Coordinating independent buyers with integer-ratio time coordination and quantity discounts

Supply chain members can gain substantial benefits by coordinating their activities. However, a remaining challenge is to create useful coordination mechanisms when channel members are independent. This paper develops a coordination strategy with which a supplier uses quantity discounts to entice independent buyers to comply with an integer-ratio time coordination scheme. The problem is analyzed as a Stackelberg game in which the supplier acts as the leader by announcing its coordination policy in advance and buyers act as followers by deciding their ordering decisions with this information. The strategy is compared to a coordination mechanism with quantity discounts and power-of-two time coordination. While both strategies are able to produce substantial benefits over simple quantity discounts, integer-ratio time coordination provides a better coordination mechanism for a decentralized supply chain. It is shown that power-of-two time coordination may not be able to provide a stable equilibrium coordination strategy when buyers act independently and opportunistically. Furthermore, if this is not the case, integer-ratio time coordination is at least equally effective. Unlike a centralized solution, under which the improvement by integer-ratio over power-of-two time coordination is limited to 2% of optimality, system cost reduction from a decentralized coordination strategy could be much more significant.