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

This study explores the effective use of order-tracking information in dual-sourcing inventory systems in both backlogging and lost-sales settings. Our inventory model features a normal source, comprising a two-stage tandem queue with Erlang-distributed processing times at each stage, and an emergency source that bypasses the first stage. We show that under certain conditions the optimal policy is characterized by two thresholds and one switching curve determined by the workload at the emergency source. We establish this result in three steps: (1) reducing the state space, (2) constructing a more tractable auxiliary system and identifying its optimal policy structure by leveraging a novel functional property called the exchange axiom property, and (3) applying sample-path analysis to derive the optimal policy for the original system based on the optimal policy of the auxiliary system. When the conditions are not satisfied, we propose a heuristic policy inspired by the auxiliary optimal policy, exploiting full order-tracking information, and demonstrate its near optimality numerically. Building on these insights, we develop three simplified heuristic policies that rely on partial or no order-tracking information and evaluate their effectiveness numerically. The results highlight the significant value of order tracking, showing that the advantages of full information are notably greater under lost sales compared with backlogging.

Duke Scholars

Author Jing-Sheng Song Fuqua School of Business