The objective of this research is to highlight the factors that can optimize the total cost of a centralized supply chain through coordination of order quantities amongst the players in a supply chain. Survey of earlier research reveals that players in a supply chain usually have conflicting interests, such as reducing inventories and increasing profitability. Thus, to make coordination feasible, it is essential to provide proper incentives to individual players. Munson and Rosenblatt (2001) were the first to discuss coordination in a three level supply chain with a single player at each level. On the other hand, Viswanathan and Piplani (2001) are believed to be the first to consider cooordination in a two level supply chain with a single vendor and multiple retailers. This research extends upon these works by investigating coordination in a three level supply chain with multiple retailers. This is done by incorporating the model of Viswanathan and Piplani (2001) into that of Munson and Rosenblatt (2001). A new mathematical model is developed, with numerical examples presented and results discussed. When players in a supply chain agree to coordinate, it is possible to have some of the players benefiting more than others in the chain, if not losing. The mathematical model developed in this research work guarantees that the local costs for the players either remain the same as before coordination, or decrease as a result of coordination. Furthermore, this research work assumes that savings generated from coordination should be distributed among the players of the chain. This led to developing a scheme to fairly distribute savings amongst the players of the supply chain. Results indicate that even though players may have conflicting interests in the supply chain, coordination is recommended and should be pursued.