A Model for Assessing the Value of Warehouse Risk-Pooling: Risk-Pooling Over Outside-Supplier Leadtimes

This paper constructs and analyzes a multi-location inventory model to examine the value of warehouse risk-pooling in high service-level systems. Specifically, risk-pooling over the outside-supplier leadtime is examined. Two alternative systems of N identical retailers are formulated. In System 1, each retailer operates independently: retailers receive goods directly from an outside supplier after a fixed leadtime (L_s + L_tr), where L_s is the outside supplier's own (e.g., manufacturing) leadtime and L_tr is the transportation/receiving leadtime to the retailers. In System 2, the system order is shipped to a warehouse, arriving after a fixed leadtime (L_s + L_tw), where L_tw is the transportation/receiving leadtime to the warehouse. Upon receipt of the goods, the warehouse allocates and ships units to the retailers to equalize their inventory positions. The warehouse does not hold inventory. Allocation and reshipment in System 2 requires a fixed leadtime of (L_pw + L_tr) time periods, where L_pw is the allocation and (re)packaging leadtime at the warehouse. Hence, System 2 pools risk over the outside supplier leadtime, but at the cost of: (1) increased overall leadtime to the retailers; and (2) an `internal' pipeline inventory holding cost. Our analysis asks the question: given equal required service-levels and equal safety stock holding cost (plus pipeline inventory cost for System 2), how large can System 2's extra leadtimes (L_tw, L_pw) be? Our analysis concludes that pipeline inventory-holding cost significantly influences the overall value of these breakeven leadtimes. Specifically, when pipeline inventory holding costs can (somehow) be ignored, the corresponding breakeven leadtimes can be quite large. However, if these costs cannot be avoided, then the corresponding breakeven leadtimes are significantly reduced. Managerial interpretations are provided.