Price-dependent fuzzy demand and shortages scenario with memory effect on inventory system incorporating optimal replenishment strategy

Abstract This paper develops an optimal replenishment strategy with indeterminate demand predisposed by the item’s price. The study uses a Caputo-fractional differential equation to discuss how the memory sequel is created in the customer’s mind regarding sales pattern formulation. As the customer’s purchase pattern can’t be predicted initially, this research incorporates the triangular fuzzy in price-dependent demand and the effect of unforeseen shortages. This study provides the decisive scheme for determining the optimal number of cycles along with an estimated refilling time to attain minimal total expense and the memory effect of the customer. A numerical study under the numerical data from a retail store’s empirical findings, if the ordering of items is increased by 15% then the retailer’s cost is increased by approximately 5%. This result supports the sales strategy managerial belief that retailers must order more items to avoid stockouts owing to demand uncertainty.