A metaheuristic approach to supply chain inventory optimization with rebates, discounts, and emission controls

This study develops a sustainable production–inventory model that integrates advance booking, rebate incentives, and green investments under carbon cap-and-trade regulations, aiming to optimize profit while ensuring environmental sustainability. The model accounts for time- and price-sensitive demand influenced by discounts and advertising, and organizes the inventory cycle into four phases: advance booking before production, production with ongoing bookings, normal sales, and a deterioration phase supported by rebate strategies. The study introduces two key innovations: a dual-stage advance booking system with associated maintenance costs and deterioration control via preservation technologies. Carbon emissions arising from production, holding, transportation, and deterioration are compared to a regulatory cap, with penalties for exceeding the limit and credit trading for staying within it. Green technology investments further support emission reduction. The model’s nonlinear optimization problem is solved using the Grey Wolf Optimization algorithm to determine optimal pricing, production quantities, investment levels, and cycle times. Numerical results highlight that integrating sustainability measures, smart pricing strategies, and customer incentives enhances profitability while minimizing environmental impact. This model provides valuable insights for firms and policymakers aiming to align operational efficiency with sustainability objectives under regulatory frameworks.