A sustainable inventory model for deteriorating items with preservation investment, carbon-emission costs and trade credit under price and green sensitive demand

Deteriorating products impose large economic and environmental costs, yet inventory models rarely optimise preservation effort and shortage timing together while accounting for carbon costs, trade credit and environmentally aware demand. This study develops a sustainable inventory model for deteriorating items in which demand is sensitive to the selling price and to the product’s green degree, deterioration is reduced through preservation-technology investment, shortages are partially backlogged, and a permissible delay in payment (trade credit) applies. Carbon-emission costs linked to ordering, holding and preservation are charged through a carbon-price policy. The total average cost is minimised over the shortage point µ and the preservation investment ξ using Mathematica, with convexity established analytically (a positive-definite Hessian) and graphically. Three trade-credit cases are analysed and validated through numerical examples and an extensive ±20% sensitivity analysis. The results show that the total cost is most sensitive to the demand and pricing parameters and to the shortage cost, and that a moderate preservation investment combined with a suitably chosen trade-credit period lowers total cost while supporting sustainability. Managerial guidance is drawn on pricing, replenishment timing, preservation spend and credit-term design.