Abstract: The coordination problem of a supply chain system is studied consisting of one supplier and one retailer under the situation of considering linearly stock-dependent demand,the deteriorating products and (S,s) strategy that the retailer adopts. Volume discounts is offered to achieve the prefect coordination of supply chain. The uniqueness and existence of optimal strategies are testified theoretically,and the simple resolving method is given. Finally,the numerical examples show that the model is very effective in improving the coordination of the supply chain and the profits of the two parties.

Key words: stock-dependent demand, quantity discount, deterio ratio n, the prefect coordination