Multi-Objective Optimization of a Three-Level Sustainable Food Supply Chain: Modeling the Impact of Government Subsidies

This study develops an integrated optimization framework which supports the sustainable design of a food supply chain with three echelons: suppliers, a central manufacturer, and retailers. The model minimizes total cost and carbon emissions while simultaneously maximizing the share of products made with certified green processes, capturing economic, environmental, and social pillars of sustainability. Government policy is represented through two distinct incentives: a per-unit subsidy for green production and a per-use subsidy for alternative fuel vehicles, both directly reducing relevant costs in the decision space. For scalability, a tailored non-dominated sorting genetic algorithm II (NSGA-II) is developed and benchmarked against the exact solution method. Computational experiments based on the data of a dairy products case study indicate that carefully calibrated policy incentives can cut the total system cost by more than 40% and reduce greenhouse gas emissions by around 25% while raising the share of green output to above 80%. The results also indicated a critical range of subsidy values that trigger rapid adoption of clean technologies and demonstrate diminishing marginal returns beyond that range. Comparative tests confirmed that the heuristic achieves solutions within 1% of proven Pareto fronts on moderate examples and maintains high solution quality with substantial time savings on larger problems. The study provides an integrated tool for researchers and decision-makers to align economic performance with environmental and social goals, and it offers actionable guidance on subsidy design for low-carbon resilient food supply chain networks.