Optimal Dual-Sourcing Policies for Backlogging and Lost-sales Inventory Systems with Uncertain Lead Times and Order Tracking

Abstract

This paper studies how companies use order-tracking information to more effectively execute their dual-sourcing strategies. We consider dual-sourcing inventory systems under either backlogging or lost-sales assumptions. The normal source consists of a two-stage tandem queue with Erlang distributed processing times at each stage while the emergence source skips the first stage. We show the optimal policy is characterized by two constant thresholds and one emergency-source-state-dependent switching curve. To derive this result, we first reduce the state space by a state transformation; then construct an auxiliary system so that the resulting dynamic program becomes tractable, and show its value function satisfies supermodularity, convexity, and the exchange axiom property that appears to be new to inventory research; finally use a sample-path analysis to show the optimal policy derived from the auxiliary system is also optimal for the original system under a certain condition. Using partial or no order-tracking information, several heuristic policies are developed when the condition fails. We next assess the value of order-tracking information and demonstrate its significant value through numerical studies. Also, the value of full information is more substantial in the backlogging setting than in the lost-sales setting.

Keywords: dual-source, inventory policy, dynamic programming, tandem queue, Erlang distribution