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, 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.
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)
can be defined as
, as displayed in
Figure 2. The membership function
is defined as follows [
16]:
When any two equilateral triangle fuzzy numbers
and
and a positive number
, some main tasks of triangular fuzzy numbers
and
can be shown as follows:
Rejeb et al., [
11] addressed fuzzy numbers that could represent these linguistic variables. Let
and
denote two triangular fuzzy numbers. Therefore, the distance between them can be calculated using the vertex method as follows:
According to the above, a decision matrix can be shown as follows:
where
and
;
.
According to the claim of Chen and Lee [
17], if the fuzzy level (rating) and importance weight (closeness coefficient) of the
kth DM are
and
, where
,
, respectively, the accumulate fuzzy levels,
, of alternatives regarding every criterion can be calculated as
; here the
,
, and
and the accumulate fuzzy weights (closeness coefficient),
, of every criterion can be calculated as
; furthermore, the
,
, and
.
From the fuzzy set theory (FST) delimitation, the normalized fuzzy decision matrix can be presented as , , , where represents the normalized value of , which is calculated if the jth criterion is a benefit, then , where . Additionally, when jth criterion is a cost, , where .
Therefore, according to the normalized process, a weighted normalized fuzzy decision matrix can be obtained as
, where
,
,
. After building a weighted normalized fuzzy decision matrix, the fuzzy positive ideal solution, say
, and the fuzzy negative ideal solution, say
, are calculated as follows:
and
and where
and
.
Furthermore, is denoted with benefit criteria, but is denoted with cost criteria. The distance of every alternative from and can be obtained as , and , where represents the distance measured between two fuzzy numbers and . Finally, the weights (closeness coefficients; ) of each provider according to distance from the fuzzy positive, , and negative ideal solution, , can be obtained from , , where range appertain the closed interval [0, 1] and 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:
where
depicts the weight belonging to deviation,
depicts deviation belonging to a target value
, and then
and
are denoted as under and overachievements of the
th goal, respectively.
is a decision variable coefficient that represents the MSAL of
th segment of the
th goal,
represents a function of a binary serial number, and
is a function of resource limitations.
Furthermore, the MSGP model can be reformulated to modify MSGP achievement types as follows [
18,
30]:
where
,
,
and all other variables are defined in the MSGP model.
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
by three DMs (
,
,
) 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
, service quality
, green level
, coordination ability
, and financial risk
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 to evaluate the importance weights of every RLs provider criterion, and the weight results are shown in
Table 4.
Step 2. The three DMs scored each criterion for reverse logistics providers using the linguistic variables shown in
Table 5, and the rating results are shown in
Table 6.
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.
Step 4.
Table 7 was used to construct the normalized fuzzy decision matrix. Using the normalized fuzzy decision matrix in
Table 8, the weighted normalized fuzzy decision matrix is obtained, as displayed in
Table 9.
Step 5. The fuzzy positive ideal solution and fuzzy negative ideal solution are obtained using Equations (9) and (10) as follows:
= [(0.9,0.9,0.9),(1,1,1),(0.9,0.9,0.9),(1,1,1), (0.21,0.21,0.21)]
= [(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
and
with respect to every criterion as displayed in
Table 10.
Step 7. The
of each RL provider obtained
= 0.467,
= 0.451,
= 0.339, and
= 0.359, as shown in
Table 11.
Step 8. Establish the MSGP model according to each RLs providers’ 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 (), lowest reverse logistic cost (), and lowest delivery time (). Next, set up the MSGP model for the reverse logistics supplier to select business objectives as (1) items are to maximize the number of reverse logistics provider licenses; (2) $52.3 and $42 million to minimize total reverse logistics costs; and (3) 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).
Using the above objectives and the calculated parameters related to each candidate, AF can formulate a fuzzy MSGP model as follows:
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, 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.