Three-Warehouse Inventory Model for Non-Instantaneously Deteriorating Items with Ramp-Type Demand, Carbon Cap and Trade, Exponential Bac and Two-Part Trade Credit under Inflation

Inventory management is a key supply chain function that has evolved from classical EOQ models to more realistic approaches that consider product deterioration and other practical factors. This paper develops a sustainable three-warehouse inventory model for non-instantaneously deteriorating items under inflationary conditions, incorporating four key modelling innovations relative to the classical two-warehouse benchmark. First, demand is modelled as a ramp-type, time and price-dependent function D(t, p) = (a + bt) p⁻η, capturing simultaneous market growth and iso-elastic price sensitivity. Second, partial shortage backlogging is governed by an exponential time-dependent rate B(t) = e⁻κ(T−t), reflecting increasing customer impatience during prolonged stock-out periods. Third, environmental regulation is modelled via a carbon cap-and-trade (CCT) mechanism with an explicit emission cap and market-based trading price. Fourth, a two-part trade credit arrangement replaces the hybrid instalment scheme: the supplier extends a credit period M to the retailer, who in turn offers customers a credit period N (N ≤ M). Interest earned and charged are derived analytically. Optimal decision variables comprising three depletion times, selling price, and preservation investment are obtained through first-order conditions verified via the Hessian matrix. Numerical experiments and a five-factor sensitivity analysis confirm the model’s robustness and provide actionable managerial insights.