A three level location-inventory problem with correlated demand

• We solve a three level location-inventory problem with correlated demand.
• A conic integer programming formulation is provided.
• An outer approximation based solution algorithm is provided.
• Robust hub locations are different from the deterministic solutions.
• Neglecting demand correlation can lead to substantially sub-optimal solutions.

This paper considers a three level location-inventory problem where demand across the retailers is assumed to be correlated. We first present a reformulation scheme by which the initial formulation is transformed into a mixed integer conic quadratic program. In addition, we propose a solution approach based on an outer approximation strategy and show the algorithmic advantage of such framework for this class of programs. The results from numerical experiments show that the proposed solution procedure clearly outperforms state-of-the-art commercial solvers. In addition, we show that neglecting the effect of correlation can lead to substantially sub-optimal solutions.