method, Mixed integer linear programming.

Supply chain networks have received significant attention over the last few years owing to their pivotal role in global operations. Meanwhile, the issue of global warming and climate change has become a priority for the international community. The lofty spike in energy demand, specifically during the Covid-19 pandemic, has reinforced energy expenses, making a steady energy supply a significant driver of effective supply chain management, more so during crisis periods. Accordingly, the design of supply chain networks that address power supply aspects has emerged as a critical but challenging task, as formulating optimal and feasible solutions by no means is an easy undertaking. To overcome this difficulty, optimization techniques have been instrumental in helping research in this field move forward. One of the main challenges in supply chain design relates to possible disruptions due to delays or supply shortages in providing energy, which can significantly influence operational effectiveness. Therefore, a supply chain should be designed with resilience and be able to withstand such disruptions.

Simultaneously, energy production and consumption continue to be the largest contributors to global carbon emissions, challenging sustainability greatly. Particularly, electricity is the second most used energy source in industry, with its consumption forecasted to increase steadily through 2040. This highlights the requirement to reconcile energy security with environmental and societal concerns while simultaneously managing economic limitations. This research aims to answer the inquiry as to how to combine supply chains and traditional grid electricity considering environmental, social, and economic concerns. The problem transcends developing and developed countries and presents itself as an international issue because the utilization of electricity needs to concurrently provide environmental gains and create energy security. To address this issue, we formulate a Mixed Integer Linear Programming (MILP) model with the aim of minimizing the overall system cost. The objective function includes costs associated with facility operation and establishment, material and product processing and transportation, occupational accidents, employment, and emissions. By addressing these complex issues, this study aims to contribute towards the development of sustainable and 2.

Sustainable supply chains are a topic that has attracted widespread attention among the researchers. Previous studies highlighted supply chain network design using several methodologies, including single-objective optimization [1], multi-objective frameworks [1], and multi-level decision-making models [2]. Effectiveness evaluation and comparative studies were also done to show how they are different from each other [3] Other studies include the formulations of deterministic MILP models to optimize performance in the supply chain by [4] and [5].

Sustainable supply chain design expands beyond cost and efficiency to major concerns like health and safety risks-both physical and psychological-incorporated with environmental impacts. The principles of sustainable supply chain management are about worker safety, human rights, and fair operations. According to [6], local employment providing housing and construction is sustainability, which further necessitates responsible practices benefiting society while reducing environmental harm. Through job creation as well as carbon emissions control and eco-friendly policies providing shapes to environmentally-responsible operations, sustainability strategies concern with supply chain networks [7].

Highlight resource maximization and waste reduction as very critical strategic initiatives in enhancing sustainability and competitiveness of closed-loop supply chain networks. For a complete appraisal of sustainability, the true definition demands careful assessment of environmental impact, economic profitability, and social responsibility[8]. explores hydrogen supply chains and their connection to the operation of renewable energy-powered electricity distribution networks.Regardless of the vast studies about environmental, economic, and social considerations of supply chain network design [9], to date, even less attention has been paid to energy supply and consumption. Existing literature has provided evidence on various connections linking economic development and growth with energy consumption and the corresponding rise in carbon dioxide emissions [10]. This nexus built the platform for the development of next-generation concepts that include energy efficiency production planning, driving economic advancement in balance with sustainable practices for energy consumption[11]. Develops a MILP model to integrate a supply chain with the main power grid, optimizing the production and distribution of the product throughout the supply chain. [12] Analyzed the impact of renewable energy on the power supply chain and compared the effectiveness of renewable generators versus power grid purchases from the spot market during energy shortages. In some fields, the energy considerations may be important enough to justify decisions on the use of closed-loop supply chains. Clearly, energy considerations deserve intertwined inclusion in supply chain management to stem voluminous greenhouse gas emissions from energy supply and consumption. These emissions have been appreciably labeled as prominent contributors to environmental degradation and climate change. Though power grids have been extensively studied and improved by researchers and professionals from the industry, we still find a significant gap in the literature about the integrating of such power grids into supply chain networks. The present study proposes to look at what can be considered for the optimal design of a supply chain that incorporates energy sourcing strategies while ensuring sustainability along with operational flexibility and economic viability with respect to carbon emissions.

The network structure analyzed in this study involves the coupling of two essential entities: the supply chain of the product and the primary power grid. The networks are interconnected, with the primary power grid supplying the power directly needed for the production and transportation processes that occur within the supply chain. As illustrated in Fig. 1, the principal power grid comprises a power generation facility that produces electricity, which is subsequently sent to each component of the product supply chain to satisfy manufacturing and logistics operations' energy requirements.

The supply chain framework is a standard logistics model with producers, wholesalers, and suppliers. The producer would arrange to have the raw materials brought in and transported to the factory for production. The manufacturer takes care of the creation of the product and then sends it to the distributor, who eventually supplies the final product to the consumer. Under this logistical system, various vital considerations are made, such as the total costs of the supply chain, the expenses involved in job creation, and the economic consequences related to work-related injuries.

In addition, the study has a carbon tax policy that seeks to maximize and reduce the carbon emissions generated in the process of manufacturing as well as transporting the product throughout the supply chain. The coupling of these networks is directed towards managing the issues of energy supply, cost reduction, and environmental sustainability, along with addressing social aspects like employment and occupational health. Through the application of optimization methods, this paper seeks to develop a model that is sustainable and balanced in nature, with minimum cost and emissions and maximum robustness and efficiency of the supply

The model is then formulated through Eqs.(1)-(22).

Subject to:

(10)

(11)

(12)

(13)

(14)

(15)

(16)

(17)

(18)

(19) (20)

(21) (22)

The total cost function of the grid-connected product supply chain, illustrated in Eq. (1), encompasses different varieties of costs, giving adequate weight to supply chain efficiency and economic viability of operation. Total cost structure comprises several operational and logistical costs, as clarified in Eq. (2). Eq. (3) describes work damage costs inclusive of losses incurred through work injuries and lost productivity from interruptions to work flow in connection with equipment damage. On the other hand, the economic damages Eq. (4) quantifies lost production days that will be manufacturers and distributors due to damages on equipment and machinery. While Eq. (5) provides for an equilibrium in the supply and demand of electricity, the constraint goes a long way in ensuring that the quantity electricity supplied, mostly by the main grid, meets the total energy demand of the supply chain network. Eq. (6) protects an energy supply constraint in the network, so that there will be sufficient electricity distribution in all supply chain facilities, while Eq. (7) establishes a relationship with respect to resource consumption and the electricity consumption of the entities in the product supply chain.

Eq. (8) is used for the flow of materials, specifying input resources from suppliers to tenders and internalization to distributors from facilities. Demand versus production polynomial constraints for the given equations ensure periodic supply chain work without interruptions. In a sense, Eq. (10) actually governs particular distribution conditions whereby the demand of every market can be satisfied through just one direct distributive avenue. In Eq. (11), so as to ensure congruence between the input of raw materials and output of production from the factory, factory production levels are balanced. Limitations for production capacity were given in the following Eqs (12)-(14), there are thus defined capacity constraints related to plant production so that factory production occurs within the allowed capacity. Eq. (15) also sets a further stipulation that goods produced from every factory must be directly connected in one way or another to a single supplier for the quality of the goods produced and also for their operation in regard to the channeling of goods within the established chain of supply. The identification of a production facility is ruled then by Constraint 16, whereby there cannot be an identified factory producing a product other than one. Such constraints would allow for some additional flexibility in limiting the number of active production stations and help control the expansion of infrastructure and scalability of operations.

Constraint (16) mandates that at least one factory must be assigned for a single product. Additional constraints provided by Constraints (17) and (18) control further extension in the construction of new production locations and the scalability of their operations. Eq. (19) restricts the supply chain network design to the customer fulfillment time requirements; while Eq. (20) estimates the total carbon emissions produced in the supply chain network, which reflects environmental objectives in decision-making. Then Eqs. (21) and (22) provide definitions of the characteristics of the decision variables, differentuating between continuous and discrete variables typical in the optimization model. Taken together, these equations ensure that the mathematical model reflects real operational constraints, bringing an entire frame for the sustainable and cost-effective design of SCN.

This research presents a MILP model for developing a grid-connected supply chain integrating all main supply chain components with the major power grid. A carbon tax policy-based analysis provides an environmental-driven approach to the emissions produced by the entire system. The study does an analysis of the trade-offs among different cost components and provides consideration for economic, environmental, and operational factors together in their collective approach to the supply chain. The main theoretical contribution of this study is the development of a new mathematical framework that optimally addresses increasing electricity demand in traditional supply chains. In contrast to earlier models which strictly examined supply chain and energy systems separately, this model makes a specific approach for assuring their smooth interaction; that is, a combined interaction of supply chain networks and electricity grids. The analyses reveal that integration is plausible and the introduction of the carbon tax policy introduces additional cost elements and gives the supply chain an incentive to take into account cleaner energy sources. Though, in theory, it imposes further cost on the supply chain, it compels managers to consume cleaner energy resources while adopting this policy for sustainability. Conversely, the results show that if structured well, the supply chain energy plan can be directed toward economic efficiency and environmental sustainability. With the energy-responsive supply chain model design, businesses can not only minimize per-operation costs but also align themselves with global carbon reduction initiatives. This study further stresses the need to incorporate energy supply with environmental concerns in formulating respective strategic decisions about the supply chain owing to decision-making primarily in electricity-intensive industries.

The authors would like to express their sincere gratitude to all colleagues and collaborators who contributed to this research through their valuable insights and support.

This research received no specific grant from any funding agency in the public, commercial, or not-for-profit sectors.

The data that support the findings of this study are available from the corresponding author upon reasonable request.