Optimizing pharmaceutical inventory with memory effects using fractional differential equations and interval-valued parameters

Effective pharmaceutical inventory management ensures the availability of quality medicines and their timely delivery to customers. This becomes especially important when demand fluctuates due to infection rates influenced by environmental factors such as cold weather, fever, cough, and dehydration. While traditional models focus on factors like stock levels, time, and deterioration etc., but the role of memory in how past consumer experiences influence future demand has been unexplored. Fractional Calculus (FC) offers a novel way to address this through fractional differential equations (FDEs), which can model memory effects in inventory systems more accurately. This research incorporates memory into an uncertain pharmaceutical inventory model focusing on deterioration rate, shortage time starts, time length of ordering cycle, and impact total average cost minimization. To handle uncertainties such as fluctuating demand, order quantity, and costs, we employ an interval approach, where parameters are represented as ranges rather than fixed values. This interval representation makes the model more realistic by accounting for variability in real-world conditions. Using the Cuckoo Search Algorithm (CSA) to optimize costs with the help of Python software. The goal is to create a cost-efficient, reliable inventory system that ensures timely and affordable patient treatment, even under uncertain conditions.