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In this paper we introduce a new ordering policy for inventory control in a two-echelon inventory system consisting of one central warehouse and a number of non-identical retailers. The warehouse uses a modified one-for-one policy, but the retailers apply a new policy which is different from the traditional inventory policies described in the literature of inventory and production control systems. In this system, each retailer constantly places an order for one unit of product to the central warehouse in a pre-determined time interval; i.e., the time interval between any two consecutive orders from each retailer is a fixed number and the quantity of each order is one. We then show how the inventory costs can be determined for this system. The most important advantage of this policy is that the warehouse is facing a uniform and deterministic demand originated by each retailer. Furthermore, a numerical example is provided to compare the performance of the new policy with the performance of the one-for-one policy in a two-echelon inventory system in terms of the total system cost.

We consider a two-echelon inventory system consisting of one central warehouse and a number of non-identical retailers (Fig. 1). We assume the retailers face independent Poisson demand and unsatisfied demand will be lost. The transportation time for an order to arrive at a retailer from the warehouse is assumed to be constant. The warehouse orders to an external supplier. The lead time for an order to arrive at the warehouse is assumed to be constant. Full-size image (24 K) Fig. 1. Two-echelon inventory system. Figure options Andersson and Melchiors (2001) consider a similar model, but in their model they adopt the one-for-one ordering policy for both the retailers and the warehouse. In the new policy called one-for-one period (Haji and Haji, 2007) the quantity of each retailer's order is one, and the time interval between two consecutive orders from each retailer is fixed. An important advantage of this easy-to-apply policy is that its application amounts to a uniform and deterministic demand for the central warehouse on the part of each retailer. For this policy, the total system cost in steady state, consisting of holding and shortage costs of all retailers and holding cost of the warehouse is evaluated. In this study, the optimal time interval between any two consecutive orders for each and all retailers which minimizes the total system cost is determined. The paper is organized in 6 sections. Section 2 is devoted to literature review. Section 3 describes motivation and advantages of using this new policy in a two-echelon system. In Section 4, cost evaluation for the steady state is presented. Section 5 gives some numerical results and Section 6 provides the conclusions.

In this paper we used a new ordering policy and analyzed its application in a two-echelon inventory system. The most important advantage of this policy is that the warehouse is facing a uniform and deterministic demand on the part of each retailer. This advantage facilitates the inventory planning and leads to elimination of holing inventory at the warehouse. We provided a numerical example, which specifies under some conditions the new ordering policy once applied to a two-echelon system outperforms the one-for-one policy in terms of the total system cost.