Shale gas energy is the most prominent and dominating source of power across the globe. The processes for the extraction of shale gas from shale rocks are very complex. In this study, a multiobjective optimization framework is presented for an overall water management system that includes the allocation of freshwater for hydraulic fracturing and optimal management of the resulting wastewater with different techniques. The generated wastewater from the shale fracking process contains highly toxic chemicals. The optimal control of a massive amount of contaminated water is quite a challenging task. Therefore, an on-site treatment plant, underground disposal facility, and treatment plant with expansion capacity were designed to overcome environmental issues. A multiobjective trade-off between socio-economic and environmental concerns was established under a set of conflicting constraints. A solution method—the neutrosophic goal programming approach—is suggested, inspired by independent, neutral/indeterminacy thoughts of the decision-maker(s). A theoretical computational study is presented to show the validity and applicability of the proposed multiobjective shale gas water management optimization model and solution procedure. The obtained results and conclusions, along with the significant contributions, are discussed in the context of shale gas supply chain planning policies over different time horizons.

Natural resources are a boon for human beings, and their conservation for future uses is indispensable. Most importantly, energy-food-water security (EFWS) nexus management is the utmost need of our time. An effective managerial policy for the current distribution and conservation to meet future demand is necessary and challenging. Thus, this paper investigates an interconnected and dynamic EFWS nexus optimization model by considering the socio-economic and environmental objectives with the optimal energy supply, electricity conversion, food production, water resources allocation, and CO${}_2$ emissions control in the multi-period time horizons. Due to real-life complexity, various parameters are taken as intuitionistic fuzzy numbers. A novel method called interactive neutrosophic programming approach (INPA) is suggested to solve the EFWS nexus model. To verify and validate the proposed EFWS model, a synthetic computational study is performed. The obtained solution results are compared with other optimization approaches, and the outcomes are also evaluated with significant practical implications. The study reveals that the food production processes require more water resources than electricity production, although recycled water has not been used for food production purposes. The use of a coal-fired plant is not a prominent electricity conversion source. However, natural gas power plants’ service is also optimally executed with a marginal rate of production. Finally, conclusions and future research are addressed. This current study emphasizes how the proposed EFWS nexus model would be reliable and beneficial in real-world applications and help policy-makers identify, modify, and implement the optimal EFWS nexus policy and strategies for the future conservation of these resources.

Purpose: Supplier selection problem is the key process in decision making of supply chain management. An effective selection of vendors is heavily responsible for the success of any organization. Vendor selection problem (VSP) reflects a more practical view when the decision makers involved in the problem are present on different levels. Moreover, vendor selection consists of various random parameters to be dealt with in real life. The purpose of this paper is to present a decentralized bi-level VSP where demand and supply are normal random variables and objectives are fuzzy in nature. Decision makers are present at two levels and are called as leader and follower. As the next purpose, this paper extends and presents a solution approach for fuzzy bi-level multi-objective decision-making model with stochastic constraints. Different scenarios have been developed within a real-life case study based on different sets of controlling factors under the control of leader. Design/methodology/approach: This study uses chance-constrained programming and fuzzy set theory to generate the results. Stochastic constraints are converted into deterministic constraints using chance-constrained programming. Decision variables in the bi-level VSP are partitioned between the two levels and considered as controlling factors. Membership functions based on fuzzy set theory are created for the goals and controlling factors and are used to obtain the overall satisfactory solutions. The model is tested on a real-life case study of a textile industry and different scenarios are constructed based on the choice of leader’s controlling factors. Findings: Results showed that the approach is quite helpful as it generates efficient results producing a good level of satisfaction for the decision makers of both the levels. Results showed that on choosing the vendors that are associated with worst values in terms of associated costs, vendor ratings and quota flexibilities as controlling factors by the leaders, the level of satisfaction achieved is highest. The level of satisfaction of solution is lowest for the scenario when the leader chooses to control the decision variables associated with vendors that are profiled with minimum vendor ratings. Results also showed that higher availability of materials and budget with vendors proved helpful in obtaining quota allocations. Different scenarios generate different results along with different values of satisfaction degrees and objective values which shows the flexible feature of the approach based on leader’s choice of controlling factors. Numerical results showed that the leader’s control can be effectively incorporated maintaining satisfaction levels of the followers under various scenarios or conditions. Research limitations/implications: The paper makes a certain contribution toward the study of vendor selection existing in a hierarchical manner under uncertain environment. A wide set of data of different factors is needed which can be seen as a limitation when the available time is short for the supplier selection process. Practical implications: VSP which is generally adopted by most of the large organizations is characterized with hierarchical decision making. Moreover, dealing with the real-life concern, the data available for some of the parameters are not complete, representing an uncertainty of parameters. This study is quite helpful for decentralized VSP under uncertain environment to reduce the costs, improve profit margins and to create long-term relationships with selected vendors. The proposed model also provides an avenue to explore the decision making when the leader has control over some of the decision variables. Originality/value: Reviewing the literature available, this is the first attempt to present a multi-objective VSP where the decision makers are at hierarchical levels considering uncertain parameters such as demand and supply as per the best knowledge of authors. This research further provides an approach to construct scenarios or different cases based on the choice of leader’s choice of controlling factors.

This study proposes a novel neutrosophic fuzzy programming framework for solving multiobjective transportation problems (MOTPs) with a time-dependent survival cost function. The proposed model integrates parabolic fuzzy parameters with a neutrosophic compromise programming approach (NCPA) to manage uncertainty, indeterminacy, and imprecise information in decision-making. The inclusion of survival cost functions enables the model to capture the probabilistic nature of transportation reliability under fluctuating supply and demand conditions. The fuzzy model is transformed into an equivalent deterministic form using de-fuzzification, and the neutrosophic framework is subsequently applied to derive a compromise solution. A real-life case study in pharmaceutical logistics demonstrates the practical relevance of the model. It highlights its capability to generate more stable and balanced results compared to classical fuzzy programming. The findings suggest that neutrosophic programming provides a more comprehensive decision-support mechanism for MOTPs operating under uncertainty.