Dual Sourcing in a Serial System

We consider a finite-horizon, periodic-review model for a serial system with two uncapacitated external suppliers. While one external supplier (regular supplier) ships to the most upstream stage, the other one (emergency supplier) ships directly to a downstream stage. For this system, with general lead-times we show that the optimal cost function is multimodular with respect to inventories in transit and inventories at different stages and obtain results that show how the optimal order quantities change with respect to these inventories. Our analysis also leads to sufficient conditions under which modified echelon-basestock-type policies are optimal.