Swap trailer transport, as an efficient freight organisation mode, is widely used in developed countries. There are many kinds of vehicle combination modes for swap trailer transport in foreign countries, such as truck and trailer; tractor, semi-trailer and tractor; semi-trailer and trailer and so on. Since the Ministry of Transport issued the notice on promoting the development of swap trailer transport in 2009, the swap trailer transport has received strong support and fewer institutional constraints. However, at the present stage, the mode of vehicle combination allowed by enterprises is still limited to tractor and semi-trailer. Therefore, this paper focuses on the tractor despatch, which is the most core issue in the organisation work of swap trailer transport in China.
Compared with trucks, swap trailer transport can achieve higher vehicle efficiency by free separation and combination of the power part and the cargo part [1, 2]. The academic community generally believes that the swap trailer routing problem is very complicated and it is an NP-hard problem. Some scholars think that the traditional vehicle routing problem (VRP) is only a special case of swap trailer transport organisation problem [3]. At present, the research of the international academic community on such issues is mainly reflected in three categories. The first problem is truck and trailer routing problem (TTRP). Some customer points can be serviced by either a truck trailer or a separate truck, whereas other customers can provide only freight services by trucks. Set the number of trucks and trailers which are known, and the constraint of vehicle’s capacity. The goal is to find the lowest cost vehicle route set, if the route is closed, and each customer point is provided only one freight service. Representative study of TTRP can be found in Villegas et al. [4]. The second problem is roll-on–roll-off VRP (RRVRP) and it stems from urban garbage transport activities. The garbage truck transports the empty car to the garbage collection point. After the car is full of garbage, the garbage truck transports the heavy car to the garbage centralised processing station for unloading and subsequent processing. The operation mode of the garbage truck is similar to that of the tractor train and the semi-trailer. The research results of this problem are represented by Bodin et al. and Baldacci et al. [5, 6]. The third problem is tractor and semi-trailer routing problem (TSRP). So far, there were two main research backgrounds for the TSRP issue in the academic world: short-distance distribution and long-distance truck transportation. Short-distance transportation application background for TSRP problems includes in-plant transportation and local transportation. Liang studied TSRP for internal material transportation of large steel companies [7]. Fan established a mathematical model aiming at minimising the operating cost of collecting and despatching operations to study the scheduling problem of the towed and hoisted tractors [8]. Zhang used the LPG refinery as the tractor station and applied the tractor and semi-trailer mode to LPG transport [9]. In view of the economies of scale of the TSRP application scenario and its ability to solve the multi-to-multi relationship, this application scenario is more optimistic and the research in this paper is based on TSRP.
Most of the research on the swap trailer transport organisation problem assumes that the vehicle travel time is a certain value. However, in reality, unexpected factors such as traffic congestion, road maintenance and traffic restrictions and vehicle damage will lead to uncertainty in driving time. Therefore, it is more suitable for practical applications to consider the tractor optimisation problem with uncertain driving time. Some scholars have considered the random factors into the optimisation model of VRP and proposed the VRP with stochastic travel time (VRPSTT) [10, 11]. However, VRP is aimed at one-to-multi scenarios. This paper introduces the uncertainty of driving time into TSRP and proposes TSRP with stochastic travel time (TSRPSTT). In the multi-to-multi scenario, problems of tractor optimisation are studied, and the influence of uncertainty on the optimisation results is analysed. The TSRPTST model is discussed in Section 2, and its objective function and constraints are explained. The model solving algorithm is introduced in Section 3. In Section 4, a case study is analysed. Finally, in Section 5, the main conclusions of this paper are summarised.
The problem scenario can be described as follows. The transport network node set
Traditional studies on VRP, TTRP or TSRP mostly focus on the minimum driving distance, fleet size or other traditional parameters. Scholars are increasingly inclined to incorporate environmental factors into organisational optimisation because of environmental problems. Moreover, one of the important indicators for evaluating the pilot scheme of enterprises’ swap trailer transport is CO2 emission in China. Therefore, this paper takes CO2 emission per ton kilometre as the objective function. The lower the index, the higher the efficiency of road freight transportation, and the smaller the impact on the environment.
Due to the increasingly stringent requirements of customers for the delivery time of goods, swap trailer transport organisations must consider how to complete the freight organisation within the specified time, named as time window. Therefore, it is assumed that there is a fixed time window [
In practice, traffic congestion, road maintenance and traffic restriction, vehicle damage and other accidental factors will lead to the uncertainty of driving time. Vehicle travel time
Since the scenarios in this paper involve random variables and belong to stochastic programming problem, Chance Constrained Programming (CCP) model is selected to solve the problem [12]. The CCP model is commonly used to analyse the stochastic decision-making system, and its constraints feature is that the chance-constrained conditions are established at least with a certain probability
Subject to
Drawing on the research experience of VRP, TTRP, TSRP and VRPSTT algorithm, a simulated annealing (SA) algorithm is used to solve TSRPSTT. The specific process is as follows:
Setting the initial number of tractors A feasible tractor line set Setting initial temperature Outer loop count variable Inner loop count variable A tractor route is selected from Metropolis criterion judgement. According to the first Metropolis criterion, the freight demand satisfaction rates of route schemes Computing Judgement of inner loop termination. If Judgement of outer loop termination. If the outer loop reaches the termination temperature Solution of the optimal number of tractors. If Solution of tractor route scheme. Bring the optimal number of tractors According to the tractor route scheme, the total fuel consumption
In case study, 11 cities in a certain area of China are selected as the swap trailer transport nodes, of which the city node 1 is the centre station and the remaining 10 cities are the semi-trailer distribution points. The optimal scheme of CO2 emission per ton kilometre, the number of tractors, total fuel consumption, cargo turnover and the ratio of tractor to trailer are calculated. According to the relevant information published by the Ministry of Transport on the Model Table of Fuel Consumption of Road Transportation Vehicles, the expected driving speed of tractor is 50 km/h, the fuel consumption of tractor with trailer is 32 L/(100 km) and the fuel consumption of tractor driving alone is 18 L/(100 km). The maximum driving time
Freight volume between urban nodes (unit: veh)
1 | 0 | 1 | 2 | 1 | 2 | 1 | 3 | 1 | 0 | 0 | 0 |
2 | 1 | 0 | 6 | 0 | 4 | 7 | 18 | 0 | 1 | 3 | 3 |
3 | 1 | 4 | 0 | 1 | 2 | 2 | 3 | 1 | 1 | 1 | 1 |
4 | 1 | 0 | 1 | 0 | 0 | 0 | 0 | 0 | 1 | 0 | 0 |
5 | 2 | 3 | 2 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 |
6 | 1 | 6 | 2 | 0 | 2 | 0 | 5 | 0 | 0 | 1 | 1 |
7 | 3 | 15 | 3 | 0 | 1 | 4 | 0 | 1 | 2 | 1 | 1 |
8 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 0 | 0 | 0 |
9 | 0 | 1 | 1 | 1 | 1 | 0 | 2 | 0 | 0 | 0 | 0 |
10 | 0 | 2 | 1 | 0 | 1 | 1 | 1 | 0 | 0 | 0 | 0 |
11 | 0 | 3 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 0 |
Distance between urban nodes (unit: km)
1 | 0 | 60 | 40 | 100 | 80 | 55 | 90 | 75 | 25 | 105 | 110 |
2 | 60 | 0 | 80 | 155 | 100 | 70 | 130 | 115 | 75 | 160 | 130 |
3 | 40 | 80 | 0 | 120 | 45 | 30 | 50 | 105 | 55 | 100 | 150 |
4 | 100 | 155 | 120 | 0 | 160 | 145 | 135 | 50 | 80 | 50 | 85 |
5 | 80 | 100 | 45 | 160 | 0 | 30 | 45 | 145 | 100 | 130 | 185 |
6 | 55 | 70 | 30 | 145 | 30 | 0 | 65 | 130 | 80 | 130 | 165 |
7 | 90 | 130 | 50 | 135 | 45 | 65 | 0 | 135 | 100 | 100 | 185 |
8 | 75 | 115 | 105 | 50 | 145 | 130 | 135 | 0 | 50 | 85 | 50 |
9 | 25 | 75 | 55 | 80 | 100 | 80 | 100 | 50 | 0 | 85 | 90 |
10 | 105 | 160 | 100 | 50 | 130 | 128 | 100 | 85 | 85 | 0 | 130 |
11 | 110 | 130 | 150 | 85 | 185 | 165 | 185 | 50 | 90 | 130 | 0 |
Time windows of semi-trailer distribution points in each urban node
1 | 7:00–19:00 | 5 | 7:30–13:00 | 9 | 9:30–16:00 |
2 | 9:00–15:00 | 6 | 9:30–14:00 | 10 | 10:00–18:00 |
3 | 8:30–17:00 | 7 | 8:00–17:00 | 11 | 8:30–15:30 |
4 | 8:00–17:30 | 8 | 9:00–16:30 |
Assuming that the travelling speed of the tractor obeys the orthogonal distribution
Solution results of tractor despatching schemes with different variances
Number of tractors | 47 | 49 | 58 | 75 | 103 |
14,123 | 14,264 | 15,405 | 17,716 | 22,500 | |
567 | 567 | 567 | 567 | 567 | |
4.23 | 4.11 | 3.48 | 2.69 | 1.96 | |
67.97 | 68.65 | 74.14 | 85.26 | 108.29 |
It is easy to see that when the travel time is fixed,
In this paper, the uncertainties of travel time are introduced into TSRP, and the TSRPSTT is proposed. The model proposed in this paper considers the travel time as a random variable, which describes the unexpected situation that the vehicle may encounter in the process of travel. The modified model can better reflect the actual scene and easier be applied in practice. In the scenario of multi-to-multi, the tractor despatching problem is studied, and the influence of uncertainty on the optimisation results is analysed. The conclusions are as follows. When the travel time is a fixed value, the optimal number of tractors is the least, the ratio of tractor to trailer is the highest and the emission of CO2 per ton kilometre is the smallest. With the increase of uncertainties in travel time, the number of tractors required increases, the ratio of tractor to trailer decreases, the CO2 emission per ton kilometre increases and the range becomes larger and larger. The freight turnover of the system changes little with the increase of travel time uncertainty. In addition, this paper makes a preliminary discussion on the organisation of swap trailer transport under the condition of random travel time. However, assuming that the speed obeys the orthogonal distribution is too idealised, the model can be further validated by the actual speed probability distribution according to the actual investigation in the future, so as to enhance the practicability of the model.