Transportation structural optimization based on the evaluation of comprehensive transportation efficiency

Abstract

China is a large road transport country as its logistics costs account for 18% of GDP. In order to further reduce logistics costs, it is necessary to optimize the energy-saving and efficient comprehensive transportation structure in China. In this paper, we analyze the characteristics of comprehensive transportation efficiency evaluation, then based on data envelopment analysis (DEA), we select a fixed return method to scale CCR model and a variable return BCC model to establish a comprehensive transportation efficiency evaluation model to evaluate comprehensive transportation efficiency. we select comprehensive transportation efficiency evaluation indicators as a combination of the input-output evaluation indicator system. Input indicators include energy consumption, number of employees, and mileage value, and output indicators are converted turnover; and finally We build a comprehensive transportation structure optimization model based on the linear programming method, the minimum comprehensive redundant input under the transportation efficiency evaluation as the objective function, and we want to take the unit GDP transportation energy consumption intensity drop by 15% in this way; Finally, we analyze the transportation structure of Liaoning Province in China, respectively calculate the input and output index datum and carry out DEA efficiency evaluation analysis. The results show that the energy intensity of road transportation is much higher than other two modes of transportation, and the efficiency of road transportation is relatively low.

Keywords

Transportation efficiency evaluation structural optimization

1. Introduction

Scientific and comprehensive transport structure can reduce transport cost, improve transport efficiency and upgrade the overall level of development of the transportation. At the same time, it is of great significance to protect the environment in the energy saving and emission reduction. There are large differences in cost, profit and energy consumption among different transportation modes, such as high cost and low efficiency of long-distance transportation by road transportation. China is a large road transport country, roads and railways accounted for 79.3% and 7.9% respectively of the freight transport in 2017.

The Chinese motor vehicle environmental management reported that diesel trucks accounted for only 7.8% of the national car ownership, but the oxynitride emission of diesel trucks accounted for 57.3% of the total, and the emission of particulate matter accounted for 77.8% in 2017. And research shows that the energy consumption and pollutant emission per unit freight turnover of railway are only 1/7 and 1/13 of those of highway. The ratio of railway freight and road is 1:4.5 in the east and 1:5 in the central and western regions (2018). So there is more room for adjustment in comprehensive transport structure in China, and recently, researchers have focused on this field. In terms of comprehensive transportation efficiency evaluation research, the United States issued “the Land Comprehensive Transportation Efficiency Act” in 1991to effectively meet the needs of social and economic development. European and American countries usually adjust the transport structure on the basis of the principle of “construction first, then integration”, so that it can meet the actual needs of social development. That means transportation structure optimization can be realized through policy and technical adjustment.

It is essential to establish an effective network evaluation method in transportation system. Jin et al. [11] put forward the construction of comprehensive transportation system, namely the integration of transportation; Lu et al. [16] systematically analyzed the characteristics, functions and composition of the transportation system. And the external and internal factors of structural dynamic optimization of the transportation system are researched, and further depiction is discussed from four aspects: acquirement, technology, fund, quality and environment respectively, and the source originated from optimization dynamic of transportation system; Franco [7] analyzed a spatial general equilibrium model of a closed monocentric city with two transport modes and proposed that improving welfare and promoting more compact urban space can be achieved by parking reforms at the CBD; Gupta et al. [9] formulated an integrated multi-objective optimization model for an extended capacitated sustainable transportation problem in a coal mining industry by using the analytic hierarchy process (AHP) and data envelopment analysis (DEA) techniques, and presented a fuzzy interactive optimization approach; After that, Boulaksil et al. [3] studied nano stores by analyzing data, conducting a cluster analysis, and describing their business environment with a focus on their order behavior, which may help organize transportation toward nano stores in a fundamentally different way; Ban et al. [1] established an economic equilibrium model to describe the equilibrium state of a transportation system composed of a single driver and an electronic ride-hailing service provider (e-HSP); Ye et al. [27] presented the motivation of using MPC for TSC and how MPC-based TSC approaches are implemented to manage and control the dynamics of traffic flows both in urban road networks and freeway networks; Then, Cao et al. [4] proposed that new-generation large-scale high-speed railway station begins to transit from an integrated plane transportation system to an integrated three-dimensional transportation system, to fulfill station-city integration, to realize “zero distance” for passenger transfer, “seamless” logistic connection and “transportation service integration”; Beheshtian et al. [2] put forward a network management plan and analyzed how network-wide use support MaaS for road, and how such markets can be developed; Yang et al. [26] established a programming model to improve the system’s sustainable transportation policy which aimed to minimize the carbon dioxide emissions of the system by optimizing two types of policies (i.e., a shipping network design policy and a toll policy) simultaneously and proposed a local optimization algorithm to solve the abovementioned model; Lopez-Ospina et al. [15] proposed an integrated transportation and location optimization model for designing logistic networks through using a hybrid iterative heuristic based on a genetic algorithm and a constrained multinomial logit.

As for transportation efficiency and transportation efficiency evaluation: Zhang and Liu [28] proposed a fuzzy evaluation (appraisal) system of municipal transportation efficiency, and through case analysis, proposed a distribution combining analytic hierarchy processï¼ˆAHPï¼‰and different weight; Wang [24] proposed a hierarchical programming model with finite discrete upper-level decision variables and a relaxation model of mixed integer linear programming to study the influence of speed cost on network efficiency; Kotegawa et al. [12] used topological structures of service networks to examine trade-off between efficiency metrics that established among the passenger, airline, and air navigation service provider perspectives; Meanwhile, Qin and Ni [18] proposed a quantitative efficiency evaluation method for transportation network; Zhang et al. [29] presented a quantitative transportation network efficiency measure and found that different roads should be set different maintenance time points in terms of the retention capacities of the roads; Wu et al. [25] proposed that DEA can be used to measure transportation system efficiency about energy and environment for sustainable development in China, Kuang [13] constructed BBC model and super-cross efficiency model by using DEA theory to calculate and evaluate comprehensive efficiency, pure technical efficiency and scale efficiency; He et al. [10] obtained that Q-H method could reflect the influence of network structure, traffic demand and user route choice behavior on transportation network efficiency well, and through the analysis of the network efficiency calculated by Q-H method, it can get a conclusion that a specific appropriate demand existed in the given transportation network; Liu et al. [14] established a mathematical model to analyze energy loss and energy efficiency of every component of the crude oil pipeline transportation, and finally concluded that the total oil transportation cost and the energy loss are significantly better in the effective utilization; Last year, Tang et al. [22] proposed a parallel slacks-based measure model to measure transportation efficiency; Resat and Turkay [19] presented a multi-objective mixed-integer programming problem including different objective functions, such as total transportation cost, travel time and CO2 emissions, then, summarized the sensitivity analysis of proposed mathematical models with pre-processing constraints for decision; Gheisariha et al. [8] proposed an enhanced multi-objective harmony search (EMOHS) algorithm and a Gaussian mutation to solve the flexible flow shop scheduling problems with sequence-based setup time, transportation time, and probable rework.

Zhou et al. [30] proposed that considering the whole travel process and the impedances of various ways, whether to cancel bus routes when OD demand is distributed on the network parallel to urban rail transit, travel cost and ticket price should be comprehensively considered; Cui and Li [6] proposed a new model-three-stage virtual frontier DEA to evaluate transportation energy efficiencies; Coogan et al. [5] proposed a control approach adjusting time-of-day signaling plans based on a prediction of future traffic flow; Tang et al. [22] proposed a hierarchical Bayesian network model (BNM) to quantitatively evaluate the resilience of urban transportation systems. Based on the full consideration in optimizing the structure of the transportation efficiency and the characteristics and requirements, Shen and Wei [20] put forward an efficiency evaluation method of integrated transport on the basis of DEA to set up evaluation index system and built the transportation structure optimization model.

In China, the researchers optimizing the comprehensive transportation structure mainly focus on the passenger or cargo or some kind of mode of transportation structure optimization nowadays and rarely consider the energy factors in the transportation optimization model; it is necessary to further study the accuracy and universality of the evaluation index system. Considering the characteristics of transportation efficiency and structural optimization, and this paper puts forward a evaluation method of comprehensive transportation efficiency considering the energy factors based on DEA to establish an evaluation index system , and then build a transportation structure optimization model. Finally, we combined with the example of Liaoning Province to conduct an empirical study.

2. Comprehensive transportation efficiency evaluation and structural optimization

2.1 Comprehensive transportation efficiency evaluation

Comprehensive transportation efficiency is based on the existing technical and economic conditions. We can make appropriate resource input for comprehensive transportation to form an efficient production and operation organization that can meet the needs of economic development and transportation.

The integrated transportation system is composed of five transportation modes, and the supply-demand relationship of the integrated transportation structure is in dynamic balance. The improvement of comprehensive transportation efficiency depends on the improvement of the supply conditions of the comprehensive transportation structure. The dynamic balance of supply and demand always affects the improvement of comprehensive transportation efficiency. Through comprehensive transportation efficiency evaluation, we can evaluate whether the operation of the comprehensive transportation system and its structure are reasonable and efficient.

2.2 Comprehensive transportation structure optimization

Many factors affect the optimization of the integrated transportation structure, such as economic level, natural conditions, transportation policies, and technological level. Constructing a coordinated comprehensive transportation structure can improve resource utilization efficiency, reduce energy consumption, and reduce environmental pollution.

We can start with the optimization of the integrated transportation structure from two aspects. One is the optimization of various transportation methods and their internal elements, and the other is the optimization of the entire transportation system and other systems.

3. Comprehensive transportation efficiency evaluation and structure optimization model based on DEA and linear programming

3.1 Comprehensive transportation efficiency evaluation method based on DEA

In the data envelopment (DEA) method, there are multiple evaluation objects, namely the decision-making unit (DMU). The unit of each indicator data is different, for example: ten thousand tons, kilometers and other units. The weights of input-output variables in the data envelopment analysis model are objective and fair, and their weights do not need to be pre-set, and the optimal weights are automatically generated, regardless of preference.

We evaluate the comprehensive transportation efficiency by the data envelopment method to obtain the input resource utilization efficiency of each transportation mode, and provide guidance for improvement and optimization. The traditional and representative evaluation models in DEA method are CCR and BCC models. We use the CCR model to evaluate the overall efficiency of the decision-making unit, that is, to evaluate the overall effectiveness of scale efficiency and pure technical efficiency; We use the BCC model to evaluate the pure technical efficiency and scale efficiency of the decision-making unit. We select the combination of fixed return to scale CCR model and variable return BCC model to evaluate the overall efficiency, pure technical efficiency and scale efficiency of comprehensive transportation.

3.1.1 DEA model of fixed compensation (CCR)

We establish the CCR model to evaluate the overall effectiveness of the decision-making unit. The process of establishing the model is as follows:

There are n decision-making units, and each decision-making unit has m inputs and s outputs;

$x_{ij}$ is the total input of the j-th decision-making unit to the i-th, $x_{ij}>0$ ; $y_{rj}$ is the j-th decision-making unit for the r-th kind total amount, $y_{rj}>0$ ; $v_{i}$ is the right of the i-th input; $u_{r}$ is the right of the r-th output; among them, $j=1,2,\ldots,n$ ; $i=1,2,\ldots,m$ ; $r=1,2,\ldots,s$ ; That is: $X_{j}=\left({x_{1j},x_{2j},\ldots,x_{mj}}\right)^{T}$ ,

$\displaystyle Y_{j}=\left({y_{1j},y_{2j},\ldots,y_{sj}}\right)^{T},$ $\displaystyle V=\left({v_{1},v_{2},\ldots,v_{m}}\right)^{T},$ $\displaystyle U=\left({u_{1},u_{2},\ldots,u_{s}}\right)^{T},$

Then, the efficiency evaluation index of decision-making unit j is

$\displaystyle h_{j}=\frac{\sum{{}_{r=1}^{s}u_{r}y_{rj}}}{\sum{{}_{1=1}^{m}v_{i% }x_{ij}}}.$

When $h_{j}\leqslant 1$ , evaluate the efficiency of the first $k\left({1\leqslant k\leqslant n}\right)$ decision-making unit and regard the efficiency index as the target. We build the CCR model as follows:

$\displaystyle\left({\overline{P}_{CCR}}\right)\left\{{s.t.{\begin{array}[]{c}{% \max\frac{U^{T}Y_{k}}{V^{T}X_{k}}}\\ {\frac{U^{T}Y_{j}}{V^{T}X_{j}}\leqslant 1,j=1,2,\ldots,n}\\ {V\geqslant 0}\\ {U\geqslant 0}\\ \end{array}}}\right.$ (1)

We can get the equivalent linear program after using Charness-Cooper conversion:

$\displaystyle\left({P_{CCR}}\right)\left\{{s.t.\begin{array}[]{c}{\max v^{T}Y_% {k}}\\ {\omega^{T}X_{j}-v^{T}Y_{j}\leqslant 1,j=1,2,\ldots,n}\\ {\omega^{T}X_{k}=1}\\ \omega\geqslant 0\\ v\geqslant 0\\ \end{array}}\right.$ (2)

After dual transformation of $\left({P_{\textit{CCR}}}\right)$ , we get:

$\displaystyle\left({H_{1}}\right)\left\{{s.t.{\begin{array}[]{c}{\min\xi}\\ {\sum{{}_{j=1}^{n}X_{j}\lambda_{j}\leqslant\xi X_{k}}}\\ {\sum{{}_{j=1}^{n}Y_{j}\lambda_{j}\geqslant Y_{k}}}\\ {\lambda_{j}\geqslant 0,j=1,2,\ldots,n}\\ \end{array}}}\right.$ (3)

Add the slack variable $t^{-}$ and the remaining variable $t^{+}$ , and convert $\left({H_{1}}\right)$ to a standard form:

$\displaystyle\left({H_{\textit{CCR}}}\right)\left\{{s.t.{\begin{array}[]{c}{% \min\xi}\\ {\sum{{}_{j=1}^{n}X_{j}\lambda_{j}+t^{-}=\xi X_{k}}}\\ {\sum{{}_{j=1}^{n}Y_{j}\lambda_{j}-t^{+}=Y_{k}}}\\ \lambda_{j}\geqslant 0,j=1,2,\ldots,n\\ t^{-}\geqslant 0\\ t^{+}\geqslant 0\\ \end{array}}}\right.$ (4)

Among them, the value of $\xi$ represents the relative efficiency of DMU-k. The value of $\lambda$ is the combined weight of DMU-k. $t^{-}$ and $t^{+}$ respectively represent redundant input and insufficient output. Suppose the optimal solution of is $\xi^{\ast}$ , $t^{-\ast}$ , $t^{+\ast}$ , $\lambda^{\ast}$ , the analysis is as follows:

If $\xi^{\ast}\leqslant 1$ , DMU-k is non-DEA effective, it means that the proportion of corresponding indicators should be adjusted to obtain better benefits. If $\xi^{\ast}=1$ , $t^{-}$ and $t^{+}$ are not equal to 0, DMU-k is weak DEA valid. If $\xi^{\ast}=1$ , $t^{-}$ and $t^{+}$ are all equal to 0, DMU-k is DEA valid. $\frac{1}{\xi^{\ast}}\sum{{}_{j=1}^{n}\lambda_{j}^{\ast}=1}$ , it means that the scale benefit of DMU is unchanged, and if the production conditions are unchanged, n times of input can obtain n times of output. $\frac{1}{\xi^{\ast}}\sum{{}_{j=1}^{n}\lambda_{j}^{\ast}<1}$ , it means that the economies of scale of DMU are increasing, and if the production conditions are unchanged, $n$ times of input will yield more than n times of output. $\frac{1}{\xi^{\ast}}\sum{{}_{j=1}^{n}\lambda_{j}^{\ast}>1}$ , it means that the scale benefit of DMU is decreasing, and if the production conditions are unchanged, n times of input will yield less than n times of output.

3.1.2 DEA model of variable compensation (BCC)

In order to consider the change in income when the scale changes, we have added a new constraint $\sum{{}_{j=1}^{n}\lambda_{j}=1}$ to the CCR model, so we can evaluate the comprehensive efficiency of the decision-making unit, that is, the technical effectiveness. This model is the BCC model. We briefly introduce the BCC model based on the investment perspective, as shown in Eq. (5):

$\displaystyle\left({H_{CCR}}\right)\left\{{s.t.{\begin{array}[]{c}{\min\xi}\\ {\sum{{}_{j=1}^{n}X_{j}\lambda_{j}+t^{-}=\xi X_{k}}}\\ {\sum{{}_{j=1}^{n}Y_{j}\lambda_{j}-t^{+}=Y_{k}}}\\ \sum{{}_{j=1}^{n}\lambda_{j}=1}\\ \lambda_{j}\geqslant 0,j=1,2,\ldots,n\\ t^{-}\geqslant 0\\ t^{+}\geqslant 0\\ \end{array}}}\right.$ (5)

After evaluating the decision-making unit, we can use “projection” to determine the improvement value of input and output. As shown in Eq. (6):

$\displaystyle\left\{{{\begin{array}[]{l}{\widehat{X}_{0}=\xi^{0}X_{0}-t^{0-}=X% _{0}}\\ {\widehat{X}_{0}=Y_{0}+t^{0+}=Y_{0}}\\ \end{array}}}\right.$ (6)

Where the remaining input is $\Delta X_{0}=X_{0}-\widehat{X}_{0}$ , and the output deficit is $\Delta Y_{0}=Y_{0}-\widehat{Y}_{0}$ , we can know from Eq. (6), $\Delta X_{0}=\left({1-\xi^{0}}\right)X_{0}+t^{0-}$ , and $\Delta Y_{0}=t^{0+}$ .

3.2 Establish a comprehensive transportation efficiency evaluation indicator system

3.2.1 Selection principle of evaluation indicator

For the input-output indicator system for comprehensive transportation efficiency evaluation, we need to be able to comprehensively and objectively reflect the comprehensive status of transportation efficiency, and be able to grasp the internal relations and external constraints of each link of transportation. The selection principles are as follows:

(1)
The range of indicators is wide, comprehensive and representative;
(2)
The indicators are easy to obtain, accurate and easy to quantify;
(3)
The indicators are refined, representative and distinguishable;
(4)
DEA efficiency evaluation method, the number of decision-making units should be greater than or equal to twice the number of indicators.

3.2.2 Selection of input and output indicators

When we select the input-output indicators for comprehensive transportation efficiency evaluation, one is because the subject being evaluated is five transportation modes, so there are fewer decision-making units and the number of indicators should not be large, otherwise the difference in efficiency evaluation results will not be obvious; The second is that the indicators we choose should try to cover as much information as possible and be able to fully reflect the actual situation of each mode of transportation. We summarize the literature on existing transportation efficiency evaluation indicators, taking into account the availability of data and the correlation between the indicators, and the research is based on transportation energy consumption, number of employees (labor input) and mileage value (infrastructure). The category is the input indicator, and the conversion turnover is the output indicator. The input-output indicators are shown in Table 1.

Table 1
Input-output indicators

Indicator type	Investment indicators			Output indicators
Name	Energy consumption	Number of employees	Mileage value	Conversion turnover
Unit	100 tons of standard coal	People	Billion ton kilometers	Billion ton kilometers

In the input indicators, energy consumption represents energy input; the number of employees represents the number of employees in each mode of transportation, which is the main labor input; The mileage value is the infrastructure of each mode of transportation, which represents capital input.

The output indicator is the converted turnover volume, which is obtained from passenger turnover and freight turnover. Its indicators can show the attributes of both transportation and economy, and have wide applicability.

In the DEA efficiency evaluation process, the total number of decision-making units is preferably greater than or equal to twice the input-output indicators. Therefore, in order to calculate and compare the transportation efficiency of decision-making units more accurately, we will select the data from the Statistical Yearbook and the Statistical Bulletin of the Ministry of Transport for the five years from 2014 to 2018.

3.3 Optimization model of comprehensive transportation structure based on linear programming

According to the results of DEA efficiency evaluation, we can obtain the comprehensive efficiency, pure technical efficiency and scale efficiency of different transportation modes. After projection analysis of invalid units, we can conclude that the input redundancy of each transportation mode is, the greater the redundancy difference. It shows that we should transform the transportation volume of this transportation method, and we can transform the transportation method with low transportation efficiency to the transportation method with high transportation efficiency.

We take the efficiency evaluation and structural optimization of the three modes of transportation as an example. We use the linear programming model for structural optimization, and we should consider the transportation capacity constraints of different modes of transportation. However, this data is difficult to obtain. Therefore, according to the national “Thirteenth in the Five” plan, the energy consumption intensity is reduced, so we increase the upper and lower limits of the evaluation area to reduce the energy consumption, so that the results are more in line with actual requirements. The specific model is as follows:

$\displaystyle\textit{MaxZ}=\beta_{1}x_{1}+\beta_{2}x_{2}$ (7) $\displaystyle S.t.\left\{{{\begin{array}[]{l}{\alpha_{1}x_{1}+\alpha_{2}x_{2}% \geqslant Y}\\ {\alpha_{1}x_{1}+\alpha_{2}x_{2}\geqslant L}\\ {\alpha_{1}x_{1}+\alpha_{2}x_{2}\leqslant U}\\ \end{array}}}\right.$ (8)

In the formula, $x_{1}$ and $x_{2}$ respectively represent the optimization goal of adjusting the turnover value of low efficiency to high efficiency transportation mode compared with the current transportation structure;

$\beta_{1}$ and $\beta_{2}$ respectively represent the redundant difference between low efficiency and high efficiency transportation mode adjustment; $\alpha_{1}$ and $\alpha_{2}$ respectively represent the energy consumption that can be reduced by adjusting unit turnover from low-efficiency to high-efficiency transportation; $Y$ indicates the amount of energy consumption that should be reduced compared to the unadjusted transportation structure (2015) when the intensity of transportation energy consumption per unit of GDP drops by 15% in 2020; $L$ shows the amount of energy consumed when the intensity of transportation energy consumption per unit of GDP drops by 10%, that is, the amount of energy consumed at least compared with when the transportation structure is not adjusted; $U$ represents the amount of energy consumption reduced when the intensity of transportation energy consumption per unit of GDP drops by 17%, that is, the energy consumption that can be reduced at most when the transportation structure is not adjusted.

3.4 Data prediction in the optimization of comprehensive transportation structure

The efficiency evaluation and structure optimization model require 2020 indicator data. We can use gray forecasting and other methods to predict the gross production value and the conversion turnover value of each transportation mode in 2020 under the current transportation structure (explained later).

4. Empirical analysis

4.1 Evaluation of comprehensive transportation efficiency in liaoning province

4.1.1 Input indicator data

We study the transportation efficiency and structural optimization of highways, railways and waterways, and select various data from 2014 to 2018 in the efficiency evaluation, and each transportation mode has five different decision-making units, and the specific input indicator is energy consumption, mileage value and number of employees, the output indicator is the converted turnover.

(1) Energy consumption

Based on the energy consumption coefficient listed in the Statistical Bulletin of the Ministry of Transport, we can find the energy consumption of each mode of transportation, as shown in Table 2.

Table 2
Energy consumption coefficient

Years	Mode of transport	Energy consumption factor (Tons of standard coal/million tons of kilometers)	Energy consumption (100 tons of standard coal)
2014	Highway	20	62249.22
	Railway	4.51	8074.57
	Waterway	2.8	22348.7
2015	Highway	19	54757.79
	Railway	4.68	7033.01
	Waterway	2.80	22302.39
2016	Highway	18	53413.74
	Railway	4.71	7179.41
	Waterway	2.70	23700.07
2017	Highway	19	58680.84
	Railway	4.70	8105.71
	Waterway	2.70	23249.48
2018	Highway	18	57265.85
	Railway	4.69	8563.28
	Waterway	2.70	17062.88

Datum come from: 2014–2019 Liaoning Province Statistical Yearbook and the Statistical Bulletin of the Ministry of Transport.

(2) Number of employees

The data of the number of employees in each mode of transportation in Liaoning Province is shown in Table 3.

Table 3

Number of employees

Years	Mode of transportation	Number of employees (person) 20
2014	Highway	136190
	Railway	119016
	Waterway	46028
2015	Highway	134523
	Railway	113752
	Waterway	30813
2016	Highway	122195
	Railway	109380
	Waterway	48621
2017	Highway	133234
	Railway	107152
	Waterway	47452
2018	Highway	122535
	Railway	107581
	Waterway	15757

Datum come from: 2014–2019 Liaoning Province Statistical Yearbook and the Statistical Bulletin of the Ministry of Transport.

(3) Mileage value

The output of comprehensive transportation is inseparable from the long-term investment in various types of infrastructure construction by various transportation methods. We only use the current transportation fixed asset investment as the capital investment index will lead to inaccurate efficiency evaluation results, so we choose mileage as the capital investment index to be more accurate and more applicable.

The input index of the model can not directly select the mileage data without transportation mode, so we need to transform it into the same dimension. Therefore, we introduce the concept of mileage value. First, we make the conversion turnover/total mileage of each transportation mode in Liaoning Province (that is, the unit mileage turnover of this transportation mode nationwide) as the unit mileage value of the transportation mode, and then we Multiplying the mileage of different modes of transportation by its corresponding unit mileage value transforms the concept of mileage of different modes of transportation into the same dimension. Table 4 shows the unit mileage turnover and mileage value of each transportation method from 2014 to 2018.

Table 4

Mileage coefficient

Years	Mode of transportation	Unit mileage turnover (10,000 tons)	Mileage value (100 million ton kilometers)
2014	Highway	257.44	2970.86
	Railway	148.09	75.53
	Waterway	660.19	26.41
2015	Highway	227.56	2740.91
	Railway	118.70	68.85
	Waterway	629.16	25.17
2016	Highway	234.39	2826.74
	Railway	120.40	67.42
	Waterway	693.35	27.73
2017	Highway	239.42	2937.68
	Railway	133.69	78.88
	Waterway	667.51	26.70
2018	Highway	244.91	3012.39
	Railway	140.56	91.36
	Waterway	486.50	19.46

Datum come from: 2014–2019 Liaoning Province Statistical Yearbook and the Statistical Bulletin of the Ministry of Transport.

The indicator of mileage value that we have introduced can reflect to a certain extent the amount of capital invested in different modes of transportation. We have unified the mileage value of the same transportation mode, so we can see the difference in the investment utilization rate of each transportation mode.

4.1.2 Output indicator data

By collating the data of transportation freight turnover and passenger turnover in the Liaoning Province’s 2019 Statistical Yearbook, we have obtained the conversion turnover data as shown in Table 5.

Table 5
Conversion turnover

Years	Mode of transportation	Converted turnover (100 million ton kilometers)
2014	Highway	3112.46
	Railway	1790.37
	Waterway	7981.68
2015	Highway	2881.68
	Railway	1502.78
	Waterway	7965.14
2016	Highway	2967.43
	Railway	1524.29
	Waterway	8777.80
2017	Highway	3088.47
	Railway	1724.62
	Waterway	8610.92
2018	Highway	3181.44
	Railway	1825.86
	Waterway	6319.59

Datum come from: 2014–2019 Liaoning Province Statistical Yearbook and the Statistical Bulletin of the Ministry of Transport.

4.1.3 Analysis of DEA efficiency evaluation results

(1) Analysis of efficiency evaluation results

According to CCR and BCC model calculations, we can get the efficiency evaluation results as shown in Table 6.

Table 6
Efficiency evaluation results

Decision unit	CCR	BCC	SE	Return to scale
	Comprehensive efficiency value	Pure technical efficiency	Scale efficiency
Highway 1	0.13999993986	0.35271179845	0.39692445922	Irs
Highway 2	0.14736841052	0.35178293978	0.41891858262	Irs
Highway 3	0.15000006329	0.42613939260	0.35199764653	Irs
Highway 4	0.14210522660	0.38156674752	0.37242560448	Irs
Highway 5	0.14999988047	0.26995921481	0.55563904563	Irs
Railway 1	0.62084220542	1	0.62084220542	Irs
Railway 2	0.59829057866	1	0.59829057866	Irs
Railway 3	0.57324832215	1	0.57324832215	Irs
Railway 4	0.57446826975	1	0.57446826975	Irs
Railway 5	0.57569275371	1	0.57569275371	Irs
Waterway 1	1	1	1	–
Waterway 2	1	1	1	–
Waterway 3	1	1	1	–
Waterway 4	1	1	1	–
Waterway 5	1	1	1	–

Note 5): irs means increasing returns to scale, drs means decreasing returns to scale, -means constant returns to scale.

Highway 1, Highway 2, Highway 3, Highway 4, and Highway 5 in the decision-making unit represent highways from 2014 to 2018, and the same applies to railways and waterways.

When all the efficiency values calculated by the CCR and BCC models are 1, we can say that the three efficiencies of the evaluated subject are all DEA valid. On the contrary, if the efficiency values are less than 1, we can call the efficiency of the decision-making unit as non-DEA Effective; when the calculation result is that the pure technical efficiency value is 1, but the comprehensive efficiency value is not 1, we can say that the pure technical efficiency of the evaluated subject is effective, so we can conclude that its comprehensive efficiency is invalid mainly caused by the invalid scale, and we know that if the entity does not increase the existing input, but we can also get more output. When the return to scale increases, we can increase input on the existing basis and we can obtain more output. When the return to scale decreases, we can increase the investment on the existing basis, but we can not obtain the corresponding proportion income.

The comprehensive efficiency value of waterway 1, waterway 2, waterway 3, waterway 4, and waterway 5 is 1, which is effective for DEA. We can see that the resource allocation is reasonable and this method is more efficient than other decision-making units. The comprehensive efficiency values of railway 1, railway 2, railway 3, railway 4, and railway 5 have not reached the DEA effective value, and the efficiency values are only 0.6208, 0.5983, 0.5732, 0.5745, 0.5757, and there is still a certain gap from the DEA effective efficiency value 1. However, their pure technical efficiency values have reached 1. For pure technical efficiency to be effective, we can conclude that the reason for the ineffectiveness of the overall efficiency of railway transportation is mostly caused by the invalid scale, and we can show that railway transportation does not need to increase in other aspects. Investment, but we can also get more output. Highway 1, Highway 2, Highway 3, Highway 4, Highway 5 have not reached DEA.

(2) Invalid unit projection analysis

According to the DEA efficiency evaluation, we can get the invalid unit projection analysis, as shown in Table 7.

Table 7

Projection analysis of invalid units

Decision unit	Comprehensive	Investment redundancy			Insufficient output
	efficiency value	$t_{1}^{+}$ (Energy consumption)	$t_{2}^{+}$ (Practitioners)	$t_{3}^{+}$ (mileage)	$t_{1}^{-}$ (Converted turnover)
Highway 1	0.13999993986	53534.33	0	2960.56	0
Highway 2	0.14736841052	46688.22	123375	2731.61	0
Highway 3	0.15000006329	45401.68	0	2817.37	0
Highway 4	0.14210522660	50341.99	0	2928.10	0
Highway 5	0.14999988047	48675.98	114603	3003.09	0
Railway 1	0.62084220542	3061.54	108692	69.61	0
Railway 2	0.59829057866	2825.23	107939	64	0
Railway 3	0.57324832215	3063.83	100937	62.60	0
Railway 4	0.57446826975	3449.24	97649	73.53	0
Railway 5	0.57569275371	3622.46	103029	85.74	0
Waterway 1	1	0	0	0	0
Waterway 2	1	0	0	0	0
Waterway 3	1	0	0	0	0
Waterway 4	1	0	0	0	0
Waterway 5	1	0	0	0	0

A decision-making unit with an efficiency value of 1 has zero input redundancy and low output.

The decision-making unit with invalid comprehensive efficiency, such as Highway 1, has a comprehensive technical efficiency value of 0.13999, and the redundancy of the three input items are 53534.33, 0 and 2960.56, indicating that we should reduce the energy input and mileage input of the decision-making unit. We can see from the comprehensive efficiency evaluation results that water transportation has reached the best efficiency among the three modes of transportation, while the comprehensive efficiency of road transportation is relatively low. Therefore, we can conclude that the investment conversion rate of road transportation is not as good as that of railways and waterways. Liaoning’s transportation structure adjustment should give full play to the high-efficiency advantages of waterway and railway transportation, so that the entire transportation structure can achieve the purpose of reducing energy consumption and improving efficiency. At the same time, we can also greatly increase the conversion of infrastructure investment rate. Both waterway and railway transportation methods have reached the best or better efficiency. Therefore, we conclude that the transportation structure adjustment strategy should be changed from road to waterway and railway transportation.

4.2 Optimization of comprehensive transportation structure in Liaoning province

Based on the 15% reduction in energy consumption intensity per unit of GDP in the national “13th Five-Year Plan”, we determined the redundant cost of different transportation modes in Liaoning Province based on the comprehensive transportation efficiency of various transportation methods in Liaoning Province, and the overall investment redundancy was the smallest (That is to say, the maximum redundancy difference obtained after the adjustment of road traffic to other modes of transportation) is the goal, and we are constrained by a 15% reduction in transportation energy consumption per unit of GDP and the transportation capacity of different modes of transportation, we can get an optimization plan for the comprehensive transportation structure.

4.2.1 Forecast of Liaoning Province GDP and conversion turnover volume of various transportation modes

(1) GDP forecast

Based on the data of Liaoning Province’s GDP from 2015 to 2018, and using the gray forecasting method, we further forecast the GDP for the next two years, and finally analyze the energy consumption per unit of GDP in Liaoning Province.

We accumulate the raw data of Liaoning’s GDP from 2015 to 2018, and the results are shown in Table 8.

Table 8
One-time cumulative gross product (RMB 100 million)

Years	Gross product	Accumulate GDP at a time
2015	28555.6	28555.6
2016	21896.2	50451.8
2017	23409.2	73861
2018	25315.4	99176.4

Note 1) Data source: Liaoning Province Statistical Yearbook 2019

The forecast model of Liaoning Province’s GDP from 2015 to 2020 is:

$\displaystyle\widehat{g}^{\left(0\right)}\left({k+1}\right)=\left({1-e^{-0.364% }}\right)\left({28555.6+\frac{18974}{0.364}}\right)e^{-0.364k}$ (9)

We can get the forecast value of the gross product according to the forecast model of gross product, as shown in Table 9.

Table 9

Estimated GDP of Liaoning province (100 million yuan)

Years	Gross product
	Original value	Predictive value
2015	28555.6	28556
2016	21896.2	21838
2017	23409.2	23487
2018	25315.4	25261
2019		27168
2020		29219

We test the accuracy of the gray forecast value of GDP and get:

$\displaystyle\overline{g}\left(0\right)=\frac{1}{4}\left({28555.6+21896.2+2340% 9.2+25315.4}\right)=24794.1$ $\displaystyle\overline{\Delta}=\frac{1}{4}\left[{\left({28555.6-28556}\right)+% \left({21896.2-21838}\right)+\left({23409.2-23487}\right)+\left({25315.4-25261% }\right)}\right]=34.4$

The mean square error is:

$\displaystyle C=\frac{s_{2}}{s_{1}}=\frac{\sqrt{\frac{1}{3}\sum{{}_{k=1}^{3}% \left[{g^{\left(0\right)}\left(k\right)-\overline{g}^{\left(0\right)}}\right]^% {2}}}}{\sqrt{\frac{1}{3}\sum{{}_{k=1}^{3}\left[{\Delta\left(k\right)-\overline% {\Delta}}\right]^{2}}}}=\frac{\sqrt{\frac{1}{3}\sum{{}_{k=1}^{3}\left[{g^{% \left(0\right)}\left(k\right)-24794.1}\right]^{2}}}}{\sqrt{\frac{1}{3}\sum{{}_% {k=1}^{3}\left[{\Delta\left(k\right)-34.4}\right]^{2}}}}=0.0222$

The error probability is:

$\displaystyle P=P\left\{{\left|{\Delta\left(k\right)-\overline{\Delta}}\right|% <0.6745S_{1}}\right\}=1$

When the test result is $P>0.95$ and $C<0.35$ , we can show that the gray prediction results are highly accurate, the prediction effect is good, and the prediction value is available.

(2) Conversion turnover forecast for each mode of transportation

We forecast the conversion turnover of each transportation method from 2014 (or 2016) to 2020. The forecast values are as follows.

Table 10

Highway conversion turnover predicted value

Years	Highway conversion turnover		Railway conversion turnover		Waterway conversion turnover
	Original value	Predictive value	Original value	Predictive value	Original value	Predictive value
2014	3112.46	3221.5	1790.37	1790.4	–	–
2015	2881.99	2878.4	1502.78	1471.1	–	–
2016	2967.43	2976.9	1524.29	1580.5	8777.80	8777.8
2017	3088.37	3078.8	1724.62	1698.0	8610.92	8552.8
2018	3181.44	3184.1	1825.68	1824.3	6319.59	6292.3
2019	–	3293.1	–	1969.0	–	4629.2
2020	–	3405.8	–	2105.7	–	3405.7

Table 11

Accuracy test

[height=1.2cm,width=3.2cm]Accuracy check Mode of transport		Highway	Railway	Waterway
Variance ratio	C	0.0594	0.2315	0.0212
Probability of error	P	1	1	1

The predicted mean square deviations of the converted turnover of roads, railways, and waterways are $C=$ 0.0594, $C=$ 0.2315, $C=$ 0.0212, and $<$ 0.35 respectively. The error probability of road, railway, and waterway conversion turnover forecast is all $P=$ 1. The test results are both $P>$ 0.95 and $C<$ 0.35, we can show that the gray prediction results are highly accurate, the prediction effect is good, and the prediction value is available.

4.2.2 Model parameter determination

When determining the parameters, we use 2020 as the forecast year

(1) Determination of $\alpha_{1}$ , $\alpha_{2}$

According to the data from the 2018 Liaoning Statistical Yearbook, we can obtain the energy consumption that can be reduced per unit turnover for the adjustment of roads to railways and waterways, as follows:

A $=$ Highway energy consumption $\div$ Highway conversion turnover $=$ 572.66 $\div$ 3181.44 $=$ 0.18 (10 000 tons of standard coal/100 million ton kilometers) Railway energy consumption per unit turnover B $=$ Railway transportation energy consumption $\div$ Railway conversion turnover $=$ 85.63 $\div$ 1825.86 $=$ 0.049 (10 000 tons of standard coal/100 million ton kilometers) Energy consumption per unit turnover of waterway C $=$ Waterway transportation energy consumption $\div$ Waterway conversion turnover $=$ 170.63 $\div$ 6319.59 $=$ 0.027 (10 000 tons of standard coal/100 million ton kilometers)

Therefore, we obtain the reduced energy consumption per unit turnover from road to railway adjustment $\alpha_{1}=A-B=$ 0.1331; We can obtain the reduced energy consumption per unit turnover of the adjustment from road to waterway $\alpha_{2}=A-B=$ 0.153.

(2) Determination of $\beta_{1}$ , $\beta_{2}$

We take the above-mentioned efficiency evaluation results and take the optimal value in the five-year efficiency evaluation of each transportation method respectively, and then we can get the most efficient transportation method, and respectively organize the sum of the unit output redundancy value of each transportation method relative to the optimal transportation method Since we have unified the dimensions after normalization, we define this unit output redundancy value as the redundancy cost of each transportation mode, and obtain the relative redundancy cost difference between the road and the other two transportation modes. As shown in Table 12.

Table 12
Relative redundancy difference of highway

Comparison of transportation methods	Road relatively more redundant value
Road-rail	0.14
Highway-waterway	–

and so, $\beta_{1}=$ 0.14, $\beta_{2}=$ 0.

(3) Determination of $Y$

We get the current energy consumption coefficients of different transportation modes as shown in Table 13.

Table 13

Energy consumption coefficients of different transportation modes

Mode of transport	Energy consumption coefficient (ton of standard coal/million ton-km)
Highway	18
Railway	4.69
Waterway	2.70

That is, the current energy consumption coefficient is $e=\left({18,4.69,2.7}\right)^{t}$ .

According to the gray forecast, we can get the conversion turnover of each transportation mode in 2020 as shown in Table 14.

Table 14

Conversion turnover in 2020

Mode of transport	Converted turnover (100 million ton kilometers)
Highway	3405.8
Railway	2105.7
Waterway	3405.7

According to the conversion turnover in the forecast year and the current energy consumption coefficient, we can obtain the transportation energy consumption of each mode of transportation in 2020 under the current energy consumption coefficient as shown in Table 15.

Table 15

Transportation energy consumption in 2020

Mode of transport	Energy consumption (100 tons of standard coal)
Highway	61304.40
Railway	9875.73
Waterway	9195.39
Total	80375.52

Therefore, we get the total energy consumption of comprehensive transportation in 2020 to be 8.0376 million tons of standard coal.

According to the gray forecast, the GDP of Liaoning Province in 2020 is 292 million yuan. We can finally obtain that the transportation energy consumption per unit GDP of Liaoning Province in 2020 will be 2.7526 million tons of standard coal per trillion yuan.

In 2015, the total energy consumption of transportation was 8.4093 (ten thousand tons of standard coal). When the transportation energy consumption per unit of GDP drops by 15% in 2020,

Total transportation consumption $=$ Transport energy consumption per unit GDP $\times$ GDP $=$ 683.64 (10 000 tons of standard coal) Therefore, when the intensity of transportation energy consumption per unit of GDP drops by 15% in 2020, compared to 2015 when the transportation structure is not adjusted, the amount of energy we should reduce is: Y $=$ 840.93 – 683.64 $=$ 157.29 (10 000 tons of standard coal)

(4) Confirmation of $L$

When the transportation energy consumption per unit of GDP drops by 10% in 2020.

Total transportation energy consumption $=$ Transport energy consumption per unit GDP $\times$ GDP $=$ 723.37 (10 000 tons of standard coal)

Therefore, when the intensity of transportation energy consumption per unit of GDP drops by 10% in 2020, compared to 2015 when the transportation structure is not adjusted, the amount of energy we should reduce is:

$L=$ 840.93 – 723.37 $=$ 117.56 (10 000 tons of standard coal)

(5) Confirmation of $U$

When the transportation energy consumption per unit of GDP drops by 17% in 2020.

Total transportation energy consumption $=$ Transport energy consumption per unit GDP $\times$ GDP $=$ 667.13 (10 000 tons of standard coal).

Therefore, when the intensity of transportation energy consumption per unit of GDP drops by 17% in 2020, compared to 2015 when the transportation structure is not adjusted, the amount of energy we should reduce is:

$U=$ 840.93 – 667.13 $=$ 173.8 (10 000 tons of standard coal)

4.2.3 Model solving

We use the comprehensive transportation structure optimization model and substitute the calculation results of the above parameters into Eqs (7) and (8), we can get the optimization model as follows:

$\displaystyle\textit{MaxZ}=0.14\ast x_{1}+0\ast x_{2}$ (10) $\displaystyle S.t.\left\{{{\begin{array}[]{l}{0.1331x_{1}+0.153x_{2}\geqslant 1% 57.29}\\ {0.1331x_{1}+0.153x_{2}\geqslant 117.56}\\ {0.1331x_{1}+0.153x_{2}\leqslant 173.8}\\ {x_{1},x_{2}\geqslant 0}\\ \end{array}}}\right.$ (11)

4.2.4 Results and countermeasure analysis

We use Lingo software to solve the optimization model, and we can get that the turnover value of roads that should be adjusted to railways is 130.559 billion ton-kilometers, which accounts for 54.69% of the road converted turnover in 2015.

We analyze the optimization results and propose the following countermeasures:

(1)
Road transportation consumes a lot of energy. We should relatively reduce the passenger and freight share of road transportation, reduce the volume of bulk cargo road freight, increase railway freight, increase railway transportation capacity, and vigorously promote the development of “railway transfer”.
(2)
Road transportation is convenient, and we can carry out short-distance cargo transportation. In order to ensure the effective use of the existing road routes, we can increase the freight share of part of the road transportation in the short-distance transportation, and strive to shorten the goods circulation cycle.
(3)
Railway and waterway transportation are more efficient. We should make full use of the low energy consumption and high efficiency characteristics of railway and waterway transportation, strengthen “container water-rail transportation”, and accelerate the development of multimodal transportation.
(4)
Road transportation has high energy consumption and high environmental pollution. We can actively promote new technologies, encourage the purchase and use of new energy vehicles, and promote energy conservation and emission reduction in road transportation.

5. Conclusion

By combining CCR and BCC efficiency evaluation models and selecting a scientific evaluation index system, this paper evaluates the comprehensive transportation efficiency from the perspective of input and output; Based on the efficiency evaluation and gray prediction results, the comprehensive input under the transportation efficiency evaluation is redundant. The goal is to minimize the balance of energy, and the reduction of energy consumption intensity is the constraint to construct a comprehensive transportation structure optimization model. Based on the forecast of Liaoning’s gross production value and the conversion turnover of each transportation mode, we optimize the comprehensive transportation structure and make recommendations. The research provides ideas for the construction of an energy-efficient and efficient comprehensive transportation structure. The integrated transportation system is a huge and complex system, and the practicability of the model method system needs further discussion.

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Transportation structural optimization based on the evaluation of comprehensive transportation efficiency

Abstract

Keywords

1. Introduction

2. Comprehensive transportation efficiency evaluation and structural optimization

2.1 Comprehensive transportation efficiency evaluation

2.2 Comprehensive transportation structure optimization

3. Comprehensive transportation efficiency evaluation and structure optimization model based on DEA and linear programming

3.1 Comprehensive transportation efficiency evaluation method based on DEA

3.1.1 DEA model of fixed compensation (CCR)

3.2.1 Selection principle of evaluation indicator

Table 1 Input-output indicators

4. Empirical analysis

4.1 Evaluation of comprehensive transportation efficiency in liaoning province

4.1.1 Input indicator data

Table 2 Energy consumption coefficient

Table 5 Conversion turnover

Table 6 Efficiency evaluation results

4.2.1 Forecast of Liaoning Province GDP and conversion turnover volume of various transportation modes

Table 8 One-time cumulative gross product (RMB 100 million)

Table 12 Relative redundancy difference of highway

References

Table 1
Input-output indicators

Table 2
Energy consumption coefficient

Table 5
Conversion turnover

Table 6
Efficiency evaluation results

Table 8
One-time cumulative gross product (RMB 100 million)

Table 12
Relative redundancy difference of highway