A discrete-time model for common lifetime inventory systems

Zhaotong LIAN*, Liming LIU, Marcel F. NEUTS

*Corresponding author for this work

Research output: Journal PublicationsJournal Article (refereed)

33 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)718-732
Number of pages15
JournalMathematics of Operations Research
Volume30
Issue number3
DOIs
Publication statusPublished - Aug 2005
Externally publishedYes

Fingerprint

Discrete-time Model
Inventory Systems
Lifetime
Cost functions
Cost Function
Inventory control
Phase-type Distribution
Ordering Policy
Markov processes
Inventory Control
Renewal Process
Inventory Model
Discrete Distributions
Optimal Policy
Batch
Markov chain
Closed-form
Discrete-time
Uncertainty
Numerical Results

Bibliographical note

The first author thanks the University of Macau for partial support through Grant RG002/01-02W(S)/LZT/FBA. The second author thanks Research Grant Council of Hong Kong for partial support through Grant N_HKUST023/00.

Keywords

  • Discrete-time model
  • Optimization
  • Perishable inventory
  • Random common lifetime

Cite this

LIAN, Zhaotong ; LIU, Liming ; NEUTS, Marcel F. / A discrete-time model for common lifetime inventory systems. In: Mathematics of Operations Research. 2005 ; Vol. 30, No. 3. pp. 718-732.
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A discrete-time model for common lifetime inventory systems. / LIAN, Zhaotong; LIU, Liming; NEUTS, Marcel F.

In: Mathematics of Operations Research, Vol. 30, No. 3, 08.2005, p. 718-732.

Research output: Journal PublicationsJournal Article (refereed)

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AU - LIU, Liming

AU - NEUTS, Marcel F.

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AB - 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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