Sustainable Evaluation of Major Third-Party Logistics Providers: A Framework of an MCDM-Based Entropy Objective Weighting Method

Abstract

This study aims to efficiently assist decision makers in evaluating global third-party logistics (3PL) providers from the perspectives of economic, social, and environmental sustainability and explore the determinants of the 3PL providers’ performance. In doing so, an integrated framework for an MCDM-based entropy objective weighting method is proposed for the first time in a logistics industry assessment. In the first stage, the entropy method defines the weight of the decision criteria based on real data collected from the top 15 global 3PL providers. This study lists the prominent quantitative evaluation criteria, taking into consideration the sustainability perspective. The advantage of the entropy method is that it reduces the subjective impact of decision makers and increases objectivity. In the second stage, the measurement of alternatives and ranking according to compromise solution (MARCOS) method is used to rank the 3PL providers according to their performance on the basis of these criteria. Sensitivity analysis and comparative analysis are implemented to validate the results. The current research work is devoted to the emerging research topic of sustainable development in the logistics industry and supply chain management. The proposed model identifies key performance indicators in the logistics industry and determines the most efficient 3PL providers. Consequently, the results show that the carbon dioxide emissions (20.50%) factor is the most important criterion for the competitiveness of global logistics companies. The results of this study can help inefficient 3PL providers make strategic decisions to improve their performance. However, this study only focuses on 15 companies due to a lack of data. The integration of these two techniques provides a novel way to evaluate global 3PL providers which has not been addressed in the logistics industry to date and as such remains a gap that needs to be investigated.

1. Introduction

In today’s business world, it is very challenging for a company to be competitive without working in close collaboration with external partners. In light of this, logistics outsourcing is a crucial component of every firm as a result of the strain of rising enterprise expenses and the globalization of business activities [1]. The idea of supply chain management developing in this direction aims to manage the physical and informational flow exchanged among all participants in a supply chain as optimally as possible, with the dual goals of simultaneously reducing costs along the entire supply chain and increasing the perceived value of goods or services. A globally based company must be competitive in a healthy market environment while collaborating closely with its associated stakeholders [2]. To focus on their core competencies, businesses frequently outsource their logistics activities to a third-party logistics (3PL) provider.

In 2021, the worldwide 3PL market was estimated to be worth USD 962.1 billion. It is expected to reach USD 2018.22 billion by 2030, expanding at an 8.58% CAGR (compound annual growth rate) over the forecast period (2022–2030) [3]. The market is dominated by North America. The large-scale application of 3PL services in the manufacturing, retail, automotive, hospitality, construction, telecommunication, online retail, and food and beverage (F and B) industries can be attributed to the rising demand for the outsourcing of crucial transportation and logistics functions to reduce shipping costs and manage delivery times. The market is currently growing in this setting. The introduction of supply chain management (SCM), the cloud, enterprise resource planning (ERP), transportation management systems (TMS), and international trade logistics systems (ITLS), among other significant technological advancements, contributes to this and is a further growth-inducing factor. These developments aid in reducing energy use and improving operational efficiency [4]. Additionally, the widespread adoption of radio-frequency identification (RFID) chips to track product locations, orders, and freight shipments by manufacturers and consumers using a variety of electronic devices is fueling market expansion. In addition, the sudden global spread of the coronavirus disease (COVID-19) pandemic and the ensuing implementation of mandatory lockdowns facilitated an increase in the demand for third-party logistics services across a variety of e-commerce and online platforms for inventory management and the completion of product deliveries within specified time frames. Other elements, such as the growing trading activities brought on by globalization and the widespread use of installed mobile apps, also contribute to the market’s promising future.

The majority of multinational 3PL companies specialize by differentiating their services, with the scope of services encompassing a range of options from narrow services to broad supply chain activities. Transportation, outbound (distribution), warehousing, inventory control, packaging, and reverse logistics are all tasks related to contract logistics [5]. For transportation, activities include freight transport (air, ocean, land, and railway), shipping, intermodality management, package express carrying, (de)consolidation, forwarding, customs brokering, perishable/hazardous goods management, and freight bill payment/auditing. For outbound (distribution), activities include order fulfillment/processing, merge in transit, picking, sorting, dispatching, postproduction configuration, and installation of products at the customer’s site. For warehousing, activities include storage, receiving, (de)consolidation, cross-docking, and perishable/hazardous goods. For inventory management, activities include slotting/layout design, forecasting, location analysis, and storage/retrieval management. Design, assembly/packaging, labeling, and palletizing are activities of the packaging sector. Finally, reverse logistics consists of pallet flow management, repair, reuse, recycling, remanufacturing disposal management, testing/product serving, and return shipment management.

The decision to choose a 3PL provider often presents particular difficulties due to the wide range of 3PL service options offered by the sector’s rapidly expanding 3PL market. High order volumes, a lack of inventory space, rising fuel prices, the need to find new talent, and environmental issues are just a few of the difficulties that may arise. Since the 3PL user is contractually obligated to rely on the 3PL to deliver prompt and reasonably priced logistics services to its end customers, failure to address these issues could seriously disrupt the supply chain operations of the 3PL user and have the opposite effect. Most importantly, environmental concerns have become worse in the logistics management industry for a number of reasons [6]. For instance, after the electrical industry, logistics and transportation rank second in terms of greenhouse gas production. In addition, the need for transportation of products has increased greatly in recent years, and it is supposed to continue to increase in the next years [7]. As a result, major 3PL companies are concentrating on growing their core businesses in order to maintain supply chain competition, satisfy their customers’ needs globally in a challenging economic environment, and uphold the objective of developing sustainable supply chains. In order to create a more environmentally friendly supply chain in the modern world, corporations must improve their performance indicators to reduce unfavorable external factors of their own logistics activities, such as carbon emissions [8]. Therefore, knowledge and tactics are crucial for 3PL providers to survive and function effectively and sustainably. These businesses must measure efficiency in order to improve their chances of being efficient.

Emulating best-practice 3PLs that can be found by setting a reliable performance standard is one way to increase the operational effectiveness and, as a result, the competitiveness of 3PLs. An industry norm, a benchmark, and a financial and a nonfinancial audit are a few examples of such standards. Benchmarking appears to be the most suitable method of setting a reliable performance standard and then comparing the operational efficiency of the 3PL with that of its competitors, because a 3PL needs to evaluate its operational performance in relation to those of its competitors and to previous years to continuously strengthen its market position. A strategic action plan for achieving superiority can be created by an organization using benchmarking, a continuous quality improvement process that allows it to assess its strengths and weaknesses, compare the competitive advantages of its top rivals, and find the best practices of functional leaders in the industry.

Therefore, this study proposes a holistic evaluation framework for the performance of 3PL service providers. In this benchmark setting, key performance indicators are identified in light of sustainability practices (economic, service level, social, and environmental aspects), and the most efficient leading providers are determined according to identified indicators. In doing so, a framework of an MCDM-based entropy objective weighting method and the MARCOS (measurement of alternatives and ranking according to compromise solution) method is proposed. The MARCOS method is a powerful and robust tool for optimizing multiple goals that uses the ratio method and the reference point method to generate a scheme of basic comprehensive decision information. Recognizing the limitations inherent in many multicriteria models such as degree of inconsistency and misjudgment of alternatives, there arises a necessity to explore new tools that facilitate rational and reliable decision making. In this context, the newly developed MARCOS method plays a pivotal role in bolstering the robustness of MCDM. Unlike models based on fuzzy logic systems, the MARCOS model demonstrates remarkable flexibility and proficiency in solving multicriteria models with more criteria. Notably, it maintains its simplicity even as the number of criteria or options increases. When compared to other methods, MARCOS distinguishes itself by its simplicity, effectiveness, and ease of application and enhancement. For example, when compared to the TOPSIS method, MARCOS shows greater stability and robustness of the results when changes are made in the measurement scales of the decision attributes [9]. In comparison with some well-established MCDM methods such as the MABAC, SAW, ARAS, WASPAS, and EDAS methods, the MARCOS method shows an extremely high rank correlation [9].

In this paper, in order to illustrate the proposed framework, fifteen leading 3PL companies of the world are ranked based on the collection of real data; then, a sensitivity analysis and a comparative analysis are conducted to validate the model. In terms of theoretical contributions, the applied methods are used to take the benefits of the MARCOS method to make a sustainable 3PL evaluation framework with objective weighting assessments with quantitative data; as well, the sensitivity and comparative analyses are conducted to allow decision makers to observe the stability of the results. The present study at the same time can be utilized without modifications in other industries. In terms of managerial implications, this paper provides valuable insights for practitioners and decision makers or policy holders to review their latest current performance in light of sustainability development, benchmark the performance of their rivals in order to help a 3PL key player to navigate, and focus on strengthening strategies as soon as possible to reinforce its competitiveness.

The structure of this study is organized as follows. The literature review is presented in Section 2. In Section 3, materials and methodologies are presented. In Section 4, the result analysis is demonstrated. Section 5 describes the results validation. In Section 6, discussion of the implications in terms of research and practice are presented. Finally, in Section 7, the conclusion and suggestions for future research are discussed.

2. Literature Review

This study presents an objective weighting evaluation framework for 3PLs using entropy-based and MARCOS methods. The literature related to this study is in two separate streams: a literature review on global 3PLs performance evaluation and a literature review on multicriteria decision-making (MCDM) methodologies. Below, we review relevant studies and point out the gaps in the literature.

2.1. Scholarly Works on Performance Evaluation of 3PL Service Providers

Leading 3PL organizations that compete on a worldwide scale can employ efficiency analysis to identify their strengths and shortcomings and improve their performance. Numerous eminent research studies used various MCDM methodologies that take into account numerous criteria to assess the performance of 3PL providers. Considering quantitative indicators in the performance evaluation, the data envelopment analysis (DEA) method is widely used and is proven to be a powerful tool. Min and Joo [10] used the DEA method, which was shown to be valuable for gauging the operational effectiveness of different for-profit and nonprofit companies, using as examples the major 3PLs in the USA. The study assisted 3PLs in locating possible inefficiency causes and offered helpful insight into the ongoing enhancement of operational efficiency, established specific policy guidelines for allocating financial resources in a priority manner, as well as assessed the effects of financial investment on 3PL profitability. Liu et al. [11] employed the DEA method to evaluate 25 3PLs using the collected real data. A study by Min [12] used a survey questionnaire to investigate the prevalent logistics outsourcing practices used by US businesses and identify the major factors affecting those decisions. In terms of customer value propositions, the study also examined the current developments in logistics outsourcing. Min et al. [13] employed the DEA technique to compare the performance of 24 of the top 3PLs in North America to their rivals in international 3PL marketplaces based on slack-based efficiency, pure technical efficiency, and mixed efficiency. In particular, the work advanced the Banker, Charnes, and Cooper (BCC) model as well as the Charnes, Cooper, and Rhodes (CCR) model under constant returns to scale. Joo and Yun [14] applied DEA models and one-way analysis of variance (ANOVA) to examine the comparative performance of 32 3PL companies out of 40 top North America 3PL companies based on the availability of data.

On the other hand, the analytical hierarchy process (AHP) method is one of the MCDM methods proven effective in taking into consideration experts’ preferences when it is necessary to involve subjective judgments about the relative importance of common criteria that are nonmonetary, intangible, and difficult to assess, such as social and environmental factors. For example, Perçin [15] proposed a two-stage analytical hierarchy process (AHP) and the technique for order preference by similarity to ideal solution (TOPSIS) approach in the evaluation of 3PL providers. Daim et al. [16] applied AHP in a 3PL provider for international business. Kucukaltan et al. [17] used the analytic network process (ANP) method to evaluate the Turkish logistics industry under 15 indicators with regard to environmental concerns. Ashtiani and Abdollahi [18] proposed a hybrid framework of fuzzy AHP (FAHP) and fuzzy vlsekriterijumska optimizacija i kompromisno resenje (FVIKOR) while combining fuzzy logic with this approach lets the proposed model the vague, uncertain and subjective nature of trust.

2.2. Research Gap and Contributions of Present Study

Given the above discussion, by exhaustively reviewing the literature in terms of key indicators and approaches in evaluating 3PL performance, in this research, the decision criteria for 3PL performance analysis are extracted based on the existing literature review and recognition by experts, including economic, service level, social, and environmental aspects, as shown in

Table 1. The considered aspects and criteria for 3PL performance evaluation.

Dimension	Criteria	Reference
Economic	Revenue	[11,16,17,19,20,21]
	Transportation expenses	[16,17,19,21]
	Operating expenses	[10,21]
	Total warehousing space	[10,11,13,16,17,20]
Service level	Air freight transported	[13,20]
	Ocean freight transported	[13,20]
	Land freight transported	[13,20,22]
	Contract logistics	[13,20,22]
Social and environmental	Number of employees	[11,13,17,20]
	Accidents	[22]
	Employee satisfaction rate	[16,17,22]
	CO2 emissions	[20,22]

.

In terms of methodologies, this paper proposed a model combining entropy (objective weighting for criteria) and MARCOS (alternatives ranking) methods for the first time for the sustainable evaluation of major 3PL providers. In the MCDM process, deciding on the criteria weights is crucial because it greatly affects the outcomes [23]. Subjective weighting, objective weighting, and a combination of weighting approaches can all be used to determine the selection criteria’s weights [24]. Expert opinions and experiences are evaluated using subjective weighting methods, and decision makers directly weigh in on the analyst’s questions to determine the relative importance of the criteria. It takes a lot of time to use the subjective weighing methods, especially when decision makers do not regularly take the discussion of the weight value into account [25]. In contrast, the objective weighting methods omit the decision makers’ subjective assessment information in favor of obtaining weights with mathematical methods based on the structural analysis of the data. The efficiency of the computations can greatly benefit from the objective weighting methods. Therefore, objective weighting methods must be used to produce more meaningful results and enhance the standard of decision making. Mean weight, standard deviation, statistical variance procedure, the entropy approach, criteria importance through intercriteria correlation (CRITIC), and simultaneous evaluation of criteria and alternatives (SECA) are some of the common objective weighting techniques [26,27,28,29]. Each of these has strengths and weaknesses as well as varying degrees of effectiveness. For industrial robot selection issues, four objective weighing techniques—the Shannon entropy, CRITIC, ideal point, and distance-based approaches—were also presented and contrasted [30]. Entropy, an objective weighting technique, was utilized in this study to determine how much each relevant criterion was worth. Shannon developed the entropy approach, which determines the weight for each criterion depending on data gathered [31]. Numerous fields make extensive use of the entropy technique. For problems involving material selection, Hafezalkotob [32] created the Shannon entropy–MULTIMOORA integration method. Wang et al. [33] developed the AHP–entropy–ANFIS model to forecast the unfrozen water of saline soil. Sengül et al. [34] used the fuzzy TOPSIS approach to analyze renewable energy supply systems and the Shannon entropy method to determine each criterion’s weight value. Using the aggregate entropy–PROMETHEE technique, a framework for the sustainability assessment of port regions was proposed [35].

MARCOS was introduced in 2020 [9] as a novel, effective MCDM technique that empowers the decision-making environment by handling many deficiencies of other techniques, such as neglecting the relative importance of distances and exhausting calculations. The method considers different parameters based on the alternatives’ performance to determine their final performance score using utility-based functions. Then, the extended version of MARCOS considers parameters in an uncertain environment through triangular numbers (TFNs), i.e., the novel fuzzy MARCOS method, which was developed by Stanković et al. [36].

The development of an integrated MCDM approach is lacking; such an approach would strengthen the robustness of the methodology and take into account sustainable performance metrics of the 3PL service providers. Furthermore, the use of objective weighting MCDM methods for performance evaluation, such as the innovative MARCOS approach and entropy-based methods, has been disregarded. There are also few studies on environmental sustainability in the logistics service sector, despite the fact that several studies looked at the outsourcing of logistics and 3PLs. This highlights certain new features of environmental and social issues in the 3PL sector that received little attention in prior studies. Consequently, this paper intends to cover this gap. Hence,

Table 2. A comparison of the present paper with the previous studies.

Authors	Nature of the Method	Name of Method	Nature of Evaluation	Operational Performance Measurement	Financial Performance Measurement	Association with Service Level	Social and Environmental Performance Measurement	Sensitivity Analysis	Comparative Analysis
Min and Joo [10]	Single	DEA	Objective		x
Min et al. [13]	Single	DEA	Objective	x	x	x
Liu et al. [11]	Single	DEA	Objective		x
Daim et al. [16]	Single	AHP	Subjective	x	x	x
Min [12]	Single	Survey	Subjective	x	x	x
Kumar and Singh [19]	Integrated	AHP, TOPSIS	Subjective		x	x
Pamucar et al. [2]	Integrated	BWM-WASPAS-MABAC	Subjective			x		x
Pal Singh et al. [37]	Integrated	MOORA, COPRAS, CRITIC	Objective	x	x	x		x	x
Wang et al. [38]	Integrated	AHP, VIKOR	Subjective	x		x	x
Mishra et al. [39]	Integrated	CRITIC, EDAS	Subjective	x			x		x
This work	Integrated	Entropy, MARCOS	Objective	x	x	x	x	x	x

Note: DEA: data envelopment analysis; AHP: analytic hierarchy process; TOPSIS: technique for order of preference by similarity to ideal solution; BWM: best worst method; WASPAS: weighted aggregates sum product assessment; MABAC: multiattributive border approximation area comparison; MOORA: multiobjective optimization method on the basis of ratio analysis; COPRAS: complex proportional assessment; CRITIC: criteria importance through intercriteria correlation; VIKOR: vlse kriterijumska optimizacija i kompromisno resenje; EDAS: evaluation based on distance from average solution; MARCOS: measurement of alternatives and ranking according to compromise solution.

presents a summary of the extant literature that shows the present study’s contribution.

3. Materials and Methods

3.1. Research Framework

MCDM is considered a complexity tool to balance the goals, risks, and constraints of a problem. This paper proposed a research framework for the sustainable evaluation of major third-party logistics providers (3PLs) by considering 12 criteria and 15 alternatives; this framework is shown in Figure 1. In the first phase, the weight coefficients for each criterion are computed by entropy objective weighting method. Then, the MARCOS method is applied to rank the alternatives. Sensitivity analysis of criteria weights and comparative analysis of MCDM methods are conducted to test the effectiveness and the applicability of the proposed model.

3.2. Entropy Objective Weighting Method

The entropy theory was proposed by Shannon [31] to measure uncertain information and entropy. The basic concept of entropy weight measurement is that a higher weight index value is more valuable than a lower index value. As the weight of any criterion reflects its importance, this method was used to determine each criterion’s objective weights based on the dispersion of original data [40]. Following are the steps to apply the entropy objective weighting method to an MCDM problem [41].

Step 1: Establish the initial decision-making matrix $X$ of the multicriteria problem with $n$ criteria and $m$ alternatives using Equation (1).

$$X={\left[x_{ij}\right]}_{m\times n}=\left[\begin{array}{cccc}{x}_{11}& x_{12}& \dots & x_{1n}\\ x_{21}& x_{22}& \dots & x_{2n}\\ \dots & \dots & \dots & \dots \\ x_{m1}& x_{m2}& \dots & x_{mn}\end{array}\right];i=1,2,\dots ,m;j=1,2\dots n$$

(1)

where $x_{ij}$ is the performance scores of the $i^{th}$ alternative to the $j^{th}$ criterion, $m$ is the total number of alternatives, and $n$ is the total number of criteria.

Step 2: Compute the normalized decision-making matrix using Equation (2).

$$v_{ij}=\frac{x_{ij}}{\sum _{i=1}^m{x}_{ij}}$$

(2)

where $v_{ij}$ is the normalized value of alternative $A_i$ about $C_j$; $x_{ij}$ is the actual value of alternative $A_i$ with respect to $C_j$; and $m$ is the total number of evaluated alternatives.

Step 3: Compute the entropy value of the $jth$ criterion using Equation (3). The entropy $e_j$ can thus measure the amount of decision information contained on the normalized matrix and queued in each criterion.

$$e_j=-k\sum _{i=1}^m{v}_{ij}\ln \left(v_{ij}\right)=-\frac{1}{\ln \left(m\right)}\sum _{i=1}^m{v}_{ij}\ln \left(v_{ij}\right)$$

(3)

where $\ln \left(∎\right)$ is the logarithm based on $e$, and $e_j$ is [0, 1].

Step 4: Compute the degree of diversification $d_j$ using Equation (4).

$$d_j=1-e_j,j\in [1,\dots ,n]$$

(4)

Step 5: Compute the objective weighting for each criterion using Equation (5).

$$w_j=\frac{d_j}{\sum _{j=1}^n{d}_j}$$

(5)

These obtained objective weights will be used in the MARCOS model in the next phase to determine the performance of each alternative.

3.3. MARCOS Ranking Method

Measurement of alternatives and ranking according to compromise solution (MARCOS) is one of the MCDM ranking methods which is suitable for solving decision-making problems with more criteria and alternatives. The concept of this method is based on defining the relationship between alternative and reference values (i.e., ideal and anti-ideal alternatives) [42]. This ranking method has three starting points, including the reference points, relationship between alternatives, and utility degree of alternatives that help decision makers make a robust decision [43]. The algorithm of the MARCOS method is presented as follows [44].

Step 1: Develop an initial decision-making matrix including a set of $n$ criteria and $m$ alternatives using Equation (6).

$$X={\left[x_{ij}\right]}_{m\times n}=\left[\begin{array}{cccc}{x}_{11}& x_{12}& \dots & x_{1n}\\ x_{21}& x_{22}& \dots & x_{2n}\\ \dots & \dots & \dots & \dots \\ x_{m1}& x_{m2}& \dots & x_{mn}\end{array}\right];i=1,2,\dots ,m;j=1,2\dots n$$

(6)

where $x_{ij}$ is the performance of the $i^{th}$ alternative to the $j^{th}$ criterion, $m$ is the number of alternatives, and $n$ is the number of criteria.

Step 2: Establish an extended initial decision-making matrix by defining the ideal $\left(AI\right)$ and anti-ideal $\left(AAI\right)$ solutions using Equation (7).

$${\mathrm{X}}^{\prime }=\begin{array}{c}\left(AAI\right)\\ A_1\\ \begin{array}{c}{A}_2\\ \cdots \\ \begin{array}{c}{A}_m\\ \left(AI\right)\end{array}\end{array}\end{array}\stackrel{\begin{array}{ccc}{C}_1& C_2& \begin{array}{cc}\cdots & C_n\end{array}\end{array}}{\overbrace{\left[\begin{array}{ccc}{x}_{aa1}& x_{aa2}& \begin{array}{cc}\cdots & x_{aan}\end{array}\\ x_{11}& x_{12}& \begin{array}{cc}\cdots & x_{1n}\end{array}\\ \begin{array}{c}{x}_{21}\\ \cdots \\ \begin{array}{c}{x}_{m1}\\ x_{ai1}\end{array}\end{array}& \begin{array}{c}{x}_{22}\\ \cdots \\ \begin{array}{c}{x}_{m2}\\ x_{ai2}\end{array}\end{array}& \begin{array}{cc}\begin{array}{c}\cdots \\ \cdots \\ \begin{array}{c}\cdots \\ \cdots \end{array}\end{array}& \begin{array}{c}{x}_{2n}\\ \cdots \\ \begin{array}{c}{x}_{mn}\\ x_{ain}\end{array}\end{array}\end{array}\end{array}\right]}}$$

(7)

The ideal $\left(AI\right)$ solution is an alternative with the best performance, while the anti-ideal $\left(AAI\right)$ is the worst alternative. Depending on the nature of the criteria, the set of $\left(AI\right)$ and $\left(AAI\right)$ are defined using Equations (8) and (9).

$$AI=\underset{i}{\max }{x}_{ij}ifj\in Band\underset{i}{\min }{x}_{ij}ifj\in C$$

(8)

$$AAI=\underset{i}{\min }{x}_{ij}ifj\in Band\underset{i}{\max }{x}_{ij}ifj\in C$$

(9)

where $B$ denotes a benefit group of criteria while $C$ denotes a group of cost criteria.

Step 3: Compute the normalization of the extended initial decision-making matrix, which is $N={\left[n_{ij}\right]}_{m\times n}$ using Equations (10) and (11).

$$n_{ij}=\frac{x_{ij}}{x_{ai}}ifj\in B$$

(10)

$$n_{ij}=\frac{x_{ai}}{x_{ij}}ifj\in C$$

(11)

where elements $x_{ij}$ and $x_{ai}$ denote the elements of the matrix ${\mathrm{X}}^{\prime }$.

Step 4: Compute the weighted matrix $V={\left[v_{ij}\right]}_{m\times n}$. The weighted matrix $V$ is obtained by multiplying the normalized matrix $N$ with the weight coefficients of the criterion $w_j$ using Equation (12). In this paper, the weight coefficients of each criterion are calculated using the entropy objective weighting method in the previous phase.

$$v_{ij}=n_{ij}\times w_j$$

(12)

Step 5: Compute the utility degree of alternatives $K_i$ using equations (13) and (14). The utility degrees of an alternative in relation to the ideal ${(K}_i^{+})$ and to an anti-ideal ${(K}_i^{-}$) solution are computed.

$$K_i^{+}=\frac{S_i}{S_{ai}}$$

(13)

$$K_i^{-}=\frac{S_i}{S_{aai}}$$

(14)

where $S_i$ ($i=1,2,\dots ,m$) represents the sum of the elements of the weighted matrix $V$, as can be seen in Equation (15).

$$S_i=\sum _{i=1}^n{v}_{ij}$$

(15)

Step 6: Compute the utility function of alternatives $f\left(K_i\right)$ using Equation (16). The utility function is the compromise of the observed alternative in relation to the ideal and anti-ideal solutions.

$$f\left(K_i\right)=\frac{K_i^{+}+K_i^{-}}{1+\frac{1-f\left(K_i^{+}\right)}{f\left(K_i^{+}\right)}+\frac{1-f\left(K_i^{-}\right)}{f\left(K_i^{-}\right)}}$$

(16)

where the utility function in relation to the ideal $f\left(K_i^{+}\right)$ and anti-ideal $f\left(K_i^{-}\right)$ solutions are determined by using Equations (17) and (18).

$$f\left(K_i^{+}\right)=\frac{K_i^{-}}{K_i^{+}+K_i^{-}}$$

(17)

$$f\left(K_i^{-}\right)=\frac{K_i^{+}}{K_i^{+}+K_i^{-}}$$

(18)

Step 7: Ranking the alternatives based on the final values of the utility function $f\left(K_i\right)$. The best alternative is the one that is closest to the ideal and at the same time furthest from the anti-ideal reference point. It means that the alternative with higher utility function value is more preferred.

4. Results Analysis

4.1. A Case Study

In this paper, the source of data is a list of 15 global 3PL companies published by Armstrong & Associates, Inc. (2021), which has been a leading provider of 3PL market information and consulting since 1980. We selected 15 3PL companies from the 50 top 3PL companies of the world based on the availability of data, as shown in

Table 3. The list of third-party logistics providers.

DMU	Third-Party Logistics Provider	Symbol	Headquarters
3PL-01	Kuehne + Nagel	Kuehne + Nagel	Switzerland
3PL-02	DHL Supply Chain & Global Forwarding	DHL	Germany
3PL-03	DSV	DSV	Denmark
3PL-04	DB Schenker	DB Schenker	Germany
3PL-05	FedEx	FedEx	United States
3PL-06	Sinotrans	Sinotrans	China
3PL-07	Nippon Express	Nippon	Japan
3PL-08	Expeditors	Expeditors	United States
3PL-09	UPS Supply Chain Solutions	UPS	United States
3PL-10	CEVA Logistics	CEVA	France
3PL-11	XPO Logistics	XPO	United States
3PL-12	NFI	NFI	United States
3PL-13	Kerry Logistics	Kerry	Hong Kong
3PL-14	Maersk Logistics	Maersk	Denmark
3PL-15	Kintetsu World Express	Kintetsu	Japan

.

Table 4. The list of criteria and their symbols.

Dimension	Criteria	Type	Symbol
Economic	Revenue	Benefit	C1
	Transportation expenses	Cost	C2
	Operating expenses	Cost	C3
	Total warehousing space	Benefit	C4
Service level	Air freight transported	Benefit	C5
	Ocean freight transported	Benefit	C6
	Land freight transported	Benefit	C7
	Contract logistics	Benefit	C8
Social and environmental	Number of employees	Benefit	C9
	Accidents	Cost	C10
	Employee satisfaction rate	Benefit	C11
	CO2 emissions	Cost	C12

shows the list of criteria which were selected after reviewing the literature in the logistics industry. By using related reports from each 3PL company (sustainability reports, annual reports, financial reports, etc.), their data according to defined criteria were collected and analyzed according to

Table 5. Statistical analysis on data collection.

Dimension	Criteria	Unit	Max	Min	Avg	SD
Economic	Revenue	USD millions	97,287.00	2680.00	36,274.91	30,464.83
	Transportation expenses	USD millions	75,367.00	1219.65	20,292.03	19,093.64
	Operating expenses	USD millions	84,477.00	2575.27	30,086.73	27,597.76
	Total warehousing space	Million square feet	139.60	5.43	45.60	41.96
Service level	Air freight transported	Million tonnes	1.80	0.07	0.76	0.49
	Ocean freight transported	Million TEUs	4.53	0.13	1.60	1.33
	Land freight transported	USD millions	8647.00	1314.00	4136.74	2142.46
	Contract logistics	USD millions	10,035.00	2012.56	4981.16	2600.98
Social and environmental	Number of employees	Persons	592,263.00	14,500.00	138,595.27	175,311.21
	Accidents	Number of accidents	9.00	1.00	4.33	2.05
	Employee satisfaction rate	%	93.02	71.80	85.44	5.69
	CO2 emissions	Million tonnes	66.13	0.05	17.05	21.70

.

4.2. Calculation of Criteria Weights with Entropy Model

In this phase, the weights of significance are determined with objective references using the entropy weighting method. According to the entropy calculation process, the initial decision-making matrix is established in

Table A1. The initial decision-making matrix of the entropy model.

3PL	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11	C12
Kuehne + Nagel	38,955.00	24,498.00	32,664.00	109.86	1.42	4.53	4659.66	5484.33	78,087.00	5.00	82.90	16.73
DHL	84,795.35	33,606.49	76,440.00	139.60	1.80	2.86	5023.26	6548.21	592,263.00	9.00	84.00	39.36
DSV	29,920.00	15,284.06	21,834.37	14.10	1.27	2.49	7146.85	9458.24	77,958.00	2.00	78.60	12.78
DB Schenker	47,075.00	45,125.56	53,354.00	94.00	0.99	2.05	3577.70	5085.59	72,000.00	6.00	78.20	18.52
FedEx	83,959.00	33,655.00	78,102.00	30.79	0.26	2.69	6836.47	7833.00	249,000.00	7.00	88.65	35.60
Sinotrans	19,097.00	10,289.53	16,648.13	5.43	0.53	3.75	2540.28	2566.18	33,794.00	3.00	87.60	0.25
Nippon	18,612.00	9018.29	13,480.11	31.70	0.72	0.66	2355.72	2719.35	73,350.00	2.00	71.80	1.61
Expeditors	16,680.00	12,058.16	14,614.19	25.00	0.93	1.01	3024.13	4206.30	19,000.00	4.00	90.10	0.05
UPS	97,287.00	75,367.00	84,477.00	17.30	0.99	0.62	8647.00	10,035.00	534,000.00	5.00	91.30	58.63
CEVA	7416.00	5689.24	6803.00	18.10	0.44	1.08	2283.00	3376.00	78,000.00	6.00	85.70	0.27
XPO	16,250.00	10,902.49	13,290.00	101.00	0.07	0.13	4646.57	3012.24	102,000.00	5.00	93.02	1.29
NFI	2680.00	1219.65	2575.27	53.68	0.21	0.32	1826.40	2012.56	14,500.00	3.00	85.91	0.13
Kerry	10,600.30	7858.27	8925.88	8.80	0.49	1.02	2238.00	2526.01	51,473.00	3.00	92.00	2.33
Maersk	61,787.00	16,591.21	22,900.00	14.70	0.17	0.13	5932.00	7396.00	85,375.00	4.00	89.00	66.13
Kintetsu	9010.00	3217.58	5193.00	20.00	1.12	0.66	1314.00	2458.34	18,129.00	1.00	82.80	2.10

(Appendix A). Following that, the normalized decision-making matrix of the entropy model is developed in

Table A2. The normalized decision-making matrix of the entropy model.

3PL	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11	C12
Kuehne + Nagel	0.0716	0.0805	0.0724	0.1606	0.1242	0.1885	0.0751	0.0734	0.0376	0.0769	0.0647	0.0654
DHL	0.1558	0.1104	0.1694	0.2041	0.1572	0.1191	0.0810	0.0876	0.2849	0.1385	0.0655	0.1539
DSV	0.0550	0.0502	0.0484	0.0206	0.1114	0.1038	0.1152	0.1266	0.0375	0.0308	0.0613	0.0500
DB Schenker	0.0865	0.1483	0.1182	0.1374	0.0868	0.0854	0.0577	0.0681	0.0346	0.0923	0.0610	0.0724
FedEx	0.1543	0.1106	0.1731	0.0450	0.0230	0.1120	0.1102	0.1048	0.1198	0.1077	0.0692	0.1392
Sinotrans	0.0351	0.0338	0.0369	0.0079	0.0466	0.1561	0.0409	0.0343	0.0163	0.0462	0.0684	0.0010
Nippon	0.0342	0.0296	0.0299	0.0463	0.0631	0.0275	0.0380	0.0364	0.0353	0.0308	0.0560	0.0063
Expeditors	0.0307	0.0396	0.0324	0.0365	0.0812	0.0422	0.0487	0.0563	0.0091	0.0615	0.0703	0.0002
UPS	0.1788	0.2476	0.1872	0.0253	0.0866	0.0258	0.1394	0.1343	0.2569	0.0769	0.0712	0.2292
CEVA	0.0136	0.0187	0.0151	0.0265	0.0385	0.0450	0.0368	0.0452	0.0375	0.0923	0.0669	0.0011
XPO	0.0299	0.0358	0.0294	0.1476	0.0061	0.0053	0.0749	0.0403	0.0491	0.0769	0.0726	0.0050
NFI	0.0049	0.0040	0.0057	0.0785	0.0187	0.0135	0.0294	0.0269	0.0070	0.0462	0.0670	0.0005
Kerry	0.0195	0.0258	0.0198	0.0129	0.0433	0.0425	0.0361	0.0338	0.0248	0.0462	0.0718	0.0091
Maersk	0.1136	0.0545	0.0507	0.0215	0.0152	0.0056	0.0956	0.0990	0.0411	0.0615	0.0694	0.2585
Kintetsu	0.0166	0.0106	0.0115	0.0292	0.0981	0.0276	0.0212	0.0329	0.0087	0.0154	0.0646	0.0082

(Appendix A). As the results, the weights of all 12 criteria for each dimension including economic, service level, social, and environmental are obtained in

Table 6. The criteria weights calculated using entropy method.

Dimension	Criteria	Symbol	$\mathbf{Entropy}{\mathit{e}}_{\mathit{j}}$	$\mathbf{Deflection}\mathbf{Degree}{1-\mathit{e}}_{\mathit{j}}$	$\mathbf{Weight}{\mathit{w}}_{\mathit{j}}$
Economic	Revenue	C1	0.8740	0.1260	0.0897
	Transportation expenses	C2	0.8611	0.1389	0.0989
	Operating expenses	C3	0.8572	0.1428	0.1017
	Total warehousing space	C4	0.8586	0.1414	0.1007
Service level	Air freight transported	C5	0.9175	0.0825	0.0588
	Ocean freight transported	C6	0.8725	0.1275	0.0908
	Land freight transported	C7	0.9514	0.0486	0.0346
	Contract logistics	C8	0.9514	0.0486	0.0346
Social and environmental	Number of employees	C9	0.7834	0.2166	0.1543
	Accidents	C10	0.9575	0.0425	0.0303
	Employee satisfaction rate	C11	0.9992	0.0008	0.0006
	CO2 emissions	C12	0.7121	0.2879	0.2050

. The top five criteria of a significant level are visualized in Figure 2. As can be seen, CO₂ emissions (C12), number of employees (C9), operating expenses (C3), total warehousing space (C4), and transportation expenses (C2) criteria have the most influence percentages, at 20.50%, 15.43%, 10.17%, 10.07%, and 9.89%, respectively. These figures elaborate that social and environmental factors are of tremendous importance in the sustainable evaluation of the services that third-party logistics provide besides dimensions of economic and service level.

4.3. Ranking Alternatives with MARCOS Model

After calculating the objective weights of criteria, the application of the MARCOS method for obtaining the ranks of third-party logistics providers is performed. The decision tree for sustainable performance evaluation of third-party logistics providers is presented in Figure 3. The formation of a multicriteria model consists of 12 criteria under the four dimensions of economic, service level, social, and environmental, and 15 logistics companies.

According to the MARCOS calculation process, the ideal $\left(AI\right)$ and anti-ideal $\left(AAI\right)$ solutions in relation to each criterion are determined. The ideal $\left(AI\right)$ is the highest value of each criterion while the lowest value is the anti-ideal $\left(AAI\right)$. Consequently, the normalized and weighted normalized decision-making matrix of the MARCOS model are presented in

Table A3. The normalized decision-making matrix of the MARCOS model.

3PL	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11	C12
Kuehne + Nagel	0.4004	0.0498	0.0788	0.7870	0.7900	1.0000	0.5389	0.5465	0.1318	0.2000	0.8912	0.0030
DHL	0.8716	0.0363	0.0337	1.0000	1.0000	0.6319	0.5809	0.6525	1.0000	0.1111	0.9030	0.0013
DSV	0.3075	0.0798	0.1179	0.1010	0.7089	0.5507	0.8265	0.9425	0.1316	0.5000	0.8450	0.0039
DB Schenker	0.4839	0.0270	0.0483	0.6734	0.5521	0.4531	0.4138	0.5068	0.1216	0.1667	0.8407	0.0027
FedEx	0.8630	0.0362	0.0330	0.2205	0.1462	0.5942	0.7906	0.7806	0.4204	0.1429	0.9530	0.0014
Sinotrans	0.1963	0.1185	0.1547	0.0389	0.2965	0.8280	0.2938	0.2557	0.0571	0.3333	0.9417	0.1981
Nippon	0.1913	0.1352	0.1910	0.2271	0.4012	0.1458	0.2724	0.2710	0.1238	0.5000	0.7719	0.0308
Expeditors	0.1715	0.1011	0.1762	0.1791	0.5163	0.2236	0.3497	0.4192	0.0321	0.2500	0.9686	1.0000
UPS	1.0000	0.0162	0.0305	0.1239	0.5509	0.1369	1.0000	1.0000	0.9016	0.2000	0.9815	0.0008
CEVA	0.0762	0.2144	0.3785	0.1297	0.2451	0.2387	0.2640	0.3364	0.1317	0.1667	0.9213	0.1813
XPO	0.1670	0.1119	0.1938	0.7235	0.0391	0.0281	0.5374	0.3002	0.1722	0.2000	1.0000	0.0384
NFI	0.0275	1.0000	1.0000	0.3845	0.1187	0.0715	0.2112	0.2006	0.0245	0.3333	0.9236	0.3712
Kerry	0.1090	0.1552	0.2885	0.0630	0.2752	0.2252	0.2588	0.2517	0.0869	0.3333	0.9890	0.0212
Maersk	0.6351	0.0735	0.1125	0.1053	0.0967	0.0295	0.6860	0.7370	0.1442	0.2500	0.9568	0.0007
Kintetsu	0.0926	0.3791	0.4959	0.1433	0.6240	0.1466	0.1520	0.2450	0.0306	1.0000	0.8901	0.0236

and

Table A4. The weighted normalized decision-making matrix of the MARCOS model.

3PL	C1	C2	C3	C4	C5	C6	C7	C8	C9	C10	C11	C12
Kuehne + Nagel	0.0359	0.0049	0.0080	0.0793	0.0464	0.0908	0.0186	0.0189	0.0203	0.0061	0.0005	0.0006
DHL	0.0782	0.0036	0.0034	0.1007	0.0588	0.0574	0.0201	0.0226	0.1543	0.0034	0.0005	0.0003
DSV	0.0276	0.0079	0.0120	0.0102	0.0417	0.0500	0.0286	0.0326	0.0203	0.0151	0.0005	0.0008
DB Schenker	0.0434	0.0027	0.0049	0.0678	0.0324	0.0411	0.0143	0.0175	0.0188	0.0050	0.0005	0.0005
FedEx	0.0774	0.0036	0.0034	0.0222	0.0086	0.0540	0.0274	0.0270	0.0649	0.0043	0.0006	0.0003
Sinotrans	0.0176	0.0117	0.0157	0.0039	0.0174	0.0752	0.0102	0.0088	0.0088	0.0101	0.0006	0.0406
Nippon	0.0172	0.0134	0.0194	0.0229	0.0236	0.0132	0.0094	0.0094	0.0191	0.0151	0.0005	0.0063
Expeditors	0.0154	0.0100	0.0179	0.0180	0.0303	0.0203	0.0121	0.0145	0.0049	0.0076	0.0006	0.2050
UPS	0.0897	0.0016	0.0031	0.0125	0.0324	0.0124	0.0346	0.0346	0.1391	0.0061	0.0006	0.0002
CEVA	0.0068	0.0212	0.0385	0.0131	0.0144	0.0217	0.0091	0.0116	0.0203	0.0050	0.0005	0.0372
XPO	0.0150	0.0111	0.0197	0.0729	0.0023	0.0026	0.0186	0.0104	0.0266	0.0061	0.0006	0.0079
NFI	0.0025	0.0989	0.1017	0.0387	0.0070	0.0065	0.0073	0.0069	0.0038	0.0101	0.0005	0.0761
Kerry	0.0098	0.0154	0.0293	0.0063	0.0162	0.0205	0.0090	0.0087	0.0134	0.0101	0.0006	0.0044
Maersk	0.0570	0.0073	0.0114	0.0106	0.0057	0.0027	0.0237	0.0255	0.0222	0.0076	0.0006	0.0002
Kintetsu	0.0083	0.0375	0.0504	0.0144	0.0367	0.0133	0.0053	0.0085	0.0047	0.0303	0.0005	0.0048

, respectively (Appendix A).

Table 7. Value of utility functions and final ranking of the alternatives.

3PL	${\mathit{S}}_{\mathit{i}}$	${\mathit{K}}_{\mathit{i}}^{-}$	${\mathit{K}}_{\mathit{i}}^{+}$	$\mathit{f}\left({\mathit{K}}_{\mathit{i}}^{-}\right)$	$\mathit{f}\left({\mathit{K}}_{\mathit{i}}^{+}\right)$	$\mathit{f}\left({\mathit{K}}_{\mathit{i}}\right)$	Ranking
Kuehne + Nagel	0.3304	9.2088	0.3304	0.0346	0.9654	0.3300	5
DHL	0.5032	14.0227	0.5032	0.0346	0.9654	0.5026	1
DSV	0.2472	6.8901	0.2472	0.0346	0.9654	0.2469	8
DB Schenker	0.2491	6.9417	0.2491	0.0346	0.9654	0.2488	7
FedEx	0.2935	8.1795	0.2935	0.0346	0.9654	0.2931	6
Sinotrans	0.2207	6.1497	0.2207	0.0346	0.9654	0.2204	9
Nippon	0.1695	4.7226	0.1695	0.0346	0.9654	0.1693	14
Expeditors	0.3567	9.9409	0.3567	0.0346	0.9654	0.3563	4
UPS	0.3668	10.2216	0.3668	0.0346	0.9654	0.3663	2
CEVA	0.1995	5.5604	0.1995	0.0346	0.9654	0.1993	11
XPO	0.1935	5.3933	0.1935	0.0346	0.9654	0.1933	12
NFI	0.3601	10.0339	0.3601	0.0346	0.9654	0.3596	3
Kerry	0.1435	4.0000	0.1435	0.0346	0.9654	0.1434	15
Maersk	0.1744	4.8602	0.1744	0.0346	0.9654	0.1742	13
Kintetsu	0.2147	5.9841	0.2147	0.0346	0.9654	0.2145	10

shows the calculation of the utility degree and the final utility function value of alternatives. Using these values, the final ranking of alternatives is derived. The results show that the top three third-party logistics providers are DHL Supply Chain & Global Forwarding (3PL-02), UPS Supply Chain Solutions (3PL-09), and NFI (3PL-12), ranking in the first, second, and third positions with utility function scores of 0.5026, 0.3663, and 0.3596, respectively. Figure 4 displays the final third-party logistics providers ranking from the entropy–MARCOS model.

5. Results Validation

5.1. Sensitivity Analysis of Criteria Weights

In this section of the paper, the validation of the obtained results is performed. In MCDM problems, the majority of input data is dynamic rather than continuous and stable. As a result, a sensitivity analysis can successfully aid in making sound decisions. In this study, we used the sensitivity analysis approach in MCDM problems, where we identify changes in the problem’s solutions if the weights of one criterion change. Adjustments in the weighting of other criteria, as well as changes in the final ranking of alternatives, are among the changes [45].

The removal of criteria one by one and their impact on the final ranking is performed for this purpose [46]. As a result, the sensitivity analysis of criteria weight includes 12 scenarios.

Table A5. The weights of criteria for all scenarios in sensitivity analysis.

Criteria	Base Case	Scenario 1	Scenario 2	Scenario 3	Scenario 4	Scenario 5	Scenario 6	Scenario 7	Scenario 8	Scenario 9	Scenario 10	Scenario 11	Scenario 12
C1	0.0897	0	0.0996	0.0999	0.0998	0.0953	0.0987	0.0929	0.0929	0.1061	0.0925	0.0898	0.1129
C2	0.0989	0.1087	0	0.1101	0.1100	0.1051	0.1088	0.1025	0.1025	0.1170	0.1020	0.0990	0.1244
C3	0.1017	0.1117	0.1129	0	0.1131	0.1080	0.1119	0.1053	0.1053	0.1202	0.1049	0.1018	0.1279
C4	0.1007	0.1107	0.1118	0.1121	0	0.1070	0.1108	0.1043	0.1043	0.1191	0.1039	0.1008	0.1267
C5	0.0588	0.0646	0.0652	0.0654	0.0654	0	0.0646	0.0609	0.0609	0.0695	0.0606	0.0588	0.0739
C6	0.0908	0.0998	0.1008	0.1011	0.1010	0.0965	0	0.0941	0.0941	0.1074	0.0936	0.0909	0.1142
C7	0.0346	0.0380	0.0384	0.0385	0.0385	0.0368	0.0381	0	0.0358	0.0409	0.0357	0.0346	0.0435
C8	0.0346	0.0380	0.0384	0.0385	0.0385	0.0367	0.0380	0.0358	0	0.0409	0.0357	0.0346	0.0435
C9	0.1543	0.1695	0.1712	0.1717	0.1716	0.1639	0.1697	0.1598	0.1598	0	0.1591	0.1544	0.1941
C10	0.0303	0.0332	0.0336	0.0337	0.0336	0.0321	0.0333	0.0313	0.0313	0.0358	0	0.0303	0.0381
C11	0.0006	0.0007	0.0007	0.0007	0.0007	0.0006	0.0007	0.0006	0.0006	0.0007	0.0006	0	0.0007
C12	0.2050	0.2253	0.2276	0.2283	0.2280	0.2178	0.2255	0.2124	0.2124	0.2424	0.2114	0.2052	0

(Appendix A) shows the weight of criteria in all scenarios.

Table A6. The prospect values of alternatives for all scenarios in sensitivity analysis.

Solutions	Base Case	Scenario 1	Scenario 2	Scenario 3	Scenario 4	Scenario 5	Scenario 6	Scenario 7	Scenario 8	Scenario 9	Scenario 10	Scenario 11	Scenario 12
Kuehne + Nagel	0.3300	0.3231	0.3608	0.3585	0.2790	0.3014	0.2632	0.3227	0.3224	0.3662	0.3342	0.3297	0.4141
DHL	0.5026	0.4663	0.5537	0.5556	0.4470	0.4716	0.4897	0.4999	0.4974	0.4120	0.5149	0.5023	0.6314
DSV	0.2469	0.2410	0.2653	0.2615	0.2633	0.2182	0.2167	0.2263	0.2221	0.2680	0.2391	0.2466	0.3094
DB Schenker	0.2488	0.2257	0.2731	0.2715	0.2013	0.2299	0.2284	0.2430	0.2397	0.2720	0.2514	0.2484	0.3121
FedEx	0.2931	0.2371	0.3213	0.3226	0.3013	0.3023	0.2631	0.2754	0.2758	0.2700	0.2979	0.2928	0.3681
Sinotrans	0.2204	0.2228	0.2316	0.2279	0.2407	0.2157	0.1598	0.2178	0.2192	0.2502	0.2169	0.2200	0.2261
Nippon	0.1693	0.1671	0.1730	0.1668	0.1628	0.1548	0.1716	0.1656	0.1657	0.1775	0.1590	0.1689	0.2048
Expeditors	0.3563	0.3745	0.3842	0.3767	0.3762	0.3463	0.3695	0.3566	0.3542	0.4154	0.3597	0.3559	0.1904
UPS	0.3663	0.3040	0.4047	0.4043	0.3935	0.3549	0.3893	0.3438	0.3438	0.2689	0.3716	0.3660	0.4603
CEVA	0.1993	0.2114	0.1976	0.1790	0.2071	0.1964	0.1954	0.1970	0.1945	0.2116	0.2003	0.1989	0.2038
XPO	0.1933	0.1959	0.2022	0.1933	0.1340	0.2029	0.2098	0.1810	0.1895	0.1971	0.1931	0.1928	0.2331
NFI	0.3596	0.3923	0.2894	0.2872	0.3569	0.3747	0.3884	0.3650	0.3655	0.4207	0.3605	0.3593	0.3565
Kerry	0.1434	0.1468	0.1421	0.1270	0.1524	0.1352	0.1352	0.1393	0.1395	0.1537	0.1375	0.1429	0.1747
Maersk	0.1742	0.1288	0.1852	0.1812	0.1819	0.1790	0.1886	0.1559	0.1541	0.1797	0.1719	0.1737	0.2188
Kintetsu	0.2145	0.2265	0.1964	0.1827	0.2225	0.1890	0.2213	0.2168	0.2135	0.2480	0.1900	0.2141	0.2635

(Appendix A) displays the prospect value of alternatives in all scenarios, and Figure 5 depicts their ranking. While the prospect values of the alternatives change, the final ranking remains unchanged (e.g., except for scenario 9), with DHL Supply Chain & Global Forwarding (3PL-02) being the best third-party logistics provider across all scenarios. The sensitivity phase results indicate that, in this case study, the alternative ranking is robust regardless of the criteria’s weight change. As a result, the proposed entropy–MARCOS model is highly stable and applicable.

5.2. Comparative Analysis of MCDM Methods

In order to confirm the stability and reliability of the proposed entropy–MARCOS model, five different combined MCDM models are considered [47]. The gained results are compared with the obtained results using the following MCDM methods: simple additive weighting (SAW) [48], weighted aggregated sum product assessment (WASPAS) [49], complex proportional assessment of alternatives (COPRAS) [50], combinative distance-based assessment (CODAS) [51], and additive ratio assessment (ARAS) [52]. The same weights of criteria are used during the comparative analysis process, and the obtained results are presented in

Table A7. Results of the comparative analysis of MCDM methods.

3PL	Entropy and MARCOS		Entropy and SAW		Entropy and WASPAS		Entropy and COPRAS		Entropy and CODAS		Entropy and ARAS
	Value	Ranking	Value	Ranking	Value	Ranking	Value	Ranking	Value	Ranking	Value	Ranking
Kuehne + Nagel	0.3300	5	0.3304	5	0.2167	5	0.5209	5	1.2400	5	0.2378	5
DHL	0.5026	1	0.5032	1	0.3072	1	0.8441	2	4.9173	1	0.3929	3
DSV	0.2469	8	0.2472	8	0.1708	9	0.3934	13	−0.9867	8	0.1759	11
DB Schenker	0.2488	7	0.2491	7	0.1646	10	0.3926	14	−0.6395	7	0.1788	10
FedEx	0.2931	6	0.2935	6	0.1855	8	0.4697	7	0.5215	6	0.2184	6
Sinotrans	0.2204	9	0.2207	9	0.1882	7	0.4566	8	−0.9945	9	0.2001	7
Nippon	0.1693	14	0.1695	14	0.1498	13	0.4411	10	−2.4316	14	0.1406	13
Expeditors	0.3563	4	0.3567	4	0.2846	2	0.3991	12	2.9932	2	0.4319	1
UPS	0.3663	2	0.3668	2	0.2168	4	0.6065	4	2.3877	3	0.2843	4
CEVA	0.1993	11	0.1995	11	0.1910	6	0.4931	6	−1.7098	12	0.1984	8
XPO	0.1933	12	0.1935	12	0.1554	12	0.4563	9	−1.4310	11	0.1621	12
NFI	0.3596	3	0.3601	3	0.2712	3	1.0000	1	2.1929	4	0.4077	2
Kerry	0.1434	15	0.1435	15	0.1222	14	0.4048	11	−2.8624	15	0.1231	15
Maersk	0.1742	13	0.1744	13	0.1110	15	0.2421	15	−1.9031	13	0.1279	14
Kintetsu	0.2145	10	0.2147	10	0.1629	11	0.6316	3	−1.2940	10	0.1913	9

(Appendix A). The comparison of entropy–MARCOS with other MCDM methods is visualized in Figure 6.

The form in Figure 6 offers a technique to immediately comprehend the rank change for each alternative in various models based on the comparison results. The comparative analysis demonstrates that, as anticipated, the various methodologies produce slightly varied ranking results. This may be because this study considered a very large number of alternatives (i.e., 15 alternatives in relation to 12 criteria). Moreover, the Spearman’s rank correlation coefficient [53] between entropy–MARCOS and entropy–SAW, entropy–WASPAS, entropy–COPRAS, entropy–CODAS, and entropy–ARAS was 100%, 91.5%, 66%, 98.8%, and 87.2%, respectively. It can be concluded that the rankings of alternatives are in very high correlation. The top three third-party logistics providers, DHL Supply Chain & Global Forwarding (3PL-02), UPS Supply Chain Solutions (3PL-09), and NFI (3PL-12), changed slightly. Therefore, it is evident that the proposed entropy–MARCOS model has a good performance in prioritizing the 15 third-party logistics providers.

6. Discussions

6.1. Implications for Research

This study has several important research implications. First, the present work proposes a sustainable evaluation framework with objective weighting assessments with quantitative data, which extends the existing literature related to the performance evaluation of 3PL service providers that mostly adopt single MCDM methods, such as DEA, and subjective weighting methods, such as AHP, TOPSIS, and ANP, to name a few. Deviating from the existing studies, this study aggregates multiple MCDM methods, thus leading to higher robustness and eliminating method-specific disadvantages. Additionally, the incorporation of the entropy-based and MARCOS methods with real collecting data instead of subjective, biased, and ambiguous judgments facilitates real-life implementation. The sensitivity and comparative analysis allow decision makers to observe the stability of the proposed evaluation framework.

Second, there is an absence of research on the determination of social and environmental aspects and its impact on the performance of 3PL service providers. This study contributes to the literature on the environmental aspects of 3PL service providers by determining the carbon dioxide emissions and their impact on performance. The relationships between environmental performances and differentiation advantage from the perspective of 3PLs was proven [6], which demonstrates that incorporating environmental initiatives involves opportunities to identify and eliminate inefficiencies and reduce the carbon footprint in the supply chain, which can lead to increased competitiveness and profitability of major 3PL firms in the long term [54]. Logistics improvements from an environmental standpoint, therefore, could gain a strategic role in enhancing a company’s eco-efficient performances and, as a result, its global competitiveness for the implementation of sustainable strategies in supply chain operations. Customers frequently query 3PLs about how well they function in terms of the environment.

Finally, to the best of the authors’ knowledge, no other study has so far applied integrated indicators of economic, service level, social, and environmental aspects in an objective weighting MCDM approach in the area of 3PL performance evaluation. Therefore, the integration of entropy-based and MARCOS methods was proposed for the first time in the logistics literature and the relative priority of environmental aspects was presented in the outcome of this study.

6.2. Implications for Practice

This study’s accurate and practical results, based on the integration presented, will benefit practitioners and researchers in the logistics area in determining which metrics to pay closer attention to in order to increase their level of competitiveness in the market. Therefore, logistics managers can compare the priorities of their own companies with the ideal advised ranking using the suggested priority of the indicators.

The findings show that carbon dioxide emissions rank first among all indicators, followed by employee count, operating costs, and total warehouse area. Remarkably, these 4 indicators represent more than half of the total percentage of the 12 indicators; as a result, the logistics industry should place the majority of its attention on these indicators in order to remain competitive. Employee satisfaction and accidents are the two indicators in the developed model that are ranked at the bottom of the scale. However, since the rankings only show the relative priorities of the 12 indicators chosen for the decision model, their final priority from the results of this study should not be interpreted as meaning that these indicators are not at all important.

This result reinforced that the lower the carbon footprint is and the higher the number of employees is, the higher the competitiveness will be for the 3PL providers in the industry. This outcome is also consistent with the argument of Raut et al. [6], who noted that the global 3PL market highlights carbon emissions reduction, which positively affects the reputation, customers’ concerns, and sustainable performance of a logistics service organization. Additionally, the outcome may be also explained by the fact that the logistics industry has an emissions-intensive and labor-intensive nature in [10,37].

Finally, the results of this study assist practitioners and decision makers in comprehending the influence of the pertinent indicators and the environmental concept on their logistics businesses. The results are therefore useful for different stakeholders in their selection of logistics service providers because they can be used as a reference to understand the norms of the logistics industry as the world faces climate change and global warming. In other words, the results of this study are useful not only for logistics companies but also for various stakeholders in the industry.

7. Conclusions

Effective and efficient outsourcing decisions are essential to an organization’s success in today’s competitive market. I the supply chain management and logistics industries, environmental sustainability is an increasing research topic of interest and is the focus of the current study. This paper proposes an integrated MCDM framework for benchmarking the sustainable performance of global 3PL companies, which studies and develops practical guidelines for improving the performance of these key players to achieve better environmental as well as economic performance, ultimately leading to truly sustainable outcomes, taking into account a highly competitive business environment in the logistics industry and supply chain management. In order to equip logistics companies with key indicators to measure their performances, this study focuses on identifying and then prioritizing those measures that are the most appropriate for their strategic, tactical, and operational needs toward sustainable development. To satisfy these objectives and ensure the impact of each of these indicators, a two-stage framework with a comprehensive evaluation model for logistics performance indicators was suggested in this study. In the first phase, the weight coefficients for each criterion are computed by entropy objective weighting method. Then, the MARCOS method is applied to rank the 3PL companies in accordance with the defined criteria. Sensitivity analysis of criteria weights and comparative analysis of MCDM methods are conducted to test the effectiveness and the applicability of the proposed model.

As a result, carbon dioxide emissions and number of employees are found to be the most significant factors. For the final ranking, DHL is the most efficient 3PL provider, follow by UPS, NFI, and Expeditors. The contributions of this study are threefold. First, the key indicators for 3PL performance evaluation are determined by means of a literature review, aiming for sustainable development of 3PL businesses. Methodologically, the entropy-based MARCOS integrated MCDM framework is proposed for the first time for logistics industry assessment. Finally, both academic researchers and practitioners can benefit from the developed model and its results. The list of indicators and the model presented serve as a frame of reference that will help logistics managers to better understand important logistics indicators, because choosing significant performance indicators is a difficult and time-consuming task for decision makers. According to the findings, this study assists logistics decision makers in identifying their operational prioritization in order to increase their competitiveness in the market. In other words, both the model and the method give managers insights into assessing operations in light of sustainable performance and the relative positions of companies within their industry.

This study offers several interesting research directions. Incorporating weighting methods besides the entropy method and MARCOS can provide more information. Scholars may also be drawn in by the use and integration of various approaches and cutting-edge elements. The size of the data set is a minor limitation. This work is limited to only 15 3PL service providers, the majority of whom are from developed countries, and 12 indicators due to a lack of data. Rich context-specific insights can be obtained by applying the suggested methodology to 3PL service providers in emerging market nations.