Emergency supply in two-echelon inventory systems

Abstract

We consider a single-period two-echelon inventory system which consists of a single warehouse and single/multiple retailers. Each retailer faces a stochastic demand and an emergency supply option from the warehouse. The objective is to find the optimal ordering policy from an external supplier so that the system cost is minimised.We derive the optimal ordering policy for the special case with only one retailer. We also consider two settings for the case with multiple retailers. Under the first setting of incomplete demand information, we find an iterative method to obtain the optimal solution. Under the second setting of complete demand information, we show the convexity of the cost function and use an iterative method to find the optimal solution of small scale problems.At last, vast computations with different parameter settings show the benefits of the emergency supply and complete demand information.