Global energy consumption is increasing exponentially, especially in developing nations where it plays an important role in socioeconomic development (Habib et al., 2021). Scientists have been looking for alternative energy sources due to issues including global warming, energy scarcity, and food scarcity, as well as the strong desire for a better quality of life (Wang P. et al., 2022). Renewable energy has gained the attention of academic and industrial experts in order to secure future energy reliability and sustainability (Shang et al., 2023). As a result, a sustainable approach toward sources of renewable energy is one option to satisfy society’s growing energy demands (Li et al., 2023). Due to technical advancements and the industrialization, globally societies became more dependent on fossil fuels (Wang et al., 2023). Furthermore, the combustion of fossil fuels greatly affects the surroundings by raising carbon emissions and the Earth’s average temperature (Mishra et al., 2020). Even while fossil fuels are essential to society’s development, they have a negative effect on climate change (Xu et al., 2022). Over the past century, the usage of fossil fuels in the manufacturing and building industries has resulted in huge emissions that have sparked the global warming process (E et al., 2019). Traditional fuels could be replaced with agricultural waste, forestry waste, and their byproducts (Wan et al., 2022). As a result, over the past 20 years, interest in biofuels generated from biomass has greatly expanded on a global scale (Guo et al., 2023).

It is evident that adoption of sustainable unconventional energy resources as an alternative to fossil fuels might help to reach the world’s energy demands in the future (Shah et al., 2018). Biodiesel is one of the unconventional fuels that may be used instead of traditional fuels and still be considered environmentally friendly. The popularity of biodiesel as an alternative energy source has a number of advantages over other petroleum-based products, including a higher flash point, increased flowability, and minimal toxicity (Banković-Ilić et al., 2014). It is still debatable whether or not biodiesel made from first-generation sources can be considered sustainable due to the fact that it is more expensive than fossil fuel (Victor T. Wyatta et al., 2005) (Ghaderi et al., 2018). The main reason for the restricted use of biodiesel in business settings is that its manufacturing is rather expensive. The cost of the raw materials accounts for anything between 70 and 95 percent of the entire cost of producing biodiesel. Because diesel fuel derived from petroleum is more cost-effective than biodiesel made from food-grade oils, it is essential to find alternative oily feedstocks that are both new and less expensive in order to produce biodiesel (Gui et al., 2008; Leung et al., 2010; Balat, 2011). It is possible to increase the production economics of a product that is both environmentally friendly and sustainable by making use of inexpensive used-cooking oils, by-products from consumable-oil refineries, and non-consumable oils (Zhang S. et al., 2022). The conversion of used-cooking oil into biodiesel is seen as a good way to deal with issues relating to food security, the energy disaster, and environmental issues (Yu et al., 2023a). Waste cooking oil, on the other hand, has not been recycled for use in industry in a satisfactory manner during the previous several years (Zhang et al., 2017). Researchers have recently been interested in waste cooking oil because of its potential to serve as a feedstock that is economically sustainable (Kleinová et al., 2011). However, it is evident that there is need to focus on how to minimize production costs when using biodiesel made from waste cooking oil (Kim et al., 2011; Ji et al., 2022). According to Singhabhandhu and Tezuka (Singhabhandhu et al., 2010) there are some of the benefits of utilizing waste cooking oil as feedstock as opposed to using other forms of feedstock. For example, as compared to feedstocks, waste cooking oil is more cost-effective in terms of profitability; and easy to dispose and maintain its steady supply. Whereas, due to commercialization, social and environmental issues, desire is to have sustainable development in biodiesel fuels, considering all three components as: economics, environment, and society (Babazadeh et al., 2017). Similarly, having an effective supply chain network (SCND) for biodiesel fuels needs making strategic choices at the level of defining the volume, location, and capacity of manufacturing plants (Babazadeh et al., 2013). This prompted academics to build SCND optimization models so that systematic supply chains from feedstock source locations to demand zones may be built (Qu et al., 2022).

This research is different from the previous one as it introduces a mathematical model that considers waste cooking oil collection and pretreatment, biorefineries, and biodiesel demand zones, with the aim of minimizing costs and the percentage of carbon emissions related to biofuel production and distribution. In addition, to address uncertainties in the optimal solution, a fuzzy modified possibilistic chance constrained programming approach (MPCCP) is proposed. Moreover, the study proposes an interactive fuzzy programming technique to solve the waste cooking oil-based biodiesel supply chain model. The research’s emphasis on reducing costs and carbon emissions in the biofuel supply chain aligns with the objective of fostering responsible consumption and production practices which is very important among sustainable development goals (SDG) given by United Nation (UN). By implementing strategies to optimize efficiency and environmental impact, the study contributes to the promotion of sustainable resource management and sustainable development. Moreover, the research is mapped with another SDG such as climate action as it aims to reduce carbon emissions by integrating a carbon tax and implementing strategies to minimize environmental impact in the biodiesel supply chain. Initially, the relevant literature review is presented in the following Section 2. While Section 3 presents problems at hand. Subsequently, Section 4 presents formulation of desired supply chain model and fuzzy possibilistic programming method to manage uncertainty. Section 5 presents the application of model as a case study. The results obtained and the sensitivity analyses carried out are also presented in this paper in Section 6. Lastly, conclusion, limitations of study and future scopes are presented in Section 7.

There is a high degree of unreliability in the logistics chain network owing to the capacity limitations of local firms and changes in global market demand (Munir et al., 2022). Various types and degrees of uncertainties may be found throughout the biodiesel supply chain (Geng et al., 2021a). The manufacturing of biodiesel from a huge variety of biofuels, which may be broken down into two categories: edible and non-edible, was the subject of discussion in a number of research articles (Xiao et al., 2022). Biofuel generation from edible fuel sources has been shown to be significantly discouraged due to competition with the food market (Naik et al., 2010; Mohr et al., 2013; Safieddin Ardebili et al., 2018). In recent years, there has been a huge amount of interest in the use of biodiesel as an alternative fuel. This is due to the fact that biodiesel offers a number of benefits over petroleum diesel, particularly in form of how well it performs in engines and how well it is for these kinds of efforts may also assist reduce reliance on oil imported from other countries and the consequences of greenhouse gases. There is a wide range of different non-edible feedstocks that may be found in the study that has been conducted. (Ahmed et al., 2018). developed a mathematical framework for the manufacturing of biodiesel using agricultural residuals as feedstock. This model took into account the fact that both the demand for biodiesel and the availability of feedstock were unknown variables (Ahmed et al., 2018). Under the unpredictability of distribution (Zahraee et al., 2020) created a deterministic planning and forecasting framework. A multiperiod and multilevel (MILP) model was constructed by Giarola et al. (Giarola et al., 2012) in order to handle the issues of organic material allocation, production machinery selection, and plant placement. This model took into consideration the unpredictability of biomass supply as well as a CO₂ emission quota trading scheme, with the goal of increasing the total present value of the supply chain and decreasing CO2 emissions (Zhang et al., 2022b). The procurement process has a number of major uncertainty issues, one of the most important of which is the uncertainty over the availability of biomass (Zhang et al., 2022c). On the other hand, the supply of biomass is clearly seasonal since it is dependent on planting and harvesting activities and needs a relatively constant growth cycle (Li et al., 2020). However, there is a regional and temporal variation in how waste cooking oil and other municipal wastes are used by urban inhabitants and the economic growth of the city. Due to competition from the unlawful “gutter oil” manufacturing chain, the real quantity of biomass gathered by refining facilities is further exacerbated by ambiguity about biomass (Nguyen et al., 2018). Biodiesel supply chain network design employing Jatropha carcass L. and cooking oil as feedstocks was created by (Babazadeh et al., 2013) for decreasing SC cost and environment effect in the face of epistemic uncertainties. The authors developed a unique solution methodology to reduce the overall risk values in order to reduce the uncertainty effect on this innovative solution methodology (Kim et al., 2011). (Hu et al., 2017) modelled a supply chain that included a service need, an unpredictable supply and demand, and a profit-sharing agreement. From this model, they were able to extract the best ordering policy for the buyer as well as the ideal supply policy for the provider (Hu et al., 2017).

Supply chain sustainability has emerged as a new technique for making business choices by considering the effects on the environment, economy, and society all at once (Geng et al., 2021b). In a biofuel supply chain network design challenge, (Yu et al., 2023b), used a MILP to improve economic, energy, and environmental goals. Each megajoule of biofuel manufacturing requires a certain amount of fossil fuel energy to produce. In the early stages of an engineering project, attention is often paid to environmental concerns (Wang Y. et al., 2022). As a result of these uncertainties, they used a robust possibilistic programming (RPP) approach in order to reduce the influence of these variables (Mousavi Ahranjani et al., 2018). An economic, social, and environmental MILP model developed by (Ziolkowska, 2013) examined the SC of bioethanol generated from cellulose. A biofuel SCND aimed to reduce costs and CO₂-equivalent emissions (Yan et al., 2021). As the bioenergy sector grows, new jobs and economic vibrancy are expected to be created in rural regions, which is good for social sustainability (Baudry, 2018; Gao et al., 2019). Researchers have been pushed to build SCND optimization models as a result of the fast development of operations within the biodiesel sector (Huang et al., 2010; Ghelichi et al., 2018). The ideas and techniques of biodiesel SCND optimization have been the subject of substantial study by academics, particularly in the fields of biodiesel distribution network facility. First, a gap analysis is done by examining the current supply chain studies and discussing essential elements displayed in Table 1.

The commercial dynamics of biofuel supply chain functions are inherently riskier than those inside the conventional supply chain. This results in very uncertain data for parameters whose values are unknown. According to (Pishvaee et al., 2011) there are two primary categories of data uncertainty: Randomness causes (1) a uncertainty (2) Uncertainty originating from a lack of knowledge (epistemic uncertainty). In the first sort of randomness, the parameter itself has an unpredictability of its own. These strategies are most successful if sufficient historical data on parameter distributions are provided (Pishvaee et al., 2012). When dealing with circumstances in which the data acquired is tainted by epistemic uncertainty, the most effective method to use is called “possibilistic programming. To solve the suggested optimization model, a solution approach that is based on possibilistic chance constrained programming is used. The following are some of the ways in which the planned study would add to the current body of knowledge about the biodiesel supply chain:

• Proposing a mathematical model that takes into account the collecting and pretreatment of waste cooking oil, biorefineries, and biodiesel demand zones in order to reduce the costs associated with producing and distributing biofuels.

The supply chain is composed of three major participants in this research: a waste cooking oil supplier, an integrated biorefinery, and a market zone with its own distinct processes. At supplier’s locations, kitchen trash is generated on a daily basis (restaurants, guest houses, food market, etc.). After that, it is transferred to integrated biorefineries for preprocessing and biodiesel synthesis by small trucks. The biodiesel that was manufactured is ultimately transported to the demand regions. In the future, there will be increased unpredictability around the generation of biodiesel from used cooking oil due to factors such as the availability of feedstock, the demand for biodiesel, and the evolution of rules and policies. According to the data collected over the course of the previous decade, the overall amount of trash produced in kitchens has grown by anywhere from 1 percent to 8 percent. When it comes to planning the whole waste cooking oil supply chain, the aim is to build a possibilistic programming model that takes into account process validation and provides sustainable solutions. The particular difficulties that need to be handled by the (MPCCP) model involve determining the total cost of the waste cooking oil under the agreement that was signed by the restaurants and the biodiesel producer.

Thus, the network of supply chain facilities includes waste cooking oil supply points, waste cooking oil preprocessing units, biodiesel production units, transportation of resources between the various processing facilities and distribution. The following Figure 1 depicts the adopted framework.

In the above supply network, used cooking oil is considered a potential source of feedstock for biodiesel. Waste cooking oil is sourced from processing plants located in various regions across the country. Prior to being transported to biorefineries, the waste cooking oil undergoes preprocessing at a central facility. Following pretreatment, the fat from waste cooking oil is converted into biodiesel at the biorefineries, which is then distributed to regions with demand for the fuel. When planning the transportation of preprocessed oil and biodiesel within the network, road transport is a preferred consideration. The consumption of biodiesel and the availability of feedstock supplies are both highly unpredictable. Additionally, factors like CO₂ emissions, shipping, processing, and storage costs are challenging to accurately forecast during the design phase. Fuzzy numbers are employed to represent the parameters in this model due to their ability to handle the ambiguity of the situation.

For this proposed framework for waste cooking oil-based biodiesel supply network the notations, variables, objective functions, and constraints, and the proposed modified possibilistic chance constrained programming method are presented.

Based on the Pakistani context, the Waste cooking oil model’s effectiveness and performance is evaluated. As of right now, Pakistan uses just a small percentage of its renewable sources, the majority of which are first-generation biomass sources. On the other hand, waste cooking oil, which is now put to use in low-cost applications, has the potential to be used as a source in the production of biodiesel. The yearly consumption of edible oil in Pakistan is 3.7 million metric tones (MMT), which suggests that Waste cooking oil-based biodiesel has a considerable ability to greatly reduce the reliance that the nation has on traditional fossil fuels. In addition, the government is promoting the use of renewables to minimize harmful emissions and achieve long-term development objectives. In this regard, this research offers a useful decision-making tool that will make it possible for the government bodies to meet their objective of achieving sustainable biodiesel.

According to the collected data, there are a total of eight waste cooking oil pre-processing units, four potential sites for biorefinery facilities, and five marketplaces for biodiesel have been selected. Four sites in the area are being investigated for biorefineries with varied biodiesel production capacity. All four provinces have been truncated into four zones, which meet all the criteria of local legislation as well as environmental and industrial regulations. Figure 2 depicts the Potential locations of Waste cooking oil-based biodiesel Production facilities all across Pakistan.

The increasing demand for alternative energy sources has been prompted by the rapid exhaustion of fossil fuels. A multi-period supply chain model for biodiesel synthesis is introduced in this study for reducing the entire supply chain cost. In order to reduce carbon emissions in the biodiesel manufacturing and distribution supply chain, a carbon tax has been implemented. This information is polluted by intrinsic epistemic uncertainty due to the changing nature of the business climate for biodiesel SC and the early stages of biodiesel use in Pakistan. The MPCCP based solution approach that offers economic viability to the derived solutions is used because it is effective in dealing with epistemic uncertainty.

While Lingo 18.0 is utilized to solve the deterministic, static, multi-echelon MPCCP model, MATLAB is used for demand forecasting based on fuzzy logic. MATLAB 2019a is used to simulate FLD, demonstrating the usefulness and effectiveness of fuzzy logic designer simulation for this issue. The case-specific SC network and efficient product flow between warehouses and distributors are both developed using the output data. In addition, it is shown that the FLD simulation may be employed in place of analytical calculations, guaranteeing a reduced representation for this approach and saving time.

For this particular scenario, it was shown that by spending an additional 18 percent in costs, the strategic choices of the suggested waste cooking oil-based supply chain model may be protected from the intrinsic epistemic uncertainty. Moreover, the economic objectives analysis shows that logistics activities associated costs are the second most significant expenditure after facility construction costs. Most of the inventory cost is accounted for by logistics operations. To minimize overall logistic cost and the carbon tax paid owing to carbon emissions caused by transportation, facility placement choices play an important role.

The suggested model was tested in a real-world scenario in Pakistan and found to be accurate. However, this study has some limitations. The findings are based on a specific context in Pakistan, which may limit the generalizability of the proposed model to other regions or industries. Furthermore, the study highlights the significance of logistics activities and transportation costs in the overall supply chain costs. However, it would be beneficial to delve deeper into other cost factors and explore potential trade-offs between various objectives such as environmental sustainability and economic viability. Overall, the study provides valuable insights and lays the foundation for further research in optimizing waste cooking oil-based supply chains. Future studies could consider expanding the scope beyond a specific region, evaluating the long-term implications of the proposed model, and exploring additional cost factors and objectives for a more comprehensive analysis.