Optimization of a Fuzzy Inventory Model with Quadratic Demand, Time-Dependent Costs and Shortages Using the Convergent Gradient Adaptive Search Algorithm

Abstract

Inventory decisions for deteriorating items become complex when demand varies over time and cost parameters are uncertain. This study develops a fuzzy inventory model with quadratic demand, time-dependent holding cost, time-dependent deterioration and fully backlogged shortages. The ordering, holding, shortage and deterioration costs are represented by hexagonal fuzzy numbers and converted into representative crisp values using the graded mean integration method. The resulting total average cost function is minimized using the proposed Convergent Gradient Adaptive Search Algorithm (CGASA). The novelty of CGASA lies in combining feasible initialization, adaptive learning-rate control, descent correction and local refinement within a deterministic gradient-based procedure. A numerical example based on a hospital pharmacy inventory setting is used to demonstrate the applicability of the model to temperature-sensitive medical products. The results indicate stable convergence and support replenishment decisions for healthcare and perishable inventory systems under cost uncertainty. Sensitivity analysis further shows the influence of ordering cost, holding cost, deterioration rate and shortage cost on the inventory policy.