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The Effect of Lead Time and Demand Uncertainties in (r, q) Inventory Systems

The Fuqua School of Business, Duke University, Durham, North Carolina 27708, and Antai College of Economics and Management, Shanghai Jiao Tong University, Shanghai 200052, China
Institute of Applied Mathematics, Academia Sinica, Beijing 100080, China, and Business School, National University of Singapore, Singapore
Yanshan University, Qinhuangdao 066004, Hebei Province, China
Dalian University of Technology, Dalian 116024, China
jssong{at}duke.edu
hanqin{at}amt.ac.cn
hym_1220{at}163.com
mzhwang{at}dlut.edu.cn

We study a single-item (r, q) inventory system, where r is the reorder point and q is the order quantity. The demand is a compound-Poisson process. We investigate the behavior of the optimal policy parameters and the long-run average cost of the system in response to stochastically shorter or less-variable lead times. We show that although some of the properties of the base-stock system can be extended to this more general model, some cannot. The same findings also apply when the comparison is conducted on the lead-time demand distributions.

Subject classifications: inventory system; reorder-point/order quantity; stochastic lead time; variability; optimal policy; stochastic comparison.
History: Received January 2007; revision received December 2008; accepted January 2009.