Optimal Dual-Souring Inventory Policies with Order Tracking: Backlogging and Lost Sales Under Uncertain Lead Times

Dual-Sourcing in the Dark? Order Tracking as Your Guide This research unlocks the power of real-time order tracking in dual-sourcing inventory systems, tackling both backlogging and lost-sales scenarios. We model a hybrid supply chain: a normal source (a two-stage tandem queue with Erlang processing times) and a fast-track emergency source that skips the first stage. We prove that, under key conditions, the optimal policy follows a dual-threshold structure with an adaptive switching curve, dictated by the emergency source’s workload. We prove this through a three-stage approach: 1) state-space simplification – cutting through complexity; 2) auxiliary system design – introducing a tractable proxy with a novel exchange axiom property to reveal optimal structure; 3) sample-path magic – bridging the proxy’s policy back to the original system. When reality breaks the ideal conditions, we craft a near-optimal heuristic that fully leverages order-tracking information. The analysis reveals a striking contrast; although order tracking benefits both systems, its impact is markedly stronger in lost-sales environments compared to backlogging scenarios.