Smart Policies for Multi-Source Inventory Systems and General Tandem Queues with Order Tracking and Expediting

Abstract

We study an inventory system with multiple supply sources and expediting options. The replenishment lead times from each supply source are stochastic, representing congestion and disruption. We construct a family of smart ordering and expediting policies that utilize real-time supply information. Such dynamic policies are generally difficult to evaluate, because the corresponding supply system is a tandem queue with state-dependent arrivals and routing, whose queue-length steady-state distribution is usually not in product form. Our main result is to identify two appealing special cases of the general policy, Policy-M and Policy-E, which possess simple product-form solutions and lead to closed-form performance measures. Policy-M retains full sourcing flexibility but ignores upstream congestion in making expediting decisions. Policy-E only orders from the normal, farthest source but makes expediting decisions based on both upstream and downstream information. A numerical study shows that the best Policy-M leads to a lower average cost than the best Policy-E in almost all cases. Also, implementing the best Policy-M parameters, the general policy only performs slightly better than Policy-M. These observations reveal the value of combining sourcing flexibility with some, but limited, dynamic expediting. Our findings are equally applicable to the equivalent tandem queue. They thus may aid dynamic routing and expediting decisions for online retailers and logistics providers, among others.

Keywords: inventory, multiple supply sources, expediting, stochastic lead times, queueing networks, product-form solutions