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Inventories with Multiple Supply Sources and Networks of Queues with Overflow Bypasses

Fuqua School of Business, Duke University, Durham, North Carolina 27708; and School of Management, Shanghai Jiao Tong University, Shanghai 20052, China
Fuqua School of Business, Duke University, Durham, North Carolina 27708
jssong{at}duke.edu
paul.zipkin{at}duke.edu

Consider an inventory system with multiple supply sources and Poisson demand. The replenishment lead times from each source are stochastic, representing congestion and disruption. We develop performance evaluation and optimization tools for a family of reasonable order policies. These policies take into account real-time supply information, which can be obtained through tracking technologies such as global positioning systems and radio frequency identification. Performance evaluation of such state-dependent policies is generally hard. The main thrust of this paper is to show that, under these policies, the supply system becomes a network of queues with a special routing mechanism called an overflow bypass. The solution has a simple product form. Thus, we obtain closed-form performance measures. These results reinterpret and extend the existing analysis of a system with two sources having deterministic lead times. We further extend the analysis to batch ordering policies, non-Poisson demand processes, and multiple demand classes.

Key Words: inventories; multiple supply sources; stochastic lead times; queuing networks; product-form solutions
History: Received: June 1, 2007;

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