1. Introduction
Sustainable supplier selection and order allocation (SSOA) has become increasingly important for companies to achieve sustainable development and maintain their competitiveness in the global market. The supply chain is a crucial aspect of a company’s operations, and suppliers play a critical role in the sustainability of the supply chain. Therefore, evaluating and selecting sustainable suppliers has become a critical strategic decision for companies [
1,
2]. Sustainable suppliers are those who are committed to environmentally friendly, socially responsible, and economically viable practices in their operations. By evaluating and selecting such suppliers, organizations can ensure that their suppliers’ performance aligns with their own sustainability goals in these three dimensions. Consumers and stakeholders are becoming increasingly conscious of the environmental, social, and economic impacts of the products and services they use. Partnering with sustainable suppliers can enhance an organization’s reputation as a socially responsible and environmentally conscious business while contributing to the economic development of the community in which they operate. By engaging with suppliers who promote ethical and fair labor practices, organizations can support social sustainability and help ensure the well-being of workers throughout the supply chain. For example, if a supplier uses unsustainable practices or materials that are subject to regulatory scrutiny, the organization may face legal or reputational risks, so collaboration with sustainable suppliers can help mitigate these risks and ensure continuity in the supply chain [
3,
4].
Sustainability issues in the supply chain have gained increasing attention in recent years due to the increasing awareness of the negative impact of business operations on the environment and society. Sustainable SSOA aims to identify and assess suppliers based on their sustainability performance, including environmental, social, and economic aspects. Evaluating suppliers based on sustainability criteria enables companies to reduce risks associated with supply chain disruptions and ensure a reliable supply of goods and services. It also helps companies meet their sustainability goals and enhance their reputation and brand image [
5,
6]. Order allocation is another critical aspect of the SSOA problem, which involves determining the most efficient and effective way of allocating orders among chosen suppliers. Companies need to consider both sustainability and efficiency factors when allocating orders to suppliers. Allocating orders to sustainable suppliers enables companies to reduce their environmental impact and promote social responsibility while ensuring the quality and reliability of goods and services. The SSOA problem is complex, and companies face numerous challenges when evaluating and selecting sustainable suppliers and allocating orders. The problem of sustainability in supply chains is further compounded by various types of complexity and uncertainty. Static complexity could emerge from the consideration of multi-echelon and multi-tier supply chains, where there are numerous nodes and interdependent processes that need to be taken into account. Dynamic complexity may also come into play when considering a supply chain in a multi-period context, where demand, supply, and other factors constantly change over time. In addition to these, there may be technological complexity related to the use of advanced manufacturing processes and digital technologies, as well as social complexity related to dealing with diverse stakeholders and communities [
7,
8,
9]. All of these types of complexity can increase the uncertainty associated with sustainability issues, making it challenging for organizations to manage their supply chains effectively and achieve their sustainability goals. Therefore, companies need to develop effective models and methods to address the SSOA problem. The development of advanced mathematical models and decision-making tools has facilitated the evaluation and selection of sustainable suppliers and order allocation, considering multiple criteria and uncertainty [
10,
11].
Multi-criteria decision-making (MCDM) approaches can help organizations to define criteria, weight criteria, evaluate suppliers, generate alternatives, and make decisions about which sustainable suppliers to select for supply chain management (SCM) [
12,
13]. By using these approaches, organizations can make informed and objective decisions that promote environmental sustainability, social responsibility, and overall business success MCDM methods are flexible and adaptable to different contexts and situations. They can be used to evaluate suppliers in different industries, regions, and supply chain contexts, and can be customized to suit the specific needs and requirements of an organization [
14,
15].
The uncertainty of information is a common challenge in the SSOA problems. There are several methods that can be used to handle uncertainty and improve the accuracy and reliability of the evaluation and selection process [
16]. In the context of sustainable supply chain management, the reliability of decisions refers to the degree to which the decisions made by a company in evaluating and selecting sustainable suppliers can be trusted to be accurate, consistent, and unbiased over time. It is important for companies to make reliable decisions in sustainable supply chain management because these decisions have significant impacts on the environment, society, and the economy. The reliability of decisions is closely linked to the quality of the data and information used to make those decisions. If the data used to evaluate and select suppliers are uncertain or imprecise, the resulting decisions will also be unreliable [
17,
18,
19]. Uncertain information refers to information that is incomplete or unpredictable, where there is a lack of clarity about the outcome or the likelihood of different scenarios. Imprecise information, on the other hand, refers to information that is not precise or exact, where there is a degree of ambiguity or vagueness in the data. Fuzzy logic can be used to deal with uncertain and imprecise information [
20,
21]. It allows for a more flexible approach to decision-making, where criteria and weights are assigned based on linguistic variables [
22]. Fuzzy MCDM is important for the evaluation and selection of sustainable suppliers for SCM because it can help to handle uncertainty and imprecision in the evaluation process [
23]. Decision-makers may have different opinions and preferences regarding the importance of different criteria, and the criteria themselves may be vague and imprecise. Fuzzy MCDM allows decision-makers to represent criteria and weights in linguistic variables, which can be more intuitive and meaningful than numerical values. It also allows decision-makers to incorporate qualitative information, such as sustainability practices and social responsibility, into the evaluation process. This is important because sustainability performance may not be easily quantifiable, and qualitative information may be critical in evaluating suppliers’ sustainability practices. Evaluating and selecting sustainable suppliers typically involves multiple criteria. These criteria may have different levels of importance and may be interdependent [
24,
25]. Fuzzy MCDM can handle this by allowing decision-makers to evaluate and rank suppliers based on multiple criteria simultaneously. Fuzzy MCDM can also be used to identify the most critical criteria and their relative weights, which can help decision-makers to prioritize the criteria and suppliers based on their importance. This process is very important in the SSOA problem [
26,
27].
In fuzzy logic, a type-2 fuzzy set is an extension of the traditional type-1 fuzzy set that allows for more uncertainty and ambiguity in the definition of the set [
28]. Type-2 fuzzy sets can be more useful in situations where there is a lot of uncertainty or imprecision in the definition of a concept or in the data being used to represent that concept [
29]. However, they can also be more computationally intensive to work with and require more complex algorithms and techniques for inference and decision-making. Type-2 fuzzy sets are well-suited for problems involving uncertainty due to imprecise or incomplete data, or when there are multiple sources of uncertainty that need to be modeled. Type-1 fuzzy sets, on the other hand, are often used when the data are well-defined and there is little uncertainty [
30]. By developing type-2 fuzzy sets for linguistic variables, we can capture the uncertainty and imprecision in the evaluation process. This can lead to more accurate evaluations of supplier performance, which can help in making better-informed supplier selection decisions in the supply chain [
31,
32,
33]. Type-2 fuzzy sets have been applied to several real-world problems in different fields [
34,
35,
36].
This study proposes a methodology to address the sustainable SSOA problem by integrating multiple techniques. First, a new ranking method based on the concept of Radius of Gyration (ROG) is introduced for interval type-2 fuzzy sets to handle the uncertainty in supplier evaluation. To determine the weights of evaluation criteria, both subjective weights obtained using the Simple Multi-Attribute Rating Technique (SMART) and expert preferences, and objective weights calculated using the Method based on the Removal Effects of Criteria (MEREC) method are combined [
37,
38]. Then, using sustainability criteria, a type-2 fuzzy decision-matrix, combined weights, and the Weighted Aggregated Sum Product Assessment (WASPAS) method [
39], supplier performance is evaluated as type-2 fuzzy sets. The ROG-based ranking method is employed to calculate the relative scores of suppliers. Finally, a multi-objective decision-making (MODM) mathematical model is presented to identify suitable suppliers and allocate their order quantities. The application of the proposed methodology is demonstrated in a sustainable SSOA problem, highlighting the methodology’s effectiveness and applicability. The analysis conducted in this study demonstrates the practicality and efficiency of the proposed approach. By integrating multiple methodologies, this methodology can effectively handle the uncertainty in supplier evaluation and selection. Additionally, the use of the ROG-based ranking method allows for more accurate supplier performance evaluation, resulting in better supplier selection decisions. The proposed approach also takes into account sustainability criteria, emphasizing the importance of sustainability in supplier selection and order allocation.
The remainder of the paper is structured as follows.
Section 2 provides an extensive literature review, discussing some of the recent studies pertaining to the SSOA problem.
Section 3 outlines the proposed methodology, which encompasses the ROG-based ranking method, a step-by-step procedure for evaluating suppliers, and an approach to solving the MODM model of the sustainable SSOA problem. The results and discussion concerning the proposed methodology are presented in
Section 4, where an example of the sustainable SSOA problem is illustrated, along with a sensitivity analysis. Finally,
Section 5 presents the concluding remarks, summarizing the key findings of the study and highlighting future research directions.
2. Literature Review
The SSOA is an essential problem for many organizations as they directly impact the quality of the end product and the overall efficiency of the supply chain. Selecting the right suppliers and allocating orders optimally can help organizations reduce costs, increase profits, and maintain a competitive edge in the market. Over the years, several studies have been conducted on the SSOA problem, with a focus on different aspects such as sustainability, risk, and uncertainty. In this section, some of the recent studies on this topic, highlighting their contributions, are reviewed.
Esmaeili-Najafabadi et al. [
40] enhanced the process of SSOA within a centralized supply chain, by devising a mixed integer nonlinear programming (MINLP) mathematical model that incorporates two precautionary measures aimed at mitigating disruption risks. The investigation revealed that as the likelihood of disruptions increases, the variables that influence decisions regarding SSOA undergo alterations.
Moheb-Alizadeh and Handfield [
41] proposed a sustainable supplier management tool by simultaneously tackling the challenges of sustainable SSOA. These issues have received limited attention in the literature. They developed an MODM model that is comprehensive, considering multiple periods, products, and transportation modes, as well as discount and shortage conditions. They select the preferred solution based on the data envelopment analysis (DEA) super efficiency score of all purchasing firms. The proposed approach was applied to a real-world case study in the automotive industry.
Hosseini et al. [
42] developed an efficient solution for managing supply chain disruptions by developing a resilient SSOA approach. The researchers proposed a graphical model to obtain the likelihood of disruption scenarios for the supplier selection problem and a stochastic MODM model to help with decision-making on when and how to use both reactive and proactive strategies in SSOA.
Kellner and Utz [
43] devised a decision support approach that helps purchasing managers build mid-term supplier portfolios while weighing purchasing costs, supplier sustainability and overall supply risk trade-offs. To achieve this, the researchers developed an MODM model that prioritized supplier sustainability, selected the suppliers with the lowest costs, and reduced supply risk. They used the ε-constraint method to deal with the MODM model.
Duan et al. [
44] presented an integrated model for green SSOA that can aid companies in cutting costs, enhancing their green performance, and gaining a competitive edge by combining the alternative queuing method (AQM), linguistic Z-numbers, and an MODM model. The study employed the step-weight assessment ratio analysis technique to determine the weights of criteria, and an extended AQM to rank the given suppliers while establishing an MODM model to find the optimal order quantity for the selected suppliers based on their scores.
Mohammed et al. [
45] developed a hybrid approach based on MCDM and MODM techniques for sustainable SSOA. The authors put forward an integrated approach based on the fuzzy analytic hierarchy process (AHP) and fuzzy Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to evaluate and rank suppliers based on three sets of criteria and created an MODM model for selecting suppliers and determining optimal order quantities.
Safaeian et al. [
46] proposed an MODM model for SSOA that takes into account incremental discounts in a fuzzy environment. The researchers utilized the Zimmermann fuzzy approach to transform the MODM model into a single objective format, which was then solved using Genetic Algorithm and Non-dominated Sorting GA (NSGA). Finally, the methodology’s effectiveness and performance were evaluated and discussed.
Alegoz and Yapicioglu [
47] developed a hybrid approach for SSOA that takes both qualitative and quantitative criteria into account. The goal was to identify appropriate suppliers and make optimal order allocations. To achieve this, the researchers used trapezoidal type-2 fuzzy AHP, fuzzy TOPSIS and goal programming. The study also compared the use of MCDM methods regarding their effectiveness.
The purpose of the study made by Mari et al. [
48] was to establish resilient criteria for SSOA in an uncertain environment, aiming to mitigate low probability disruption risks that can have a high impact and enhance supply chain resilience. To accomplish this aim, the study proposed a possibilistic fuzzy MODM model and an interactive fuzzy optimization methodology to help organizations balance resilience and cost in their supply chains.
Laosirihongthong et al. [
49] introduced a comprehensive approach for assessing suppliers based on sustainability indicators, as well as allocating purchase orders among the top-ranked suppliers. To achieve this goal, the researchers used a mixed-methods approach and utilized the fuzzy AHP to rank suppliers. Furthermore, the study devised a cost-minimization method for allocating purchase orders. The findings of the study demonstrated that both economic and environmental factors are essential considerations.
Feng and Gong [
50] proposed an integrated approach for green SSOA in the automobile manufacturing industry using MODM and the linguistic entropy weight method (LEWM). The LEWM was used to analyze the performance and select qualified green suppliers on each evaluation criterion. The order allocation model aimed to minimize carbon emission and total cost and maximize supply value. The study found that the proposed framework could effectively deal with green SSOA for automobile manufacturers.
Khoshfetrat et al. [
51] established an MODM model for a sustainable SSOA problem in the automotive industry that considers various criteria in a fuzzy environment. To achieve this goal, the study combined the evaluation process of suppliers, which used the AHP method, with the process of order allocation to determine the ideal quantity needs to be purchased from each supplier in each period. Furthermore, the study provided a sensitivity analysis to analyze the best suppliers and their allocated orders.
Jia et al. [
52] The study addressed the issue of uncertain factors, such as emissions, supply capacity, per-unit cost, demand, and minimum order quality, whose probability distributions were imprecise, by estimating their distributions. The study proposed a robust MODM model for sustainable SSOA, which optimized four conflicting objectives while considering the sustainability dimensions. The proposed model effectively balanced multiple objectives and solved the sustainable SSOA problem by structuring ambiguous distribution sets.
Wong [
53] studied the complicated issue of selecting eco-friendly suppliers. To address this problem, the study created a fuzzy goal programming model that considered various factors such as suppliers’ dynamic risk, importance functions, and green market segmentation. The effect of different ratios of environmentally conscious consumers was studied and a solution was proposed to incorporate market incentives and result in mutually beneficial outcomes for the environment and the economy.
The aim of the research carried out by You et al. [
54] was to create a unique framework for SSOA that could benefit organizations in accomplishing sustainable development goals. To deal with the uncertainty involved in evaluating the sustainable performance of suppliers, the researchers employed Double Hierarchy Hesitant Linguistic Term Sets (DHHLTSs). They proposed an extended approach to select efficient and sustainable suppliers and established a linear MODM model to apportion rational order quantities among the selected suppliers, taking quantity discounts into account.
Rezaei et al. [
55] proposed an integrated approach for SSOA in lean manufacturing companies by utilizing both MODM and MCDM techniques. The study was conducted in four phases. Firstly, relevant leanness criteria were identified from previous research. Secondly, the AHP method was employed to evaluate these criteria for supplier selection. Next, a fuzzy AHP method was used to choose suppliers based on the lean supplier selection criteria. Finally, an MODM mathematical model was developed to determine the optimal allocation of orders.
Kaviani et al. [
56] developed a new approach that combined fuzzy multi-objective optimization and intuitionistic fuzzy AHP to tackle the SSOA problem. They started by using intuitionistic fuzzy AHP to establish the key criteria weights for evaluating suppliers and then utilized a fuzzy MODM mathematical model to determine the optimal order quantity for each supplier. The authors concluded that their innovative decision-making tool could handle decision-makers’ uncertainty and had demonstrated practical usefulness.
Rezaei et al. [
57] addressed the issue of risk and uncertainty in SSOA for closed-loop supply chain (CLSC) networks and reverse logistics. They proposed a two-stage model based on stochastic programming that uses a conditional value-at-risk (CVaR) risk measurement tool to assess both risk-averse and risk-neutral scenarios. The goal of the study was to explore how changes in key problem parameters affect a company’s sourcing strategies. The researchers recommended that firms consider purchasing from spot markets and backup suppliers to mitigate uncertainties.
Wang et al. [
58] devised a model based on the analytic network process (ANP) and integer programming that leverages MCDM techniques to optimize the SSOA problem. The researchers aimed to evaluate how different emission trading schemes (ETS) scenarios could affect a company’s overall cost structure and the creation of a low-carbon supply chain, taking into account the carbon competitiveness of suppliers by factoring in the carbon embedded in raw materials and carbon emission trading schemes.
Çalık [
59] developed a framework for managing the sustainable SSOA problem in the agricultural machinery industry in Turkey. To achieve this, an MODM mathematical model was developed, which included sustainability dimensions. The weight of the criteria was determined using an approach based on the AHP method and interval type-2 fuzzy sets. The proposed approach offered an integrated model that considered the integration of quantitative and qualitative evaluation criteria, taking into account varying preferences.
Khalili Nasr et al. [
60] proposed a two-stage model to deal with the SSOA problem in CLSCs that could minimize waste. In the first stage, a fuzzy Best-Worst Method (BWM) was used to evaluate suppliers based on various criteria. In the second stage, a linear MODM model was used to design a CLSC network incorporating vehicle scheduling, inventory-location-routing, and quantity discounts. To solve the MODM model a fuzzy goal programming approach was proposed.
Kaur and Prakash Singh [
61] presented a multi-stage hybrid model for the SSOA problem that would account for risks and disruptions arising from positive and negative events, such as natural/man-made disasters and Industry 4.0, and optimize the distribution of orders to suppliers over multiple periods in a manner that would minimize costs as well as the disruption risk. The proposed model involved supplier segmentation and evaluation using the DEA, fuzzy AHP, and TOPSIS. Moreover, the risk related to each supplier was assessed using the model.
Islam et al. [
62] developed a new two-stage approach to handle SSOA problems with uncertain demand. The study introduced a Relational Regressor Chain method for demand forecasting in the first stage. In the second stage, suitable suppliers and order quantities from each supplier were determined based on the forecasted demand and an MODM model. To obtain efficient solutions ε-constraint and weighted-sum methods were employed. The outcomes indicated the efficiency of the proposed method over the other methods in terms of forecasting accuracy.
Rezaei et al. [
63] devised an effective framework for SSOA in a centralized supply chain while considering collaboration between the supplier and buyer and the strategies for risk reduction. The study employed MINLP models and risk reduction strategies such as protected suppliers, emergency stock, reserving additional capacity, backup suppliers, and geographical separation. It also employed the risk priority number constraint and Failure Mode and Effects Analysis (FMEA) technique to account for suppliers’ reliability.
Firouzi and Jadidi [
64] proposed a fuzzy MODM model for the SSOA problem that could manage the uncertainties brought about by disasters in Japan. The researchers acknowledged that such catastrophes could have unfavorable effects on businesses and markets, resulting in increased demand for certain goods or a reduction in the suppliers’ ability to provide them in the appropriate quantity, quality, and time. To effectively consider decision makers’ preferences, the study used a weighted additive function to solve the MODM model with parameters defined by fuzzy sets.
Li et al. [
65] presented an inclusive mathematical model to assist in SSOA while considering both qualitative and quantitative factors in the risk management of supply chains. The study noted the emerging trend of environmental considerations in this field and highlighted the importance of dynamic SSOA. The presented model included the preliminary selection of suppliers based on the risk value assessed through quantitative and qualitative methods. This was followed by developing an MODM model for dynamic SSOA.
Yousefi et al. [
66] developed a two-stage hybrid approach that could be utilized to select efficient suppliers, allocate orders, and determine prices in a coordinated supply chain. The first stage of the proposed model employed the DEA technique and an MODM mathematical model to evaluate suppliers and minimize costs simultaneously. The second stage of the proposed approach utilized the order quantity specified in the first stage, the bargaining game, the Nash equilibrium concept, and a quadratic programming model to determine the price.
Beiki et al. [
67] introduced a new approach to tackle the SSOA problem by combining an MODM model with the language entropy weight method. The authors emphasized the need to improve the collaboration between potential suppliers and supply chain practitioners to achieve sustainable development goals. An MODM model based on three objectives was developed, aiming to maximize procurement value while minimizing total cost and carbon emissions. The language entropy weight method was utilized in the study to evaluate suppliers based on their sustainability performance.
Esmaeili-Najafabadi et al. [
68] proposed a multi-objective model for integrated SSOA in a centralized supply chain based on a risk-averse decision-maker and the risks of disruption. Two types of risks including local disruption risks and regional disruption risks were considered in the study. Risk-averse and risk-neutral and models were developed, and the decision maker’s behavior was analyzed using two risk assessment tools, value-at-risk (VaR) and CVaR. The model was solved using the particle swarm optimization (PSO) algorithm.
Mohammed et al. [
69] aimed to put forward a new technique for SSOA that takes into account green and resilience aspects by devising an integrated framework. The proposed framework was based on calculating importance weights using the AHP method, assessing suppliers using the TOPSIS method, and applying an MODM mathematical model with the ε-constraint method to solve the problem. The purpose of the study was to support companies in augmenting their supply chain resilience while fulfilling their environmental responsibilities.
Hosseini et al. [
70] developed a solution methodology for the SSOA challenges under uncertainty. An integration of the evidential reasoning and BWM was used to propose an approach for the evaluation of suppliers based on sustainability dimensions. Stochastic programming and dynamic programming were utilized to solve the MODM model, and its results were compared with some other techniques. The effect of uncertainties in suppliers’ availability, quantity discounts, and demand was examined through a sensitivity analysis.
Ali et al. [
71] devised a comprehensive method for SSOA in a sustainable supply chain under uncertainty. The study utilized a fuzzy AHP approach to compute the criteria weights and a fuzzy TOPSIS technique to assess the performance of suppliers and ascertain their final ranks. Then an MODM model based on goal programming was used for allocating the optimum order quantity to the selected suppliers. The results of the study and analyses indicated that the suggested model was able to deal with uncertainties associated with the SSOA problem.
Goodarzi et al. [
72] aimed to develop a model that integrated a decision-making approach to evaluate green suppliers and allocate optimal orders while accounting for uncertainty. The fuzzy Delphi method was employed to refine supplier evaluation criteria and use green and resilient indexes were for the prioritization of suppliers. The gray Correlation method and TOPSIS were utilized to analyze the results.
Liaqait et al. [
73] proposed a decision-support framework based on the integration of fuzzy MCDM techniques, demand forecasting, and MODM mathematical models. The focus of the research was on a multi-modal transportation network to demonstrate the effect of transportation on travel time, the supply chain’s total cost, and environmental impact. The findings of the proposed model showed that the multi-modal transportation network had a substantial impact on the supply chain’s travel time, total cost, and environmental impact.
The study of Gai et al. [
74] aimed to present an integrated two-stage MCDM approach that incorporated both quantitative and qualitative analyses for dealing with the challenges of SSOA in green supply chain management. In the first stage, the evaluation of green suppliers was made using linguistic Z-Numbers and the MULTIMOORA (Multi-Objective Optimization on the basis of a Ratio Analysis plus the full Multiplicative form) method. In the second stage, an MODM mathematical model was employed to determine the number of orders allocated to the preferred suppliers.
Aouadni and Euchi [
75] developed a hybrid solution methodology for SSOA based on the best-worst method and TOPSIS technique in the first phase to find a robust ranking of suppliers and to use the Linear Programming approach in the second phase to determine the weight of the objective function. The study applied the methodology to a real case of the Tunisian Electric Society, and the experimental results showed that the proposed model provided effective gains concerning solution quality.
The purpose of the study made by Galankashi et al. [
76] was to tackle the problem of merging agile manufacturing with purchasing and supplier selection. The authors reviewed past research thoroughly and utilized the AHP method to finalize the criteria for choosing agile suppliers. They utilized the criteria to evaluate suppliers using a fuzzy AHP and established an MODM model based on multiple periods for allocating orders. A sensitivity analysis was conducted to provide more practical and comprehensible results.
Liu et al. [
77] put forward a linear MODM model to help manage supply chains through the efficient selection of suppliers and allocation of orders. The study introduced a modified BWM method to assess and prioritize suppliers. The authors used fuzzy variables to find the amount of raw material order quantities. The goal programming method was employed to solve the MODM model that included four objective functions. The study illustrated that the proposed model yielded lower costs and better criteria in comparison to other models.
The purpose of the study carried out by Bai et al. [
78] was to address the neglect of net-zero emissions and carbon neutrality in the SSOA problems of supply chain management. They introduced an MODM mathematical model that can assess various procurement policies and provide practical and theoretical insights. A case of an energy trading platform was used for the implementation and assessment of the model. The results indicated the importance of purchasing fossil fuels or attaining net zero through carbon emissions sequestration and carbon offsets.
Ahmad et al. [
79] developed an approach to deal with the SSOA problem in a two-echelon make-to-order supply chain. The focus of the study was on determining the acceptable tolerances for the members of a supply chain to the minimization of the variability in total costs. The authors employed an MINLP model, and the robustness of the solutions was improved by incorporating the Taguchi Method of Tolerance Design (TMTD). They tested their model and showed the effectiveness of it.
The studies reviewed here highlight the importance of considering uncertainty in handling SSOA.
Table 1 presents a summary of the reviewed studies, taking into account the uncertainty associated with SSOA can lead to more robust decisions in supply chain management. The studies also reveal that SSOA is a complex process that requires the integration of various criteria, including economic, social, and environmental considerations. Additionally, the studies demonstrate the need to address the challenges of sustainable SSOA, which has received limited attention in prior literature. Therefore, the current study focused on developing a new methodology to deal with sustainable SSOA problems under uncertainty.