The ‘‘multi-stage’’ inventory system is formed when an item moves through more than one stage before reaching the final
consumer. The supplier or a retailer at each stage traditionally makes decisions locally to restock their inventory. However,
such policies result in local improvement, and do not improve the global functioning of the system. If buyers coordinate their
orders, it would reduce the inventory cost to the manufacturer and hence the total system cost. Accordingly, factual and upto-date
data enable suppliers to coordinate supply with demand effectively. Recent studies have resulted in considerable
cost savings through information sharing [1].
As the environment becomes more competitive, multi-stage inventory-distribution systems have increasingly come to
the attention of the researchers. Jaber and Zolfaghari [2] reviewed the literature on integrated supply chain and coordinated
inventory management over the last two decades. Moreover, Glock [3] provided an up-to-date review of integrated inventory
models for multi-level supply chain.
Many authors have developed coordination models for optimizing supply chain integrated systems. Some of the recent
work in this field includes Abdul-Jalbar et al. [4], Chen and Chen [5], Sarmah et al. [6], Li and Liu [7], Chen and Chen [8]. Furthermore,
Viswanathan and Piplani [9] developed a model to analyze the coordination between a vendor and several buyers
in a supply chain using common replenishment periods. The vendor requires all buyers to order only at those periods, and
offers a price discount to encourage them to accept the strategy. Mishra [10] generalized the model of Viswanathan and