A1395
Title: A Gaussian-based approximation for a two-stage dual sourcing with delivery risk
Authors: Edson Antonio Goncalves de Souza - IESEG School of Management/University of Lille (France) [presenting]
Stefano Nasini - IESEG School of Management (France)
Tanja Mlinar - IESEG School of Management (France)
Maud Van Den Broeke - IESEG School of Management (France)
Abstract: The purpose is to develop a closed-form Gaussian approximation for a dynamic decision problem in inventory management with unreliable supply sources. The central contribution lies in establishing the analytical tractability of the value function through Gaussian partial moments and their integration into the optimality conditions. Specifically, closed-form expressions are provided for the expectations of the holding and shortage cost functions under normally distributed demand, enabling the bypass of simulation-based methods. Numerical experiments compare the Gaussian-based solution with policies derived from exponentially distributed demand. Across a broad set of parameterizations, the Gaussian approximation exhibits striking robustness: The resulting policies nearly coincide with those obtained under exponential assumptions, with average deviations negligible and maximum deviations diminishing as variability decreases. Importantly, the Gaussian formulation yields closed-form ordering rules that preserve the qualitative structure of the optimal policy while ensuring analytical simplicity. These results demonstrate that our methodology provides a powerful tool for decision-making under uncertainty, combining the interpretability of closed-form policies with accuracy comparable to simulation-driven methods, thereby offering a practically viable and computationally efficient framework for inventory decisions in settings with stochastic demand.
