a comprehensive and integrated study of any supply chain (sc) environment is a vital requirement that can create various advantages for the sc owners. this consideration causes productive managing of the sc through its whole wide components from upstream suppliers to downstream retailers and customers.  on this issue, despite many valuable studies reported in the current literature, considerabl...

We present a model of two-echelon retailer inventory systems, and we cast the problem of generating optimal control strategies into the framework of dynamic programming. We formulate two speci c case studies, for which the underlying dynamic programming problems involve thirty-three and forty-six state variables, respectively. Because of the enormity of these state spaces, classical algorithms ...

We consider a two-echelon single commodity inventory system with one warehouse(supplier) at the higher echelon and one retailer at the lower echelon. The retailer stocks individual items of a commodity and satisfies unit demands which occur according to a Poisson process. The supplier stocks these items in packets and uses these packetsto: (i) satisfy the demands that occur for single packet an...

In this paper, we apply continuous review (S-1, S) policy for inventory control in a three-echelon supply chain (SC) including r identical retailers, a central warehouse with limited storage space, and two independent manufacturing plants which offer two kinds of product to the customer. The warehouse of the model follows (M/M/1) queue model where customer demands follow a Poisson probabilit...

One of the most important aspects affecting the performance of a supply chain is the management of inventories. Managing inventory in complex supply chains is typically difficult, and may have a significant impact on the customer service level and system-wide costs. The main challenge of inventory management is that almost every inventory problem involves multiple and conflicting objectives tha...

Wepresent a new proof of the optimality of echelon order-up-to policies in serial inventory systems, first proved by Clark and Scarf. Our proof is based on a sample-path analysis as opposed to the original proof based on dynamic programming induction. © 2008 Elsevier B.V. All rights reserved.

In a production-inventory system, the manufacturer produces the items at a rate, e.g. R, dispatches the order quantities to the customers in specific intervals and stores the excess inventory for subsequent deliveries. Therefore each inventory cycle of the manufacturer can be divided into two phases, first is the period of production, the second is when the manufacturer does not do any producti...

We consider periodic review inventory control problems in directed networks, primary examples of which are distribution systems and assembly systems. External demand could occur at each node. When inventory is insufficient to meet requirements at a node, a portion of this demand is backordered and the remaining is lost. External demands, as well as lead times for inventory purchase, assembly, a...