A fractional calculus approach to enhancing supply chain performance with deterioration and preservation

This research proposes an innovative fractional-order inventory model for supply chains, incorporating donation strategies to reflect real-world dynamics and corporate social responsibility initiatives more accurately. Unlike conventional integer-order models, the present study utilizes fractional calculus to account for memory effects, where Caputo operator was dealt with by using Riemann–Liouville fractional order integral and Laplace transform techniques. The model addresses products with demand impacted by selling price and reliability, allowing for the occurrence of shortages and partial backlogging. At the end of the positive inventory cycle, a fixed percentage of the inventory is donated in a single batch. Significant analytical contributions include the simultaneous optimization of selling price, cycle duration, and donation timing under fractional dynamics, with explicit consideration of deterioration and preservation investments. The addition of a discounted partial advance payment mechanism enhances coordination between suppliers and retailers while decreasing order cancellations. Profit optimization is achieved through the application of meta-heuristic optimization methods. Numerical findings illustrate the greater efficiency of the fractional-order model compared to traditional models. These results provide practical insights for supply chain managers, fostering more sustainable and cost-effective operations, while emphasizing the importance of fractional calculus in improving inventory theory and its applications. • Develop a fractional calculus model that captures realistic supply chain dynamics. • Incorporate donation strategies into inventory cycles for social responsibility. • Model demand sensitivity to price and product reliability with partial shortages. • Improve performance through preservation investment and advance payments. • Validate the model with numerical analysis and sensitivity studies for managers.