A two-echelon push control system with one central warehouse and m branch warehouses is considered. The system is replenished once every cycle from an outside supplier and each cycle is divided into two different phases. While retaining the safety stock at the central warehouse, the bulk of inventories is directly shipped to the branch warehouses at the beginning of the first phase, and at the beginning of the second phase, a second replenishment is coordinated by the central warehouse through monitoring all the inventory levels in the branch warehouses. The authors call this kind of system a two-phase push control system. The objective of the system is to minimize the expected number of system backorders. Based on an extended model from Jönsson and Silver, an optimal allocation policy is developed for the non-transshipments condition, and the existence of an optimal second replenishment period which minimizes the expected number of system backorders is also shown. The relationship between the optimal second replenishment period and system conditions is examined through numerical examples.
