Coordination between two di_erent business entities is an important way to gain com-petitive advantage as it lowers supply chain cost. In this projest, we consider a two-echelon supply chain: a single retailer holds a _nished goods inventory to meet a time-varying market demand, and a single manufacturer produces the retailer's replenishment orders on a make-to-order basis. The objective of this project is to minimize the joint total cost. We solve the problem with the conditions of unequal replenishments periods and time-dependent partial backlogging rate during the _nite planning horizon. We then simplify the search process by providing an intuitively good starting value for the optimal number of replenishments.
Finally, numerical examples are used to illustrate the bene_t of integration. A sensitivity analysis is also performed to explore the e_ect of key parameters on replenishment numbers, lot size, and joint total cost.
