Assessment of Sustainable Reverse Logistic Provider Using the Fuzzy TOPSIS and MSGP Framework in Food Industry

Abstract

As consumers become ever more conscious of environmental issues, socially responsible corporate practices, and government regulations, companies are increasingly motivated to incorporate reverse logistics (RLs) into their operations, thus raising the question of provider selection. In previous studies, the food industry generally lacked a systematic reference method for RLs provider selection, especially during the post-COVID-19 pandemic. This study aims to develop a comprehensive approach that combines a technique for order preference by similarity to ideal solution (TOPSIS) and multi-segment goal programming (MSGP) models to select optimal RLs providers. Furthermore, this method will enable decision makers (DMs) to evaluate and select the best RLs provider considering the limited resources of the business. This approach allows DMs to consider both qualitative and quantitative criteria, set multiple target segmentation expectations, and achieve optimal RLs provider selection. This study also provides case studies of applications by food manufacturers. The main finding is that considering multiple criteria in making a decision produces better results than using a single criterion.

1. Introduction

As the business environment gradually intensifies, there is a growing interest in building efficient supply chain relationships. The fundamental principle of supply chain management (SCM) involves increasing efficiency by maintaining sustainable relationships between companies in the supply chain, including logistics management [1]. Logistics processes include both forward logistics and reverse logistics (RLs). RLs cover a range of operations in a food supply chain system, including the return of products from downstream members to upstream, product reprocessing, and remanufacturing [2,3]. The selection of an RLs provider is an important issue in food SCM. As the demand for environmental protection continues to grow and the potential for personalized services increases, consumers have become increasingly conscious of the need to reuse or recycle excess inventory environments, thus creating more opportunities to reduce costs from returned goods, which has prompted the idea of RLs [4]. Furthermore, the topic of RLs has received considerable attention from researchers owing to environmental concerns, mandatory regulation, and social concerns, which are widely adopted by the industry through RLs partners [5]. RLs are defined as the process of planning and controlling the effective recovery management of raw materials, intermediate inventories, final products, and relevant data from consumer perception to the origin for value recovery or reasonable disposal [6].

With growing awareness about environmental sustainability, the demand for product recovery activities is also increasing [7]. RLs has become a competitive need for sustainability [8]. The return of used products is becoming a paramount logistical activity owing to government legislation and the heightened cognizance of preserving the environment and minimizing waste [9]. The evaluation and selection of RLs operation processing is a critical success factor for businesses aiming to gain a reputational advantage and achieve their performance goals. Thus, the incorporation of business RLs procedures, such as product return, source reduction, regeneration, material replacement, item reuse, waste cleaning, reprocessing, maintenance, and remanufacturing in logistics activities will have a significant impact on operational performance [5].

RLs focus on the reverse flow of materials from customers to suppliers to maximize the value of returned merchandise or minimize the total cost of RLs [9]. As an illustration, researchers have conducted numerous studies with different techniques to improve the efficiency of RLs within food supply chains [10]. Selecting the appropriate RLs provider can significantly reduce RLs costs, improve a company’s competitive advantage, and improve customer satisfaction. Therefore, selecting the best RLs partner in the food supply chain has become a key strategic consideration for numerous companies.

However, evaluating an RLs partner is a critical decision for a business owing to the numerous complexities associated with it. Hence, it is considered as a multi-criteria decision making (MCDM) problem [5]. The selection of RLs providers is an exceedingly significant domain, and they should be consulted on strategic matters for the effective management of food supply chains. Recently, various companies have attempted to build strategic unions with RLs providers to improve their management abilities and enterprise competitiveness [11,12]. This selection of the RLs provider process is essentially considered an MCDM problem in that it is influenced by unlike substantial and unsubstantial criteria.

Although task coordination between manufacturers and their RLs providers is usually an important link in the distribution channel of a food supply chain, there have been studies using various methods to select RLs suppliers, thus providing a basis for the decision-making process [13,14]. However, decision-makers (DMs) must consider many criteria and attributes when selecting a RLs provider, such as tangible (i.e., cost) and intangible (i.e., service) criteria. Recently, many studies that utilized combined MCDM methods have evaluated RLs provider selection, as shown in

Table 1. Methods of provider evaluation and selection.

Authors	Methods	Research Direction
Mishra and Rani [4]	Criteria importance through intercriteria correlation (CRITIC) and Combined compromise solution (CoCoSo)	third-party reverse logistics provider (3PRLP) selection.
eZarbakhshnia et al. [10]	Fuzzy stepwise weight assessment ratio analysis (SWARA)	selection of sustainable third-party reverse logistics provider.
Guneri et al. [15]	Fuzzy-lp	for a supplier selection problem in SCM.
Sasikumar and Haq [16]	VlseKriterijuska optimizacija I komoromisno resenje (VIKOR)- Multi-objective optimization problem (MOOP)	to optimize closed supply chain network and select the best 3PRLP for the battery industry.
Cheng and Lee [17]	ANP	to investigate the selection criteria and select the best 3PRLP among alternatives.
Liao and Kao [18]	Fuzzy TOPSIS and MCGP	for supplier selection in SCM.
Aguezzoul [19]	Literature review	to select of 3PRLPs.
Senthil et al. [20]	AHP and FTOPSIS	evaluation and selection of 3PRLPs for plastic industry.
You et al. [21]	VIKOR	reverse logistic provider selection.
Parameshwaran et al. [22]	Delphi, AHP, TOPSIS, and VIKOR	to select robots considering subjective and objective criteria in fuzzy environment.
Prakahs and Barua [23]	FAHP and VIKOR	for the final selection of reverse logistics partner.
Büyüközkan and Göçer [24]	Fuzzy- MCDM	based on fuzzy approach for the supplier selection problem.
Chatterjee, and Stević [25]	Two stage fuzzy AHP andFuzzy TOPSIS	for provider selection and evaluation in green manufacturing environment.
Durmić et al. [26]	Rough simple additive weighting (RSAW)	sustainable supplier selection.
Fu, et al. [27]	Fuzzy AHP, Fuzzy additive ratio assessment (FARAS) and MSGP	selection of suppliers in flight duty-free products.
Wang and Chen [28]	AHP and Genetic algorithms (GA)	choose the best supplier during the COVID-19 pandemic.
Kao [29]	Fuzzy MSGP	apparel and textile provider selection for the COVID-19 era.
Fu and Liao [30]	Fuzzy TOPSIS and MSGP	catering food reverse logistics provider selection in the airline industry.

, in addition to the fuzzy technique for order preference by similarity to ideal solution (TOPSIS) and multi-segment goal programming (MSGP), which compares the research gaps or research problems between the proposed method and competing methods.

The remanufacturing, repair, and recycling of recycled materials can create lucrative business opportunities. To manage food returns, companies can reuse, resell, or destroy them. Retailers may log returns due to seasonality, expiration, or shipping damage. Customers may return a product because of its poor quality. Managing product returns can improve customer service levels, thereby improving customer satisfaction [18]. Recently, the food industry has faced many recovery issues regarding agricultural products (i.e., food). However, food companies usually lack an orderly frame of reference for RLs partner selection, and there is no research on the selection of food RLs providers in previous literature, especially during the post-COVID-19 pandemic. To fill this gap, this study proposes a fuzzy MCDM approach for selecting the best RLs partner. Selecting an appropriate provider is a difficult MCDM problem involving quantitative and qualitative standard uncertainties associated [31,32]. The advantage of this approach considers both qualitative and quantitative criteria, which allows the DM to set multiple levels of segment expectations for RLs partner selection. Additionally, the impact on supplier selection during the COVID-19 pandemic has not previously been considered, especially for any company. To our knowledge, this comprehensive approach has not been considered in the food SCM literature.

The remainder of this paper is organized as follows. Section 2 reviews the selection methods of RLs providers. Section 3 presents fuzzy TOPSIS and MSGP methods. Section 4 presents a hybrid approach that uses fuzzy TOPSIS and MSGP. Section 5 applies a case study to the reverse logistics supplier selection problem. Finally, conclusions and recommendations for future research are provided in Section 6.

2. Literature Review

2.1. The Criteria of Provider Selection

Business RLs activities can help companies achieve cost efficiency, customer satisfaction, and improved delivery performance through outsourcing. Currently, outsourcing logistics procedures have become a prevalent management trend whereby various companies can achieve their objectives through this activity [33]. If a company adopts RLs outsourcing as a strategy, the choice of RLs partners or suppliers becomes an important topic. Consequently, the problem of evaluating and selecting RLs partners has recently received considerable attention in the academic literature. Many decision criteria have been proposed to address the RLs partner selection problem. Kanana et al. [7] developed a model for selecting and evaluating 3PRLP based on quality, delivery, RLs cost, shipping error rate, technical proficiency, engineering capability, meeting incremental requirements, and willingness and attitude to cooperate. Lin et al. [34] used price, service satisfaction, quality, trust, and delivery as key criteria to evaluate RLs partners in the electronics industry market. To evaluate and select the best 3PRLP, Ho et al. [3] address four criteria: financial stability, logistics/transportation costs, transportation standards, and marketing effectiveness. Senthil et al. [18] proposed six criteria for RL operation channel selection such as economic factors, reverse logistics functions, management efficiency, delivery time, delivery flexibility, and information sharing. However, evaluating the right 3PRLP is a complex MCDM problem [35]. Choosing the correct 3PRLP will help enterprises obtain expected ecological and economic benefits [36].

In addition, Prakash and Barua [5] developed several criteria, including service quality, fixed asset size and quality, management quality, delivery performance, operational performance, compatibility, financial stability, geographic distribution and scope, information capability, information sharing and trust, long-term relationships, reputation, best cost, expansion capability, and flexibility of operations and delivery to select the best partner for RLs of Indian electronics firms. Tavana et al. [37] addressed quality, cost, RLs capacity, delivery and services, and green technology capability to select optimal RLs providers. Zarbakhshnia et al. [8] proposed quality, cost, delivery and services, green technology capability, health and safety, and employment stability for evaluating and selecting sustainable third-party RLs providers using fuzzy SWARA. Bai and Sarkis [38] and Govindan et al. [39] used RLs practices, quality, cost, management system, green level, low carbon, and RLs capacity criteria for third-party RLs providers (3PRLPs) selection issues. Mishra and Rani [4] proposed several criteria for selecting the best RLs provider, including on-time delivery, fill rate, quality of service, capacity usage, total order cycle time, unit operating cost, coordination ability, market share increment, research and development, system flexibility index, environmental spending, and customer satisfaction. Furthermore, Kao [29] proposes financial stability, product quality, company reputation, pandemic containment capability, and personal protective equipment capability to choose a provider in the COVID-19 pandemic.

2.2. Summarizes the Provider Selection Criteria

This study summarizes the supplier selection criteria in the literature, as shown in

Table 2. The criteria of the provider selection.

Authors	Selection Criteria
Ho et al. [3]	✓ financial stability ✓ logistics/transportation costs ✓ transportation standards ✓ marketing effectiveness
Mishra and Rani [4]	✓ on-time delivery ✓ fill rate ✓ quality of service ✓ capacity usage ✓ total order cycle time ✓ unit operating cost ✓ coordination ability ✓ market share increment ✓ research and development ✓ system flexibility index ✓ environmental spending ✓ customer satisfaction
Prakash and Barua [5]	✓ service quality ✓ fixed asset size and quality ✓ management quality ✓ delivery performance ✓ operational performance compatibility ✓ financial stability ✓ geographic distribution and scope ✓ information capability ✓ information sharing and trust ✓ long-term relationships ✓ reputation ✓ best cost ✓ expansion capability ✓ flexibility of operations and delivery
Kanana et al. [9]	✓ quality ✓ delivery ✓ reverse logistics cost ✓ shipping error rate ✓ technical proficiency ✓ engineering capability ✓ meeting incremental requirements ✓ willingness and attitude to cooperate
Zarbakhshnia et al. [10]	✓ Quality ✓ Cost ✓ delivery and services ✓ green technology capability ✓ health and safety ✓ employment stability
Kao [29]	✓ financial stability ✓ product quality ✓ company reputation ✓ pandemic containment capability ✓ personal protective equipment capability
Lin et al. [34]	✓ Price ✓ service satisfaction ✓ quality ✓ trust ✓ delivery time
Tavana et al. [37]	✓ Quality ✓ Cost ✓ RLs capacity ✓ delivery and services ✓ green technology capability
Bai and Sarkis [38] and Govindan et al. [39]	✓ quality ✓ cost ✓ management system ✓ green level ✓ low carbon ✓ RLs capacity

, which will be used in this study to select the most suitable items through group decision-making.

According to Table 2, in this study, considering the qualitative and quantitative criteria, a combined fuzzy TOPSIS and MSGP model was used to solve the multi-objective RLs partner selection problem. First, linguistic values indicated in triangular fuzzy numbers are used to evaluate the weights and ratings of the reverse logistics provider selection criteria. Second, the hierarchical multiple models based on fuzzy set theory are shown, and the weights of every provider are obtained using the fuzzy positive (PIS) and fuzzy negative ideal solutions (NIS). Finally, an MSGP pattern based on the qualitative and quantitative criteria of the firm and its reverse logistics suppliers is constructed and applied to the optimal selection using LINGO computing software. Figure 1 illustrates this integrated process.

3. Methodology

3.1. Fuzzy TOPSIS

TOPSIS directly and simple technology can be used to solve MCDM problems such as the reverse logistics partner selection model. In this study, fuzzy set theory is presented to indicate the linguistic terms of the process of evaluating and selecting reverse logistics suppliers. Some basic definitions and operations of fuzzy set theory are reviewed in the next section, according to Rejeb et al. [13], Fu et al. [27], Fu and Liao [30], Liao [40], and Kumar [41]. In reality, the selection process for various phenomena may not proceed adequately and accurately because the obtainable information is inherently fallacious, inaccurate, vague, and uncertain. Here, several basic concepts of fuzzy numbers and linguistic variables are defined as follows: The positive triangular fuzzy number (TFN) $\tilde{n}$ can be defined as $(n_1,n_2,n_3)$, as displayed in Figure 2. The membership function $u_{\tilde{n}}(x)$ is defined as follows [16]:

$$u_{\tilde{n}}(x)=\{\begin{array}{c}0,\\ \frac{x-n_1}{n_2-n_1},\\ \frac{n_3-x}{n_3-n_2},\\ 0,\end{array}\begin{array}{c}x\le n_1\\ n_1\le x\le n_2\\ n_2\le x\le n_3\\ x\le n_3\end{array}$$

(1)

When any two equilateral triangle fuzzy numbers $\tilde{m}=(m_1,m_2,m_3)$ and $\tilde{n}=(n_1,n_2,n_3)$ and a positive number $k$, some main tasks of triangular fuzzy numbers $\tilde{m}$ and $\tilde{n}$ can be shown as follows:

$$\tilde{m}\hspace{0.17em}(+)\hspace{0.17em}\tilde{n}=(m_1\oplus n_1,m_2\oplus n_2,m_3\oplus n_3)$$

(2)

$$\tilde{m}\hspace{0.17em}(-)\hspace{0.17em}\tilde{n}=(m_1\hspace{0.17em}\mathsf{\Theta }\hspace{0.17em}{n}_3,m_2\hspace{0.17em}\mathsf{\Theta }\hspace{0.17em}{n}_2,m_3\hspace{0.17em}\mathsf{\Theta }\hspace{0.17em}{n}_1)$$

(3)

$$\tilde{m}\hspace{0.17em}(\times )\hspace{0.17em}\tilde{n}=(m_1\otimes n_1,m_2\otimes n_2,m_3\otimes n_3)$$

(4)

$$k\hspace{0.17em}(\times )\hspace{0.17em}\tilde{n}=(k\otimes n_1,k\otimes n_2,k\otimes n_3)$$

(5)

$$\tilde{m}\hspace{0.17em}(÷)\hspace{0.17em}\tilde{n}=(m_1÷n_3,m_2÷n_2,m_3÷n_1)$$

(6)

Rejeb et al., [11] addressed fuzzy numbers that could represent these linguistic variables. Let $\tilde{m}=(m_1,m_2,m_3)$ and $\tilde{n}=(n_1,n_2,n_3)$ denote two triangular fuzzy numbers. Therefore, the distance between them can be calculated using the vertex method as follows:

$$d(\tilde{m},\tilde{n})=\sqrt{\frac{1}{3}[{(m_1-n_1)}^2+{(m_2-n_2)}^2+{(m_3-n_3)}^2]}.$$

(7)

According to the above, a decision matrix can be shown as follows:

$$\tilde{X}=\left[\begin{array}{cccc}{\tilde{x}}_{11}& {\tilde{x}}_{12}& \cdots & {\tilde{x}}_{1n}\\ {\tilde{x}}_{21}& {\tilde{x}}_{22}& \cdots & {\tilde{x}}_{2n}\\ ⋮& ⋮& ⋮& ⋮\\ {\tilde{x}}_{m1}& {\tilde{x}}_{m2}& \cdots & {\tilde{x}}_{mn}\end{array}\right],\tilde{W}=[{\tilde{w}}_1,{\tilde{w}}_2,\dots ,{\tilde{w}}_n],$$

(8)

where ${\tilde{w}}_j=(w_{j1},w_{j2},w_{j3})$ and ${\tilde{x}}_{ij}=(a_{ij},b_{ij},c_{ij})$; $i=1,2,3,\dots m,\hspace{0.17em}$ $j=1,2,3,\dots ,n$.

According to the claim of Chen and Lee [17], if the fuzzy level (rating) and importance weight (closeness coefficient) of the kth DM are ${\tilde{x}}_{ijk}=(a_{ijk},b_{ijk},c_{ijk})$ and ${\tilde{w}}_{jk}=({\tilde{w}}_{jk1},{\tilde{w}}_{jk2},{\tilde{w}}_{jk3})$, where $i=1,2,\dots ,m$, $j=1,2,3,\dots ,n$, respectively, the accumulate fuzzy levels, ${\tilde{x}}_{ij}$, of alternatives regarding every criterion can be calculated as ${\tilde{x}}_{ij}=(a_{ij},b_{ij},c_{ij})$; here the $a_{ij}=\underset{k}{\min }\left\{a_{ijk}\right\}$, $b_{ij}=1/K{\displaystyle {\sum }_{K=1}^K{b}_{ijk}}$, and $c_{ij}=\underset{k}{\max }\left\{c_{ijk}\right\}$ and the accumulate fuzzy weights (closeness coefficient), ${\tilde{w}}_j$, of every criterion can be calculated as ${\tilde{w}}_j=(w_{j1},w_{j2},w_{j3})$; furthermore, the $w_{j1}=\underset{k}{\min }\left\{w_{jk1}\right\}$, $w_{j2}=1/K{\displaystyle {\sum }_{K=1}^K{w}_{jk2}}$, and $w_{j3}=\underset{k}{\max }\left\{w_{jk3}\right\}$.

From the fuzzy set theory (FST) delimitation, the normalized fuzzy decision matrix can be presented as $\tilde{R}=[{\tilde{r}}_{ij}]$, $i=1,2,3,\dots m$, $j=1,2,3,\dots ,n$, where ${\tilde{r}}_{ij}$ represents the normalized value of ${\tilde{x}}_{ij}=(a_{ij},b_{ij},c_{ij})$, which is calculated if the jth criterion is a benefit, then ${\tilde{r}}_{ij}=\left(\raisebox{1ex}{$a_{ij}$}\!\left/ \!\raisebox{-1ex}{$c_j^{*}$}\right.,\raisebox{1ex}{$b_{ij}$}\!\left/ \!\raisebox{-1ex}{$c_j^{*}$}\right.,\raisebox{1ex}{$c_{ij}$}\!\left/ \!\raisebox{-1ex}{$c_j^{*}$}\right.\right)$, where $c_j^{*}=\max c_{ij}$. Additionally, when jth criterion is a cost, ${\tilde{r}}_{ij}=\left(\raisebox{1ex}{$a_j^{-}$}\!\left/ \!\raisebox{-1ex}{$c_{ij}$}\right.,\raisebox{1ex}{$a_j^{-}$}\!\left/ \!\raisebox{-1ex}{$b_{ij}$}\right.,\raisebox{1ex}{$a_j^{-}$}\!\left/ \!\raisebox{-1ex}{$a_{ij}$}\right.\right)$, where $a_j^{-}=\min a_{ij}$.

Therefore, according to the normalized process, a weighted normalized fuzzy decision matrix can be obtained as $\tilde{V}={\left[{\tilde{v}}_{ij}\right]}_{m \times n}$, where ${\tilde{v}}_{ij}={\tilde{x}}_{ij} \otimes \hspace{0.17em}{\tilde{w}}_j$, $i=1,2,3,\dots m$, $j=1,2,3,\dots ,n$. After building a weighted normalized fuzzy decision matrix, the fuzzy positive ideal solution, say $S^{*}$, and the fuzzy negative ideal solution, say $S^{-}$, are calculated as follows:

$$\begin{array}{l}{S}^{*}=\left\{\left(\underset{i}{\max }\hspace{0.17em}{\tilde{v}}_{ij}|j\in J\right),\left(\underset{i}{\min }\hspace{0.17em}{\tilde{v}}_{ij}|j\in J^{\prime }\right)\right\}\\ =({\tilde{v}}_1^{*},{\tilde{v}}_2^{*},\dots ,{\tilde{v}}_n^{*}),\mathrm{where}i=1,2,\dots ,m,j=1,2,3,\dots ,n,\end{array}$$

(9)

and

$$\begin{array}{l}{S}^{-}=\left\{\left(\underset{i}{\min }\hspace{0.17em}{\tilde{v}}_{ij}|j\in J\right),\left(\underset{i}{\max }\hspace{0.17em}{\tilde{v}}_{ij}|j\in J^{\prime }\right)\right\}\\ =({\tilde{v}}_1^{-},{\tilde{v}}_2^{-},\dots ,{\tilde{v}}_n^{-}),\mathrm{where}i=1,2,\dots ,m,j=1,2,3,\dots ,n,\end{array}$$

(10)

and where $v_j^{*}=\max \left\{v_{ij3}\right\}$ and ${\tilde{v}}_j^{-}=\min \left\{v_{ij1}\right\}$.

Furthermore, $J$ is denoted with benefit criteria, but $J^{\prime }$ is denoted with cost criteria. The distance of every alternative from $S^{*}$ and $S^{-}$ can be obtained as $d_i^{*}={\displaystyle {\sum }_{j=1}^{n}d({\tilde{v}}_{ij,}{\tilde{v}}_j^{*})}$, and $d_i^{-}={\displaystyle {\sum }_{j=1}^{n}d({\tilde{v}}_{ij,}{\tilde{v}}_j^{-})}$, where $d(\cdot \hspace{0.17em},\hspace{0.17em}\cdot )$ represents the distance measured between two fuzzy numbers and $i=1,2,\dots ,m$. Finally, the weights (closeness coefficients; $C{C}_i^{}$) of each provider according to distance from the fuzzy positive, $S^{*}$, and negative ideal solution, $S^{-}$, can be obtained from $C{C}_i=d_i^{-}/(d_i^{*}+d_i^{-})$, $i=1,2,\dots ,m$, where $C{C}_i$ range appertain the closed interval [0, 1] and $i=1,2,\dots ,m$ can be obtained.

3.2. Multi-Segment Goal Programming (MSGP) Associated

Multi-criteria decision analysis has become a rapidly growing topic over the past two decades, and goal programming (GP) is an essential technique for determining a satisfactory set of solutions for multiple objective decision-making (MODM) [18]. GP is a special application of linear programming, which handles the coexistence of a single main objective and multiple objectives, allowing DMs to achieve the optimal objective [42]. That is, the GP can consider various simultaneous objectives as the DM searches the optimal solution from a set of practical alternatives. However, there are various practical issues in that DMs aim to achieve multi-expectation levels that cannot be solved using traditional GP methods, such as less/lower-better or more/higher-better, or multiple-segment GP issues.

To solve the above problems, Fu and Liao [42] proposed an MSGP model that can solve the multiple segment aspiration level (MSAL) problems, in which the DMs can set MSAL for every segment level. The achievement function of the MSGP model is as follows:

$$\mathrm{Min}Z={\displaystyle \sum _{i=1}^n{w}_i(d_i^{+}+d_i^{-})}$$

(11)

$$\mathrm{s}.\mathrm{t}.f_i(x)+d_i^{+}-d_i^{-}=g_i,i=1,2,\mathrm{\dots },n,$$

(12)

$$f_i(x)={\displaystyle \sum _{j=1}^m{s}_{ij}{B}_{ij}(b)\cdot x_i}$$

$$s_{ij}{B}_{ij}(b)\in R_i(x),i=1,2,\mathrm{\dots },n,j=1,2,\mathrm{\dots },m,$$

(13)

$$d_i^{+},d_i^{-}\ge 0,i=1,2,\mathrm{\dots },n,$$

$$X\in \hspace{0.17em}F\hspace{0.17em}(F\hspace{0.17em}\mathrm{is\; a\; feasible\; set}).$$

where $w_i$ depicts the weight belonging to deviation, $d_i$ depicts deviation belonging to a target value $g_i$, and then $d_i^{+}=\max (0,f_i(x)-g_i)$ and $d_i^{-}=\max (0,\hspace{0.17em}{g}_i-f_i(x))$ are denoted as under and overachievements of the $i$th goal, respectively. $s_{ij}$ is a decision variable coefficient that represents the MSAL of $j$th segment of the $i$th goal, $B_{ij}(b)$ represents a function of a binary serial number, and $R_i(x)$ is a function of resource limitations.

Furthermore, the MSGP model can be reformulated to modify MSGP achievement types as follows [18,30]:

$$\mathrm{Min}z=w_i(d_i^{+}+d_i^{-}),\hspace{0.17em}{w}_i(e_i^{+}+e_i^{-})$$

(14)

$$\mathrm{s}.\mathrm{t}.{\displaystyle \sum _{j=1}^m{s}_{ij}{B}_{ij}(b)\cdot x_i+{\mathrm{d}}_{\mathrm{i}}^{+}-}{d}_i^{-}=g_i,g_{i,\min }\le g_i\le g_{i,\max },$$

(15)

$$\frac{1}{L_i}(b_i{s}_{ij}^{\max }+(1-b_i)s_{ij}^{\min })-e_i^{+}+e_i^{-}=1+\frac{(s_{ij}^{\max }\hspace{0.17em}or\hspace{0.17em}{s}_{ij}^{\min })}{L_i},$$

(16)

$$s_{ij}{B}_{ij}(b)\in R_i(x),b_i\in \left\{0,\hspace{0.17em}1\right\},\mathrm{and}{d}_i^{+},d_i^{-},e_i^{+},e_i^{-}\ge 0,$$

(17)

$$X\in \hspace{0.17em}\hspace{0.17em}F\hspace{0.17em}(F\hspace{0.17em}\mathrm{is\; a\; feasible\; set}).$$

(18)

where $L_i=s_{ij}^{\max }-s_{ij}^{\min }$, $i=1,2,\mathrm{\dots },n$, $j=1,2,\mathrm{\dots },m$ and all other variables are defined in the MSGP model.

4. The Proposed Method

The proposed fuzzy TOPSIS tool helps translate the DMs’ preferences and experiences into meaningful results using linguistic values to evaluate each criterion and alternative RLs providers. Furthermore, adding integration with MSGP considers the DM’s preferences and experience with RLs provider selection criteria, as well as various quantitative constraints or goals, such as the firm’s budgeted costs and the RLs provider’s lead time or logistics capabilities. Fu and Liao [42] proposed MSGP to allow DMs to organize MSALs for each segment target value to escape over or underestimated decisions. The multi-segment decision making algorithm for RLs provider selection using fuzzy TOPSIS and MSGP methods is as follows [30]:

(1)

Select the appropriate linguistic variables for the importance weight of selection criteria and the linguistic ratings for the RL provider.

(2)

Aggregate the weight ${\tilde{w}}_j$ of criterion $C_j$ and pool the DMs’ ratings to obtain the aggregated fuzzy rating ${\tilde{x}}_{ij}$ of the reverse logistics provider $S_i$ under criterion $C_j$.

(3)

A fuzzy decision matrix is created and the matrix is normalized.

(4)

Create a weighted normalized fuzzy decision matrix.

(5)

Determine the fuzzy positive ideal solution $S^{*}$ and fuzzy negative ideal solution $S^{-}$.

(6)

Calculate the distance of each RL provider from $S^{*}$ and $S^{-}$.

(7)

Calculate the closeness coefficient ($C{C}_i$) for each RL provider.

(8)

To determine the optimal RLs provider, the weights of each provider should be maximized. Thus, using the closeness coefficients obtained from Step 7 for each reverse logistic provider, the integrated MSGP model is used to determine the optimal RL provider.

5. Illustrative Case Study

In consideration of environmental protection (for example, in Taiwan, the annual amount of food waste burned into garbage is about 900,000 tons), the case company decided to take food recycling as an important issue. This case applies to the example of a large food company, A Foods (AF), for the problem of RLs provider selection. AF is a common food-manufacturing company in China. It sells food in its 156 chain stores in Fujian, China. Its main product is chocolate. The company’s chief executive officer (CEO) Chang aims to select a food RLs provider to recycle and process the returned food and packaging resources, and these recycled resources are processed and used for other purposes. However, the AF company lacked an objective method for selecting the most suitable food RL provider. Therefore, an RLs provider selection decision-making committee was formed, which included the CEO, logistics experts, and senior marketing managers.

An optimal reverse logistics provider was selected from four suitable reverse logistics providers $(S_1,S_2,S_3,S_4)$ by three DMs ($D_1$, $D_2$, $D_3$) using Delphi techniques [16] (see Appendix A [29]). Furthermore, AF company goals and strategies were to determine a stable reverse logistics supplier with the same business philosophy. The initial task was to identify the key criteria that are suitable for RLs provider selection. Based on literature review (i.e., Chatterjee and Stević [25]; Durmić et al. [26]; Wang and Chen [28]; Fu and Liao [36,42]) in the provider’s selection research, manager and expert opinion, and data analysis performed using Delphi techniques [16], the five qualitative criteria for selecting the best reverse logistics provider were RLs capability $(C_1)$, service quality $(C_2)$, green level $(C_3)$, coordination ability $(C_4)$, and financial risk $(C_5)$ for the present case, and the degree of these criteria was applied in the food industry [30].

However, fuzzy TOPSIS is used to prioritize the relative importance of qualitative evaluation criteria and the preference of DMs to estimate the candidates. This case also considers three quantitative criteria for RLs suppliers, delivery time (hours), RLs cost (dollars), and green technology capability (number of licenses). The hierarchy structure of the decision-making issue in this study is shown in Figure 3.

The integrated fuzzy TOPSIS and MSGP models were used to solve the MCDM problem, and the results are summarized as follows.

Step 1. The three DMs used the linguistic variables displayed in

Table 3. Linguistic variables for importance weights for every criterion.

Linguistic Variables	Triangular Fuzzy Number
Very low	(0,0,0.1)
Low	(0,0.1,0.3)
Medium-low	(0.1,0.3,0.5)
Medium	(0.3,0.5,0.7)
Medium-high	(0.5,0.7,0.9)
High	(0.7,0.9,1)
Very high	(0.9,1,1)

to evaluate the importance weights of every RLs provider criterion, and the weight results are shown in

Table 4. Importance weights of criteria from three DMs.

	D1	D2	D3
C1	(0.3,0.5,0.7)	(0.3,0.5,0.7)	(0.3,0.5,0.7)
C2	(0.9,1,1)	(0.7,0.9,1)	(0.3,0.5,0.7)
C3	(0.3,0.5,0.7)	(0.5,0.7,0.9)	(0.5,0.7,0.9)
C4	(0.5,0.7,0.9)	(0.3,0.5,0.7)	(0.7,0.9,1)
C5	(0.5,0.7,0.9)	(0.7,0.9,1)	(0.3,0.5,0.7)

.

Step 2. The three DMs scored each criterion for reverse logistics providers using the linguistic variables shown in

Table 5. Linguistic variables for the ratings.

Linguistic Variables	Triangular Fuzzy Number
Very low	(0,0,1)
Low	(0,1,3)
Medium-low	(1,3,5)
Medium	(3,5,7)
Medium-high	(5,7,9)
High	(7,9,10)
Very high	(9,10,10)

, and the rating results are shown in

Table 6. DM rates four candidates based on five criteria.

Criteria	Suppliers	DMs
		D1	D2	D3
C1	S1	(3,5,7)	(7,9,10)	(3,5,7)
	S2	(5,7,9)	(5,7,9)	(5,7,9)
	S3	(9,10,10)	(9,10,10)	(7,9,10)
	S4	(7,9,10)	(3,5,7)	(3,5,7)
C2	S1	(7,9,10)	(7,9,10)	(9,10,10)
	S2	(5,7,9)	(7,9,10)	(7,9,10)
	S3	(5,7,9)	(3,5,7)	(9,10,10)
	S4	(5,7,9)	(5,7,9)	(3,5,7)
C3	S1	(5,7,9)	(9,10,10)	(5,7,9)
	S2	(7,9,10)	(7,9,10)	(7,9,10)
	S3	(5,7,9)	(3,5,7)	(5,7,9)
	S4	(7,9,10)	(5,7,9)	(7,9,10)
C4	S1	(9,10,10)	(9,10,10)	(9,10,10)
	S2	(5,7,9)	(5,7,9)	(3,5,7)
	S3	(9,10,10)	(7,9,10)	(9,10,10)
	S4	(7,9,10)	(3,5,7)	(7,9,10)
C5	S1	(3,5,7)	(5,7,9)	(3,5,7)
	S2	(7,9,10)	(5,7,9)	(5,7,9)
	S3	(5,7,9)	(7,9,10)	(7,9,10)
	S4	(7,9,10)	(9,10,10)	(7,9,10)

.

Step 3. Using Table 4 and Table 6, we converted the linguistic assessments inside triangular fuzzy numbers to create a fuzzy decision matrix and settled the fuzzy weights for every criterion, as displayed in

Table 7. Fuzzy decision matrix and fuzzy weights for the four providers.

	C1	C2	C3	C4	C5
S1	(3,6.3,10)	(7,9.3,10)	(5,8,10)	(9,10,10)	(3,5.7,9)
S2	(5,7,9)	(3,7.7,10)	(7,9,10)	(3,6.3,9)	(5,7.7,10)
S3	(7,9.7,10)	(5,7.3,10)	(3,6.3,9)	(7,9.7,10)	(5,8.3,10)
S4	(3,6.3,10)	(3,6.3,9)	(5,8.3,10)	(3,7.7,10)	(7,9.3,10)

.

Step 4. Table 7 was used to construct the normalized fuzzy decision matrix. Using the normalized fuzzy decision matrix in

Table 8. Normalized decision matrix.

	C1	C2	C3	C4	C5
S1	(0.3,0.63,1)	(0.7,0.93,1)	(0.5,0.8,1)	(0.9,1,1)	(0.3,0.57,0.9)
S2	(0.5,0.7,0.9)	(0.3,0.77,1)	(0.7,0.9,1)	(0.3,0.63,0.9)	(0.5,0.77,1)
S3	(0.7,0.9,1)	(0.5,0.73,1)	(0.3,0.63,0.9)	(0.7,0.97,1)	(0.5,0.83,1)
S4	(0.3,0.63,1)	(0.3,0.63,0.9)	(0.5,0.83,1)	(0.3,0.77,1)	(0.7,0.93,1)
${\tilde{w}}_j$	(0.3,0.57,0.9)	(0.3,0.8,1)	(0.3,0.63,0.9)	(0.5,0.7,1)	(0.3,0.7,1)

, the weighted normalized fuzzy decision matrix is obtained, as displayed in

Table 9. Weighted normalized decision matrix.

	C1	C2	C3	C4	C5
S1	(0.09,0.36,0.9)	(0.21,0.75,1)	(0.15,0.51,90)	(0.45,0.7,1)	(0.09,0.4,0.9)
S2	(0.15,0.4,0.81)	(0.09,0.56,1)	(0.21,0.57,90)	(0.15,0.44,0.9)	(0.15,0.54,1)
S3	(0.21,0.55,0.9)	(0.15,0.59,1)	(0.09,0.4,0.81)	(0.35,0.68,1)	(0.15,0.58,1)
S4	(0.09,0.36,0.9)	(0.09,0.51,0.9)	(0.15,0.53,0.9)	(0.15,0.54,1)	(0.21,0.65,1)

.

Step 5. The fuzzy positive ideal solution $S^{*}$ and fuzzy negative ideal solution $S^{-}$ are obtained using Equations (9) and (10) as follows:

$S^{*}$ = [(0.9,0.9,0.9),(1,1,1),(0.9,0.9,0.9),(1,1,1), (0.21,0.21,0.21)]

$S^{-}$ = [(0.25,0.25,0.25),(0.09,0.09,0.09),(0.15,0.15,0.15),(0.45,0.45,0.45),(0.9,0.9,0.9)]

Step 6. Calculate the distance of every RL provider from $S^{*}$ and $S^{-}$ with respect to every criterion as displayed in

Table 10. Distances between FPIS (and FNIS) and reverse logistics provider levels.

		C1	C2	C3	C4	C5
FPIS	$d(S_1,S^{*})$	0.56	0.48	0.49	0.36	0.42
	$d(S_2,S^{*})$	0.52	0.58	0.44	0.59	0.49
	$d(S_3,S^{*})$	0.45	0.55	0.55	0.42	0.51
	$d(S_4,S^{*})$	0.56	0.60	0.48	0.56	0.52
FNIS	$d(S_1,S^{-})$	0.56	0.48	0.49	0.36	0.42
	$d(S_2,S^{-})$	0.52	0.58	0.44	0.59	0.49
	$d(S_3,S^{-})$	0.45	0.55	0.55	0.42	0.51
	$d(S_4,S^{-})$	0.56	0.60	0.48	0.56	0.52

FPIS = Fuzzy positive ideal solution and FNIS = fuzzy negative ideal solution.

.

Step 7. The $C{C}_i$ of each RL provider obtained $C{C}_1$ = 0.467, $C{C}_2$ = 0.451, $C{C}_3$ = 0.339, and $C{C}_4$ = 0.359, as shown in

Table 11. Results of $C{C}_i$.

	${\mathit{d}}_{\mathit{i}}{}^{*}$	${\mathit{d}}_{\mathit{i}}^{-}$	${\mathit{d}}_{\mathit{i}}^{*} + {\mathit{d}}_{\mathit{i}}^{-}$	CCi
S1	2.31	2.02	4.33	0.467
S2	2.63	2.17	4.80	0.451
S3	2.47	1.27	3.74	0.339
S4	2.73	1.53	4.25	0.359

.

Step 8. Establish the MSGP model according to each RLs providers’ $C{C}_i$ obtained in step 7 and determine the best RLs providers. The weight of the RLs providers is used as the objective function in which the closeness coefficient between RLs providers is maximized.

In addition to AF’s sales records and the returns of products for the last six years, the CEO of AF, the marketing manager, and the logistics manager stipulate three targets to maximize fit business strategy, such as selecting the highest green technology capability ($f_1(x)$), lowest reverse logistic cost ($f_2(x)$), and lowest delivery time ($f_3(x)$). Next, set up the MSGP model for the reverse logistics supplier to select business objectives as (1) $f_1\left(x\right)\ge 4$ items are to maximize the number of reverse logistics provider licenses; (2) $f_2(x)\le$ $52.3 and $\ge$ $42 million to minimize total reverse logistics costs; and (3) $f_3\left(x\right)\le 125$ h per year to minimize lead times for reverse logistics providers.

In addition, the parameter of providers in the case were obtained from the AF’ database, based on transaction records and business studies over the past six years. The logistics license, unit reverse logistics cost, and delivery time levels of the four candidate providers are as follows (

Table 12. The data of four candidate providers.

	S1	S2	S3	S4
Logistics license (item)	6	4	2	3
Unit material costs ($100)	$8~10	$8	$13	$10~12
Delivery time (time)	0.035	0.05~0.057	0.06~0.068	0.04

).

Using the above objectives and the calculated parameters related to each candidate, AF can formulate a fuzzy MSGP model as follows:

$$\mathrm{Min}\mathrm{Z}=d_1^{+}+d_1^{-}+d_2^{+}+d_2^{-}+d_3^{+}+d_3^{-}+d_4^{+}+d_4^{-}+e_1^{+}+e_1^{-}+e_2^{+}+e_2^{-}+e_3^{+}+e_3^{-}+e_4^{+}+e_4^{-}$$

(19)

$$\begin{gathered} \mathrm{s}.\mathrm{t}. \\ 0.467x_1+0.451x_2+0.339x_3+0.359x_4-d_1^{+}+d_1^{-}=1 \end{gathered}$$

(20)

$$6x_1+4x_2+2x_3+3x_4-d_4^{+}+d_4^{-}\ge 4$$

(21)

$$(10b_3+8(1-b_3))x_1+8x_2+13x_3+(12b_4+10(1-b_4))x_4-d_3^{+}+d_3^{-}\le \mathrm{52,300}\mathrm{and}\ge \mathrm{42,000}$$

(22)

$$(1/2)(10b_3+8(1-b_3))-e_3^{+}+e_3^{-}=5$$

(23)

$$(1/2)(12b_4+10(1-b_4))-e_4^{+}+e_4^{-}=6$$

(24)

$$0.035x_1+(0.057b_1+0.05(1-b_1))x_2+(0.068b_2+0.06(1-b_2))x_3+0.04x_4-d_2^{+}+d_2^{-}\le 125$$

(25)

$$(1/0.007)(0.057b_1+0.05(1-b_1))-e_1^{+}+e_1^{-}=8.14$$

(26)

$$(1/0.008)(0.068b_2+0.06(1-b_2))-e_2^{+}+e_2^{-}=8.5$$

(27)

$$b_i\in \left\{\hspace{0.17em}0,\hspace{0.17em}1\right\},i=1,\hspace{0.17em}2,\dots ,\hspace{0.17em}4,$$

$$d_i^{+},\hspace{0.17em}{d}_i^{-}\ge 0,i=1,\hspace{0.17em}2,\dots ,\hspace{0.17em}4,$$

$$e_i^{+},\hspace{0.17em}{e}_i^{-}\ge 0,i=1,\hspace{0.17em}2,\dots ,4,$$

and these equation numbers description as:

Equation (19): satisfy all obligatory goals.

Equation (20): for weighting of reverse logistics providers goal;

Equation (21): for maximizing the reverse logistics provider licenses;

Equation (22): for minimizing reverse logistics cost goal;

Equation (23): for minimizing reverse logistics cost goal of x1;

Equation (24): for minimizing reverse logistics cost goal of x4;

Equation (25): for delivery time goal;

Equation (26): for minimizing delivery time goal of x2

This RLs provider selection problem of AF can be optimally solved using LINGO [43]. The results are S₁(x₁ = 1), S₂(x₂ = 0), S₃(x₃ = 0), and S₄(x₄ = 0). Therefore, it considers both criteria of qualitative and quantitative, and AF’s selection of the best reverse logistics providers is S₁.

This model of TOPSIS+MSGP benefit is shown in

Table 13. Comparison of RLs provider selection methods.

Methods	Selection Criteria		Multiple Segment Aspiration Levels
	Qualitative	Quantitative
LP/GP	No	Yes	No
TOPSIS	Yes	No	No
SWARA	Yes	No	No
CW	Yes	No	No
SAW	No	No	No
CRITIC+CoCoSo	Yes	No	No
(Fuzzy)VIKOR	Yes	No	No
MCGP-U	No	Yes	No
DEA	No	Yes	No
CPM	No	Yes	No
AHP/ANP	Yes	No	No
MOOP	No	Yes	No
AHP+TOPSIS	Yes	No	No
This proposed method (Fuzzy TOPSIS + modify MSGP)	Yes	Yes	Yes

, including a comparison between this proposed method and the others. This proposed method combined fuzzy TOPSIS with MSGP, and it considers both two criteria of qualitative and quantitative for RLs provider selection and allows the DMs to solve the multiple segment aspiration levels problems.

6. Conclusions

Reverse logistics operations are integrated with green SCM. RLs provider choice is a principal decision-making action, and it is an essential factor in a business to obtain a competitive advantage. To perform this, DMs must select effective approach criteria for choosing a suitable and stable provider. For example, return practices can improve and expand resource utilization, helping achieve a competitive advantage. The post-COVID-19 pandemic especially has a growing impact on RLs provider selection. Therefore, seeking sustainable partners, such as reverse logistics suppliers, to improve the competitiveness of enterprises is a key issue.

The RLs provider selection is one of the MCDM issues, which entails searching for an effective approach for selecting a suitable evaluation criteria and provider. In a practical environment, the problem of RLs provider evaluation and selection is fuzzy and uncertain, so fuzzy set theory helps translate the DM’s preferences and experiences into meaningful results by applying linguistic values to measure the criteria of each RLs provider result. In the food industry there is no formal reference structure for choosing the best RLs provider, and this has not been debated in the SCM literature. This study proposes a hybrid model using fuzzy TOPSIS and MSGP to select the optimal RLs provider. The MSGP allows us to allocate order quantities to each RLs provider and maximize the best selection problem.

The contributions of this work are twofold: (1) it addressed an easy and effective model to help a food company to select the best RLs provider in practice; and (2) the combined strength of this approach is that it considers both qualitative and quantitative criteria for RLs providers selection problems, where more is better in cases such as the benefit criteria, and less is better in cases such as the cost criteria. In addition, in terms of management implications, (1) when making decisions on MCDM issues, both qualitative and quantitative criteria should be considered to meet the practicality of management, and (2) this study proposed a simple method, which can be calculated using a common Excel software tool, to help DMs select the best RLs provider in management practice. This study is limited to the food industry; therefore, the proposed method may be useful for various industry MCDM problems. Future research can adopt other methods, such as (Fuzzy)VIKOR [21], fuzzy ARAS and MSGP methods [27], QFD in RLs service process design [44,45], the mixed-integer linear programming model [46], and the fuzzy preference ranking organization method for enrichment evaluation (fuzzy PROMETHEE) [47], to estimate the criteria for provider selection. In addition, it is possible to explore the comparison between forward logistics (FLs) and RLs [48] using a. Methods in future studies can be compared the results obtained in this study.