A robust optimization approach for multi-product inventory management in a dual-channel warehouse under demand uncertainties

This study explores the multi-product inventory problem of a dual-channel warehouse to determine the optimal continuous review inventory policies. The warehouse is divided into two areas, one for fulfilling online orders and the other for storing products and fulfilling offline orders. Uncertainties are involved in the demands of the products during lead time in the two areas with their means and variances as the only known demand information. Using a distributionally robust optimization approach, the problem is formulated as a multi-product inventory model with an individual chance constraint and a multi-product inventory model with a joint chance constraint for the warehouse capacity to minimize the annual total expected cost. Two types of service levels are considered to ensure an adequate customer satisfaction. Through mathematical manipulations, the developed distributionally robust multi-product inventory models are transformed into convex programming models which can be solved efficiently, and the corresponding solution algorithms are developed. In particular, the closed-form solution of the order quantities is derived for the model with the individual chance constraint. Numerical experiments are performed to verify the effectiveness and practicality of the proposed models and the solution approaches in dealing with demand uncertainties and to draw specific managerial insights. Effects of important problem parameters on inventory policies and cost performance are also analyzed through numerical studies. Recommendations on the warehouse structure are given for business firms engaged in both online and offline sales. The continuous review inventory policies obtained by the proposed approach are robust and are flexible in making decisions for the operations of dual-channel warehouses and supply chains with only limited demand information. The proposed algorithms are proved to be very efficient through computational experiments.