(8,1) 
1.530000 
Y(8,2) 
0.6910000 
Y(3,3) 
1.513500 
Y(9,2) 
0.9385000 
Y(9,5) 
0.1339000 
Y(9,6) 
4.483100 
Total cost 
RMB 156.35 million yuan 
Therefore, alternative freight stations 2, 3, 8 and 9 were selected for transport services.
4.3 Comparison between traditional and shared freight station designs
The flows of goods in the traditional and shared freight station designs are illustrated in Figures 3 and 4, respectively. It can be seen that the shared design processed 14,250 (7.14%) more trailers and incurred RMB 769.5 yuan (9.83%) fewer total cost of shared freight station per vehicle than the traditional design.
Figure 3. The flow of goods in the traditional freight station design
Figure 4. The flow of goods in the shared freight station design
Through the above modelling and analysis, it is concluded that, in the HS TP network, the shared freight station design makes better use of freight stations than the freight station design in HS TP network in the same region. The research results show that shared freight station is the future of TP transport. The future research will further explore the freight station design from the following aspects: the informatization and profit distribution of shared distribution station; the operation of the shared trailer; the functions of demand points.
This work is supported by Scientific Research Project of Hunan Provincial Department of Education: Research on the TruckCargo Matching in Highway DropandPull Transport Based on "Internet +" (Grant No.: 18C1566).
LINGO solution for the nonshared dropandpull stations in hubandspoke networks
[OBJ]MAX=@SUM(ROUTE1(I,J):(1/(C(I,J)^2))*P(J)*Q(J)*X(I,J）))+@SUM(ROUTE2(J,K):(1/(D(J,K)^2))*P(J)*Q(J)*Y(J,K));
@SUM(ROUTE1(I,J):T*P(J)*C(I,J)*X(I,J)+g*P(J)*X(I,J))+@SUM(ROUTE2(J,K):T*P(J)*D(J,K)*Y(J,K))+@SUM(WAREHOUSES(J):P(J)*U(J))<=Z;
@SUM(WAREHOUSES(J):P(J)*K(J)*3.14*40000/179770)>= α;
@FOR(WAREHOUSES(J):A(I)=P(J)*X(I,J));
@FOR(WAREHOUSES(J):B(k)=P(J)*Y(J,K));
@FOR(WAREHOUSES(J):P(J)*M(J)>=(@SUM(FROM(I):P(J)*X(I,J))));
@FOR(TO(K):@SUM(WAREHOUSES(J):P(J)*Y(J,K))>=B(K));
@FOR(WAREHOUSES(J):@SUM(FROM(I):X(I,J))=@SUM(TO(K):Y(J,K)));
@FOR(ROUTE1(I,J):X(I,J)>=0);
@FOR(ROUTE2(J,K):Y(J,K)>=0);
@FOR(WAREHOUSES(J):@BIN(P(J)));
@FOR(WAREHOUSES(J):P(J)=@IF(@SUM(FROM(I):X(I,J))#NE#0,1,0));
END
LINGO solution for the shared dropandpull stations in hubandspoke networks
[OBJ]MAX=@SUM(ROUTE1(I,J):(1/(C(I,J)^2))*P(J)*Q(J)*X(I,J）))+@SUM(ROUTE2(J,K):(1/(D(J,K)^2))*P(J)*Q(J)*Y(J,K));
@SUM(ROUTE1(I,J):T*P(J)*C(I,J)*X(I,J)+g*P(J)*X(I,J))+@SUM(ROUTE2(J,K):T*P(J)*D(J,K)*Y(J,K))+@SUM(WAREHOUSES(J):P(J)*U(J))<=Z;
@SUM(WAREHOUSES(J):P(J)*K(J)*3.14*40000/179770)>= α;
@FOR(WAREHOUSES(J):P(J)*M(J)>=(@SUM(FROM(I):P(J)*X(I,J))));
@FOR(TO(K):@SUM(WAREHOUSES(J):P(J)*Y(J,K))>=B(K));
@FOR(WAREHOUSES(J):@SUM(FROM(I):X(I,J))=@SUM(TO(K):Y(J,K)));
@FOR(ROUTE1(I,J):X(I,J)>=0);
@FOR(ROUTE2(J,K):Y(J,K)>=0);
@FOR(WAREHOUSES(J):@BIN(P(J)));
@FOR(WAREHOUSES(J):P(J)=@IF(@SUM(FROM(I):X(I,J))#NE#0,1,0));
@FOR(FROM(I):A(I)=@SUM(WAREHOUSES(J):P(J)*X(I,J)))；
END
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