A hybrid metaheuristic model for coordinating sustainable supply chains with subsidy-induced profit structures

This study investigates a two-phase supply chain (SC) coordination strategy under the carbon tariff emissions rule that involves a single manufacturer and several retailers. Each coordination partner invests in eco-friendly technologies in an effort to lower the tariff placed on emissions. Furthermore, the government provides two types of subsidies to firms that actively coordinate investments in sustainable technologies: a fixed investment (FI) subsidy that offsets the fixed cost of investment, and a reduced-emissions (RE) subsidy that is proportional to the achieved level of emission reduction. The manufacturer operates within the supply chain, producing a distinct category of products at a fixed rate of production and distributing them to retailers in multiple shipments of equal size. The aggregate volume of demand from customers during the course of the business cycle, which varies nonlinearly depending on the price and length of storage, is equal to the retailers’ received lots. Coordinating players may have varying degrees of investment and earnings, making it difficult to distribute the overall benefit of the system among them. This study seeks to analyze various allocation strategies for maximizing the system’s profit, taking into account the members’ diverse degrees of comprehension and their investments in coordination. The relevant problems, expressed as mixed-integer non-linear programming problems, are extremely challenging from a computing standpoint. Therefore, a portfolio of hybridized metaheuristic methods, namely GASA, a hybrid of Genetic Algorithm with Simulated Annealing, ACOSA, a hybrid of Ant Colony Optimization with Simulated Annealing, GATS, a hybrid of Genetic Algorithm with Tabu Search, and ACOTS, a hybrid of Ant Colony Optimization with Tabu Search, is suggested as a solution technique. Finally, numerical experimentation has been employed to assess the effectiveness of various proposed profit distribution schemes. The comprehensive investigation reveals that implementing a forward contract between the manufacturer and retailers is an effective strategy for maximizing profits. • Analyze sustainable supply chain coordination under government subsidy programs • Model nonlinear demand with joint pricing, production, and inventory decisions • Optimize green investment and profit allocation using hybrid metaheuristics • Evaluate subsidy types and their effects on supply chain profitability • Demonstrate fairness and stability in profit sharing through numerical analysis