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In this study, the cost function of the defined system is derived first. Then, we prove this function is convex in the system's base stock level. Finally, based on the convexity of the cost function, the optimal solution for the base stock model is determined. For demonstrating the applicability of the proposed method, we resort to solving an example. © 2009 Asian Network for Scientific Information  

This study considers a two-echelon inventory system with one central warehouse and a number of non-identical retailers with Poisson demands, constant lead times, and lost sales for a single item. The warehouse works as a cross-docking terminal with no inventory and coordinates shipments to retailers. We apply the Joint order (1, T) policy in such an inventory system. In the standard (1, T) policy, the warehouse sends one unit of the item to each retailer in a fixed cycle time, which is calculated by considering each retailer separately. In the joint order (1, T) policy, the warehouse decides to replenish one unit of the item for each retailer in a cycle time which is adjusted to be an... 

The inventory system under consideration consists of one central warehouse and many identical retailers controlled by continuous review inventory policy ( R, Q). We assume independent Poisson demands with constant transportation times for the retailers and a constant lead time for replenishing orders from an external supplier for the warehouse. Unsatisfied demands are assumed to be lost in the retailers and unsatisfied retailer orders are backordered in the warehouse. We develop an approximate cost function to find optimal reorder points for given batch sizes in all installations and the related accuracy is assessed through simulation. © 2005 Elsevier B.V. All rights reserved  

In this study, a supply chain model consisting of a single product, one supplier and one retailer is considered. Transportation times are constant and demands at the retailer are assumed to be generated by a stationary Poisson process. Demands not covered immediately from inventory are backordered. The retailer carries inventory and replenishes stock according to a (Q, R) policy. The supplier has online information about the demand at the retailer and uses this information to replenish its stock. The order size at the supplier is a multiple integer to the retailer's order size. Considering order costs for the retailer and the supplier, we derive the exact cost function for this inventory... 

In this work, we consider a three-echelon serial inventory system with two warehouses (suppliers) and one retailer with information exchange. The retailer applies continuous review (R, Q) policy. The warehouses have online information on the inventory position and demand activities of the retailer. We present a new ordering policy to share information among inventory echelons. The warehouse I and II start with m 1 and m 2 initial batches of the same order size of the retailer, respectively. The warehouse I places an order to an outside source immediately after the retailer's inventory position reaches an amount equal to the retailer's order point plus a fixed value s 1, and the warehouse II... 

In this paper we consider a dyadic supply chain consisting of one warehouse and one retailer with an unequal order batch size and information exchange. Transportation times are constant and retailer faces independent Poisson demand. The retailer applies continuous review (R,Q)-policy. The supplier starts with m initial batches (of size Q), and places an order in a batch of size nQ to an outside source immediately after the retailer's inventory position reaches R+s. In this paper using the idea of the onefor- one ordering policy we obtain the exact value of the expected system costs  

In this paper we consider a dyadic supply chain consisting of one warehouse and one retailer with information exchange. We assume that the demand process to the retailer is a Poisson process and transportation times are constant. The retailer applies continuous review (R,Q)-policy. When the retailer's inventory position reaches R+s she sends information about her customer demand and inventory activities to the supplier. The supplier receives this information after a constant time lag. The supplier starts with m initial batches (of size Q), and places an order in a batch of size Q to an outside source immediately after receiving the information from the retailer. In this paper using the idea... 

This paper considers a single-item, two-echelon, continuous-review inventory model. A number of retailers have their stock replenished from a central warehouse. The warehouse in turn replenishes stock from an external supplier. The demand processes on the retailers are independent Poisson. Demand not met at a retailer is lost. The order quantity from each retailer on the warehouse and from the warehouse on the supplier takes the same fixed value Q, an exogenous variable determined by packaging and handling constraints. Retailer i follows a (Q, Ri) control policy. The warehouse operates an (SQ, (S - 1)Q) policy, with non-negative integer S. If the warehouse is in stock then the lead time for... 

This paper deals with a two-echelon inventory system consisting of onesupplier and N retailers. Each retailer faces an independent Poisson demand withthe same rate and applies a new ordering policy called one-for-one- periodordering policy for its inventory control. In this ordering policy the ordersize is equal to one and the time interval between any two consecutive ordersforms a common fixed cycle. Thus, the supplier faces a deterministic demand andadopts a deterministic inventory policy. At each cycle he orders a batch of sizeN to his own supplier. Upon receipt of each batch he sends 1 unit of theproduct to each retailer with a transportation cost. In this paper, for theabove system we... 

In this paper we consider a two- echelon inventory system consisting of one supplier and a number of retailers with independent Poisson demand. Unsatisfied demands in retailers are lost and it is assumed that there is a constraint on total lost sales for the system. Each retailer applies a new ordering policy called one-fer-one-peried ordering policy for its inventory control. In this ordering policy the order size is equal to one and the time interval between any two consecutive orders is fixed. Thus, the supplier faces a uniform and deterministic demand originated from each retailer and applies one for one ordering policy in response to orders received from all retailers. For this system... 

In this paper we consider a two-level supply chain system consisting of one warehouse and one retailer. The retailer faces Poisson demand. We introduce a new approach to inventory control in the supply chain management which is different from the classical policies used in the literature of inventory and production control systems. In this system, the retailer constantly orders a fixed amount of product to the warehouse in a predetermined time interval; i.e., the ordering size and the time interval between any two consecutive orders from the retailer to the warehouse are fixed numbers. The advantage of this policy is that the warehouse is facing a uniform and deterministic demand which... 

In this study, an inventory system consisting of a single product, one supplier, and multiple identical retailers is considered. Each retailer replenishes inventory from the supplier according to the well known (R,Q) policy. Transit times are constant and retailers face independent Poisson demand. The supplier utilizing the retailers' information in decision making for replenishment policy with a given order size starts with m initial batches (of size Q) and places an order in a batch of size Q to an outside source when a new order is placed. In this inventory system, excess demand is backordered, delayed orders are satisfied on a first-come first-serve basis, and no partial shipment is... 

In this paper, a continuous review inventory system is considered in which an order in a batch of size Q is placed immediately after the inventory position reaches R. Transportation time is constant and demands are assumed to be generated by a stationary Poisson process with one unit demand at a time. Demands not covered immediately from the inventory are backordered. In a recent paper, the exact evaluation of batch-ordering policies for two-level inventory systems was derived. This evaluation is based on a recursive procedure for determining the exact policy costs in case of one-for-one replenishment policies. In this paper, we show how this result can be applied to find the optimal... 

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...