Generalization of Classical Fuzzy Economic Order Quantity Model Based on Memory Dependency via Fuzzy Fractional Differential Equation Approach

Abstract

In this paper, an attempt to find a more generalized version of the classical EOQ model is made under the setup of fuzzy fractional calculus. Intuitively, the notions of fuzziness and fractional derivative represent the sense of uncertainty and memory, respectively. Thus, manipulating the classical EOQ model in terms of the fuzzy fractional differential equation (FFDE), the impacts of the uncertainty and system memory on the lot-sizing model are manifested here. The model describes the FFDE under Caputo gH derivative and Riemann–Liouville integration. A trapezoidal fuzzy environment is considered to find a better environment for the cost minimization perspectives. From the numerical simulation, memory introduction is established to be fruitful in favor of the cost minimization objective. Moreover, the discussed model contains the other versions (crisp integer order, fuzzy integer order, and crisp fractional order) of the classical EOQ model as particular cases.