Sustainable inventory management with trapezoidal demand and amelioration under carbon regulations

Abstract

This study develops a sustainable inventory model that addresses product quality variations, demand fluctuations, and shortages over a specific planning horizon. The model captures the dual dynamics of product utility evolving through concurrent growth (amelioration) and decay (deterioration). Though inspired by poultry farming, the approach applies to other quality-sensitive sectors such as aquaculture, dairy, beverages, and pharmaceuticals, emphasizing its relevance for diverse perishable supply chains. The model integrates a trapezoidal demand function, Weibull amelioration and deterioration, and a carbon cap and tax policy to optimize replenishment decisions while promoting environmental sustainability. A nonlinear continuous costing optimization method is developed, incorporating Weibull’s instantaneous deterioration and amelioration effects. The Black Hole Algorithm and Quasi-Newton method are employed to solve for optimal order quantities and replenishment cycles. Numerical simulations and sensitivity analysis evaluate the impact of crucial parameters on inventory performance. Results indicate moderate improvement reduces holding costs, while uncontrolled growth leads to overstock and elevated carbon penalties. The carbon cap-and-tax policy also efficiently abates emissions while maintaining cost efficiency, highlighting the necessity for a balanced replenishment strategy for sustainable operations. This research contributes a unified framework integrating biological dynamics, demand variability, environmental regulations, and hybrid optimization for sustainable, cost-effective inventory management