A third-party logistics (TLP) provider’s outsourcing mode is developed to support the economic activities for various industries. The aim of this research is to assess the efficiency of 10 large TPL providers from past to future by integrating the GM (1,1) model in grey forecasting and an epsilon-based measure model (EBM) in data envelopment analysis (DEA). The GM (1,1) model is utilized to formulate a forecast data in the future over period from 2018 to 2022. Then, via EBM model, past–current–future data are used for computing efficiency of these providers. The empirical values show that 115 cases comprise 79 efficiency cases and 36 inefficiency cases. CHRW, ECHO, and UPS get strong efficiency and keep a stable efficiency score in whole term. EXPD and KRRYF do not achieve efficiency during the period from 2013 to 2022. Excluding CHRW, ECHO, and UPS, seven TPL providers demonstrate upward trend and downward trends in every term. The increasing and decreasing variation index of 10 third-party logistics providers will help customers to select the best TPL providers.

1. Introduction

Industrial growth is enhancing international trade processes to demand world commerce with the aim of exchanging raw materials, semiproducts, and goods. With the past and current conditions, establishing logistics is a crucial factor, as it connects production and consumption to implement and control the flow of goods, services, and relative information [1, 2]. Logistics display competences of transportation by providing a supply chain to help customers reduce inventory and shorten transportation time, and so on in which the shipping service of TPL providers is reliable, as they can make the provision of fast pace and vary service to companies from all sectors [3]. Logistics is a strategic role in a firm’s success that ensures successful supply chain management [4]; notably, it can directly manage physical information [5]. As a result of competitive business environments, TPL appeared in the 1970s and 1980s when companies outsourced logistical operations to TPL; thus, it designed integrated service between warehousing and transportation [6, 7]. Customers typically prefer utilizing high-quality logistics to reduce transportation costs. TPL receives basic equipment, technology, and information to meet market demands [8]. It collects inbound shipments or outbound shipments from factories at the same time to merge in their distribution centers via information analysis system; then, they will be transferred to the final destination by an alternative transportation route on time [9, 10].

As a characteristic of TPL and based on user replies, TPL providers can reduce inventory and stock out costs and also help users to better navigate through the web of government regulations and obtains customs clearance to avoid unnecessary delays [11]. Besides, the leverage technology helps integrate information systems into systematic inventory management; the integrated factors are a fulfillment service with supply chain management that offers visible data [12]. As a result, TPL have a collaborative relation [13] and reputation to uphold for customers worldwide; it also supports augmenting positive relationships with exporters among competitive markets [14]. When receiving goods from a supplier, logistics not only take care of delivery of products, storage, loading, labelling, distribution, and unloading but also utilize the appropriate software to transmit milestones to the client.

In trade activity, TPL plays a key role in the logistics activities among outsourcing company, the marketplace, and the customer, with the function of integrating the supply; thus, this alliance will maintain effective outsourcing progress [15], inasmuch as logistics outsourcing can cut down on charges, increase flexibility, and direct delivery [16, 17]. The goal of a TPL provider builds multiple distribution functions and optimization of inventory [18]. From the criteria, TPL can define that it is a provider of an outsourced logistics service that encompasses the relative activities of delivering a product. Van Laarhoven claimed that “third-party Logistics are activities carried out by a logistics service provider on behalf of shipper and consisting of at least transportation” [19]. Selecting the right TPL is critical for wholesalers, companies, and retailers in order to maintain a supply chain [20]. Therefore, this research offers deep analysis of TPL providers from past to future to define the efficiency and inefficiency of TPL providers through their key financial factors.

Integrated capabilities between outsource and information transmission are noted to minimize the total delivery costs [6, 21]. With the aim of evaluating the efficiency in an operating process, the study integrates EBM and grey models to assess and predict the performance of TPL providers from past to future. Data envelopment analysis is an excellent analysis tools for multi models, including CCR, BBC, SBM, and dynamic SBM, to calculate and analyze financial reports or statistical data of humans, economies, and so on [22]. Koopmans and Farrell calculated the efficiency when using decision-making units (DMU) for analyzing original models; performance was conducted by the ratio between output and input of each of DMU [23, 24]. The EBM model composes the radial (technical) efficiency and the nonradial (value-dependent) efficiency [25], so that the research applies it into calculating the efficiency of TPL providers in each of periods.

A grey model is a forecast option with a biased exponential model that depends on a serial number of historical data to estimate the accuracy value, and the accumulation technique is a the accumulated generating operation (AGO), which is also used for obtaining methodical regularity and effectively reducing noise in discrete time-series data [26, 27]. The GM (1,1) model, which consists of group difference equations, is one of the more useful grey forecasting models. The prediction values are based on historical time-series in which the minimum number of data is four, and the data must be in consecutive order.

The study consists of four sections. Section 1 introduces the theory of TPL providers and overviews of grey forecasting and DEA. Section 2 proposes the input and output factors of the objectives, figures out proposal research, and sets up methodology with the equation of the GM (1,1) and EBM models. Section 3 shows estimated values and empirical analysis results. Section 4 summarises important marks.

2. Materials and Methods

2.1. Data Collection

According to the principle of DEA, the data comprises input variables and output variables. Based on the researching objective of determining the performance of TPL providers from the previous period to the future, with the list of top 50 TPLs on logisticsmgmt.com [28], the study selected input and output factors of 10 large third-party logistics providers during the period from 2012 to 2017 when their input and output variables were listed by the source of tmxmoney.com [29]. Input variables such as assets, current assets, current liabilities, and capitalization, along with output variables such as revenue and gross profit, are key points in the financial report of every company that assesses the efficiency of an operation process.

Input Variables. Assets (AS): Property, equipment, tangible assets, and intangible assets owned by an enterprise.

Current assets (CA): Cash and cash equivalents, short-term investment, and stock inventory.

Current liabilities (CL): Outstanding checks, compensation, current portion of debt, accounts payable, and other similar debts are values that the logistics must be paid within one year.

Capitalization (CP): The total amount investment expenses to establish the structure and operation business.

Output Variables. Revenue (RE): The value of goods and services from the transportation, products, and handling is held by a logistics service.

Gross profit (GP): Profit appears when the revenue deducts the cost of goods sold.

2.2. Proposal Research

The study utilizes GM (1,1) to forecast the future status and EBM model to evaluate the efficiency in each term. The final analysis result shows the efficiency and inefficiency of 10 TPL providers of every year during the period from 2012 to 2022. Figure 1 describes five stages in the research process as follows:

Stage 1. With the desirable knowledge of deep logistics, the authors determine the study objective of TPL providers. Based on the methodology, the input factors and output factors are chosen to apply into formulating the performance of TPL providers.

Stage 2. Overview the theory of TPLs, GM (1,1), and EBM model and provide the background of previous study of TPLs, GM (1,1), and EBM.

Stage 3. As criterion of foreseeing additional TPL providers, the study uses the series of historical collected data for predicting the future data by GM (1,1) model in grey forecasting. The prediction values must be tested by MAPE indicator. If the MAPE index is unsuitable, the objective must be retested.

Stage 4. Accordingly, the principle of DEA, Pearson’s coefficient of all input and output variables, must be isotonic under the condition from -1 to +1. If they are unappreciated, they will be reselected. Besides, Pearson’s coefficient in the EBM model will be utilized by formulating the value of diversity and affinity. Pearson’s coefficient is adjusted from 0 to +1. The EBM model calculates the score, theta, and slack to determine the efficiency and inefficiency of each company in every term.

Stage 5. Conduct some key points. By approaching GM (1,1) and the EBM model, the analysis result reveals their performance to seek out values from past to future.

2.3. Grey Forecast Model

GM (1,1) model is a grey forecasting model which bases on the historical data with time-series at least four years, it uses for predict further time-series with multiple inputs and outputs. GM (1,1) model only forecasts data when the primal data is a positive value and employed accordingly below steps:

Step 1. With the primal data

Step 2. Depending on the calculates time-series

Step 3. After having series it will create the mean equation

Step 4. Find out a and bChanging the linear equation into the form of a matrix as below:And then,

Step 5. Calculate the whitening equation of the different equation:

Step 6. This goes with

Step 7. Find out the prediction valuewhere

Step 8. Estimating the MAPE (mean absolute percent error) MAPE indicator is applied to measure the accuracy of forecasting value in statistics and the parameter of MAPE is given as in Table 1.

As in Table 1, the forecasting data is accepted when its MAPE indicator is under 50%. In contrast, the MAPE indicator is upper 50%, the data is unappreciated, and it must be re-examined by another prediction model.

2.4. Epsilon-Based Measure Model
2.4.1. Epsilon-Based Measure of Efficiency

Tone discussed that EBM model could test the robustness and stability of efficiency measure of DMUs relating with the parametric change of multiplier variables. It has two parameters one scalar and one vector. When having n DMU0, s inputs (i=1,2,..,s), z output bij (i=1,2,..z) and then it will denote by (j=1,..,n) with aj ϵ Rs and   ϵ Rz. Input and output data matrices by A = (aij) ϵ Rsn and B =   ϵ Rzn. Radial and non-radial models are ɛa and ɛb. The result of the principal component analysis defines the weights w- and w+. EBM model describes the following:Whereas the weight of input (i) is and   , the radial θ and nonradial slacks terms are combined by .with s- ϵ Rm being the input slack. The primal-dual is E and D. If setting the optimal solution of E is , ,

when DMU (a0, b0) fulfil and it is weak efficiency;

when DMU (a0, b0) fulfil and it is strong efficiency;

when DMU (a0, b0) fulfil, it doesn’t have efficiency.

2.4.2. Diversity Index and Affinity Index

According to the normal way, Pearson’s correlation coefficient translates the full original data. However, EBM model does not present the translation of original which established an affinity index between two input vectors instead of Pearson’s correlation coefficient [25]. S(x,y) lets the affinity index between the vector x and vector y with the properties as follows:

(P1) S(x,y) = 1

(P2) S(x,y) =S

(P3) S(tx,y) =S(x,y) (t > 0)

(P4) 1≥ S(x,y) ≥ 0

Let the diversity index is to be H(x,y) and it is denoted byNote that 0 ≤ H(x,y) = H(y,x) ≤

The affinity index is set as below:

S(x,y) = 1- 2H(x,y)

If 1 ≥ H(x,y) ≥ 0, H(x,y) is suitable with the properties (P1), (P2), (P3), and (P4).

And Pearson’s correlation of diversity and affinity is given asAccording to the normal rule of Pearson’s correlation coefficient, it ranges -1≤ r(x,y) ≤+1 [30]. In this case, the principal component analysis is not guaranteed that the principal vector consists of non-negative component so that it is adjusted 0 ≤ r(x,y) ≤+1.

3. Results and Discussion

3.1. Data Analysis

From the data of 10 TPL providers, as shown in Section 2.1, the research combines the GM(1,1) model to predict the operating process from 2018 to 2022 and the EBM model to figure out the performance from 2013 to 2022. The 10 TPL providers include C.H. Robinson Worldwide (CHRW); DSV A/S ADR (DSDVY); Echo Global Logistics (ECHO); Expeditors International (EXPD); Hub Group (HUBG); J.B. Hunt Transport Services (JBHT); Kuehne & Nagel International (KHNGY); Kerry Logistics Network (KRRYF); Panalpina Welttransport (PLWTF); United Parcel Service (UPS).

Table 2 summarizes the input and output variables of 10 TPL providers from 2013 to 2017. AS, CA, CL, CP, RE, and GP are positive elements. The significant values are highly appreciated using the GM (1,1) model for estimating and the EBM model for formulating the performance.

3.2. Forecasting Result

The prediction value is derived after utilizing the past series variables for calculation. From the historical data, the data of CHRW are selected as an example.

Based on the grey forecast model in Section 2.3, the research applies the steps of GM(1,1) into calculating the prediction values of CHRW through the data in the Table 3.

Setting the primal data Formulating seriesGenerating the mean sequence Finding out a and bTransposing the linear equationThe value of a and b is given asCalculating the whitening equationSeeking the predictionConducting the prediction value The forecasting result is given in the Table 4.

The prediction values of DMUs are shown in Tables 10 and 11, and the values are tested by MAPE indicator in Table 4.

Accordingly, the principle of MAPE is shown in Table 1, with the results shown in Table 5. The average MAPE indication of each TPL provider receives qualification, as the values are lower than 0.61847%, and their common average is 0.36783%. That means they reach the high accuracy prediction with the excellent qualifications under 10%. As a result, the GM (1,1) is an appropriate model to use for predicting of TPL providers from 2018 to 2022. The data in Tables 10 and 11 indicate that they are positive and absolutely suitable to utilize in the EBM model.

3.3. Measurement of Efficiency

To assess the operation process of TPL providers, the research proposes the EBM model in DEA to determine the efficiency of TPL providers in the past–current–future. The data in the analysis must be R+; the research implements a small analysis step to ensure all data are higher than 0. Tables 12 and 13 denote that no input data or output data are under 0.

In addition, following the rule of DEA, the relationship of input and output factors is isotonic before implementing the performance count. The condition of correlation coefficient ranges from -1 to +1 and has a good linear relation when close to 1. Tables 12 and 13 denote that Pearson’s correlation coefficients are from 0.91014 to 1. These values achieve the qualification level and receive a strong linear relation. Therefore, the data are used for estimating the efficiency of the EBM model.

New vectors are built up in the EBM model; however, the vectors must be positive. The affinity index of vectors is presented to replace Pearson’s correlation. Their values are satisfied with the condition [0≤r(x,y)≤+1] when the largest eigenvalue and eigenvector of affinity matrix are from 0 to 1.

Table 6 shows diversity is from 0 to 0.35295. Table 7 gives an affinity of 0.29411 to 1. Both approach the largest eigenvalue and eigenvector and ensure the rationale of the affinity index is determined. Input variables are calculated by the input-oriented model under the constant returns-to-scale (CSR) assumption. From that point, the results of epsilon for EBM and weight to input/output are computed as follows:

Epsilon for EBMEpsilon for EBM of 2013 = 0.521603Epsilon for EBM of 2014 = 0.515902Epsilon for EBM of 2015 = 0.490042Epsilon for EBM of 2016 = 0.520046Epsilon for EBM of 2017 = 0.496313Epsilon for EBM of 2018 = 0.487955Epsilon for EBM of 2019 = 0.496962Epsilon for EBM of 2020 = 0.506061Epsilon for EBM of 2021 = 0.45633Epsilon for EBM of 2022 = 0.44635

Epsilons for EBM during the term of 2013-2022 are positive with their results under 0.44635 so they are significant.

Weight to Input/Output. Based on the epsilon for EBM and weight to input/output, as shown in Table 8, the efficiencies of TPL providers are presented in Table 9. According to Table 9 and the theta’s rule, the empirical analysis results denote that CHRW and UPS achieved a strong efficiency during all terms when their scores and theta always obtain 1 and their slacks attain 0. ECHO receives strong efficiency as the scores and theta of ECHO is 1, and its slack is 0 as well, except 2015 when its slack of current assets and capitalization are 0.000075 and 0.000177, respectively. KHNGY with its score and theta as 1 and its slack as 0 has a strong efficiency during 2013 and from 2015 to 2022. The year 2014 is exclusive without efficiency because the score is lower than 1, and the slack is different with 0. PLWTF shows strong efficiency from 2017 to 2022, with score and theta as 1 and slack as 0; it has a weak efficiency in 2015–2016 with score as 1, and the theta is different 0. All scores, theta, and slack of PLWTF are unqualified in 2013–2014 so it does not have efficiency. JBHT obtains a strong efficiency in 2013, 2015–2016, 2018–2019, and 2021–2022; the others years do not receive efficiency because of unqualified indicators. HUBG demonstrates strong efficiency in 2014, 2016, and 2019–2022 and a weak efficiency in 2018 with score and theta as 1 and slack as difference 0. DSDVY has a strong efficiency in 2013 and 2021–2022, it does not obtain efficiency in others years. EXPD and KRRYF are TPL providers that show inefficiency during the 2013–2022 term.

The operating performance of TPL providers from past to future is identified by the analyzed values after integrating the GM (1,1) and EBM models. The relative efficiency of a comparable DMU, with its input and output factors, is defined by DEA [31]. The research quantifies the scores of 115 cases of 10 TPL providers through the EBM model. The empirical analysis result in Table 9 denotes 19 efficiency and 35 inefficiency cases; 35 inefficient cases should be improved efficiency by reducing the input variables and increasing the output variables.

Figure 2 illustrates the operating efficiency of 10 TPL providers from past to future. CHRW, ECHO, and UPS are excellent TPL providers and obtain stable enduring performance over the whole term. The PLWTF index increases slightly from 0.942 to 1 from 2013 to 2015 and obtains a balanced value over the remaining time. KHNGY is dropped in 2014, but it resumes again as soon as 2015 and maintains sustainable efficiency from 2016 to 2022. DSDVY, HUBG, and JBHT show smooth fluctuation in each term; specifically, HUBG during the term of 2013–2017 has one rising year and one falling year; JBHT is one falling year and then maintaining balance in performance value in two consecutive years; the result is repeated during all terms; the variation index of DSDVY slumps with the score indicator from 1 down to 0.707 within three continual years from 2013 to 2015; it rises slowly as the index increases lightly within six sequent years from 2016 to 2021. EXPD and KRRYF always show upward movement, but they have not obtained efficiency because their indicators are under 1. For that reason, most providers demonstrate downward and upward trends in each term, excluding CHRW, ECHO, and UPS.

4. Conclusions

TPL providers are responsible for logistics services with outsourcing activities to support enterprises for delivering the products fluently. The research integrates an EBM model in DEA and a GM (1,1) model in grey forecasting to present the efficiency progress of 10 TPL providers from the past to future. The major aims of this research are to show foreseeing future values, determining the efficient and inefficient terms of enterprises, and pointing out operating trends of companies.

The GM (1,1) model is applied into computing the accuracy-predicting values of TPL providers over the term from 2018 to 2022 based on historical time-series during the term from 2013–2017. Key financial indicators, e.g., assets, current assets, current liabilities, capitalization, revenue, and gross profit, are used for forecasting and analyzing a company’s productivity. The forecasting data discover a future operating status of 10 TPL providers.

Furthermore, the actual and estimated values are employed to compute the efficiency over the whole term via EBM model. Analysis results reveal the performance valuations of TPL providers during the period from 2013 to 2022. Moreover, the study describes an efficient picture of TPL providers from the previous to future term that supports TPL providers in understanding their operation process and strategic growth to implement a successful business plan; in addition, customers have a good overview of TPL companies to choose the best suitable TPL provider.

Although this study explores the performance of TPL providers, limitations remain. First, the study only demands us to define efficiency and inefficiency without ranking TPL providers in each year, so that further research can create more models to rank. Second, the published input and output variables may not offer enough information, e.g., number of containers, employees, etc., for examining the operation process. Thus, the next study will research more of these factors.


See Tables 1013.

Data Availability

The data used to support the findings of this study are included within the article.

Conflicts of Interest

The authors have no conflicts of interest regarding the publication of this paper.

Authors’ Contributions

Chia-Nan Wang guided the analysis method and edited the content; Jen-Der Day guided the research direction and found the solutions; Thi-Kim-Lien Nguyen designed research framework, analysed the empirical result, and wrote the paper.


This research was partly supported by MOST107-2622-E-992-012-CC3 from the Ministry of Sciences and Technology in Taiwan.