Supply Network Resilience Under Joint Demand and Supply Uncertainty with Ambiguous Correlation

We consider the optimal safety stock and backup capacity in the supply network where both demand and supply are uncertain and their correlations are ambiguous. Motivated by the difficulty obtaining sufficient joint correlation information, a data-driven distributionally robust optimization (DRO) framework with known marginal information is used to model these ambiguous correlations, and a second-order moment constraint is further integrated to reduce conservatism. Based on the super-modular property of the cost function, we derive the analytical results of the optimal solutions under fully ambiguous correlations, and develop tractable linear reformulations under partially ambiguous correlations. We show that our DRO method can provide valuable guidance to managers in selecting backup capacity suppliers and balancing safety stock and backup capacity. Extensive numerical experiments demonstrate the effectiveness of our approach and show how correlation characteristics and types affect optimal safety stock and backup capacity decisions. Several important management insights are also derived based on the experimental results.