Abstract: This paper considers a supply chain consisting of a supplier and a retailer.The supplier provides an item to the retailer facing demand assumed to be randomly increasing in the shelf space allocated to that product;the retailer's effort cost is a non-linear function as the shelf space is a limited resource.When the retailer chooses shelf space before observing demand,the shelf space subsidy policy may improve the efficiency of the channel;if the retailer chooses shelf space after observing demand,the subsidy policy reduce the efficiency.Because the level of retailer's effort is verifiable,coupling buy back with a linear subsidy mechanism for the shelf space,the supplier could coordinate the channel,which is based on the sequence of the inventory and the effort decision of the retailer.For the different sequence the supplier have to choose completely different coordinating procedure.Finally the results were analyzed by conducting numerical examples.

Key words: supply chain, inventory, shelf space, sales promotion