Dynamic stochastic-fuzzy optimization for inventory decision systems under mixeduncertainty

Abstract

This paper formulates a dynamic programming model of an inventory system in a mixed uncertainty environment where stochasticity and non-stationarity are present in a structurally different manner. The aleatory uncertainty due to demand and supply variation is modeled by stochastic processes, while the epistemic uncertainties on the cost parameters, on the service level goals, and on the managerial risk perception are represented by fuzzy sets. The proposed model integrates these two forms of uncertainty within a unified multistage decision framework and formulates a cost minimization problem that evolves through state-dependent inventory dynamics. Rigorous theoretical development is presented to establish the well-posedness of the optimization problem and to characterize fundamental properties of the optimal policy under hybrid uncertainty. A numerical example using real inventory data, along with a graphical analysis and a detailed sensitivity analysis, illustrates the applicability of the proposed model. The insights show the impact of mixed uncertainty considerations on optimal replenishment policy and also provide practical guidance to decision makers in complex and information-imperfect supply chain scenarios.