Inventory policy for degrading items under advanced payment with price and memory sensitive demand using metaheuristic techniques

The integer-order methods may fail to adequately describe the behavior of many real-world inventory systems. A fractional order inventory model can be developed to examine the memory effect on the demand. In this article, we develop a fractional order inventory control policy related to non-immediately degrading goods by incorporating memory and selling price sensitive demand. The mathematical model is developed using Caputo fractional derivatives and analyzed using Laplace transform approach. An appropriate preservation policy is established to reduce the degradation in the inventory system. It is evident from the literature that the advanced payment schemes for memory-based inventory systems have not been investigated. A partial pre-payment plan where the vendor provides a discount on the purchasing price is studied by considering memory-based demand. Particle swarm optimization and differential evolution metaheuristics are employed to handle the profit maximization problem. The usefulness of the memory-based model is examined by taking a numerical example. The proposed study also reveals that the memory indices significantly impact the optimal profit. Management insights are established by considering the model's applicability by taking numerical illustrations and performing sensitivity tests on the key inventory parameters.