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A Discrete-Time Model for Common Lifetime Inventory Systems

Faculty of Business Administration, University of Macau, Macao SAR, China
Department of Industrial Engineering and Engineering Management, Hong Kong University of Science and Technology, Hong Kong SAR, China
Department of Systems and Industrial Engineering, University of Arizona, Tucson, Arizona 85721-0020
lianzt{at}umac.mo
liulim{at}ust.hk
marcel{at}mindspring.com

We consider a discrete-time (s, S) inventory model in which the stored items have a random common lifetime with a discrete phase-type distribution. Demands arrive in batches following a discrete phase-type renewal process. With zero lead time and allowing backlogs, we construct a multidimensional Markov chain to model the inventory-level process. We obtain a closed-form expected cost function. Numerical results demonstrate some properties of optimal ordering policies and cost functions. When compared with the results for the constant lifetime model, the variance of the lifetime significantly affects the system behavior. Thus, the formalism that we create here adds a new dimension to the research in perishable inventory control under uncertainty in lifetime.

Key Words: perishable inventory; random common lifetime; discrete-time model; optimization
History: Received: October 1, 2002; revision received: October 15, 2003;