A Discrete-Time Model for Common Lifetime Inventory Systems

Zhaotong Lian · Liming Liu · Marcel F. Neuts

60 citations0/0 files storedMathematics of Operations Research

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Supply Chain and Inventory Management Reliability and Maintenance Optimization Advanced Queuing Theory Analysis

Abstract

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.

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References

1984Matrix-Geometric Solutions to Stochastic Models 1982Perishable Inventory Theory: A Review 1975Optimal Ordering Policies for Perishable Inventory—II 1975Optimal Ordering Policy for a Perishable Commodity with Fixed Lifetime 1984Modeling and Analysis of Computer Communications Networks 1980Optimal Ordering Policies for Continuous Review Perishable Inventory Models 1999(s, S) Continuous Review Models for Products with Fixed Lifetimes 1983Inventory systems of perishable commodities

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