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<p>We consider a perishable inventory system (PIS) in which demands for items arrive according to a Poisson process and items according to a renewal process. Stored items have a deterministic maximum lifetime ‘on the shelf.’ Exploiting a relation between the so-called virtual outdating time (VOT) process of this PIS and the workload process of the <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(M/G/1+D\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>M</mi> <mo stretchy="false">/</mo> <mi>G</mi> <mo stretchy="false">/</mo> <mn>1</mn> <mo>+</mo> <mi>D</mi> </mrow> </math></EquationSource> </InlineEquation> queue, we prove a decomposition property of each of these two processes. Subsequently we analyze two generalizations of the above PIS, where the quality of items on the shelf is not constant. In the first one, there are two types of items, with different maximum lifetimes. In the second, the quality of an item gradually deteriorates with age.</p>

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\(M/G/1+D\) perishable inventory systems

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  • 出版模式：

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  • 发表日期：

    2026年5月24日

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  • Onno Boxma,
  • Offer Kella,
  • David Perry,
  • Wolfgang Stadje

摘要

We consider a perishable inventory system (PIS) in which demands for items arrive according to a Poisson process and items according to a renewal process. Stored items have a deterministic maximum lifetime ‘on the shelf.’ Exploiting a relation between the so-called virtual outdating time (VOT) process of this PIS and the workload process of the \(M/G/1+D\) M / G / 1 + D queue, we prove a decomposition property of each of these two processes. Subsequently we analyze two generalizations of the above PIS, where the quality of items on the shelf is not constant. In the first one, there are two types of items, with different maximum lifetimes. In the second, the quality of an item gradually deteriorates with age.