Optimal randomized ordering policies for a capacitated two-echelon distribution inventory system

•A new formulation is proposed for inventory control in a two-echelon distribution.•A periodic randomized ordering (RO) policy is extended to manage the inventory level.•The immediate fill rate of all locations are obtained without adding new variables.•The model considers capacity limitation and lost sale situation.•The demand patterns are assumed to be stationary or non-stationary.•The model is implemented for identical and non-identical retailers.