A compound Poisson EOQ model for perishable items with intermittent high and low demand periods

O. Boxma, D. Perry (Corresponding author), W. Stadje, S. Zacks

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
1 Downloads (Pure)

Abstract

We consider a stochastic EOQ-type model, with demand operating in a two-state random environment. This environment alternates between exponentially distributed periods of high demand and generally distributed periods of low demand. The inventory level starts at some level q, and decreases according to different compound Poisson processes during the periods of high demand and of low demand. Refilling of the inventory level to level q is required when level 0 is hit or when an expiration date is reached, whichever comes first. If such an event occurs during a high demand period, an order is instantaneously placed; otherwise, ordering is postponed until the beginning of the next high demand period. We determine various performance measures of interest, like the distribution of the inventory level at time t and of the inventory demand up to time t, the distribution of the time until refilling is required, the expected time between two refillings, the expected amount of discarded material and the expected total amount of material held in between two refillings, and the expected values of various kinds of shortages. For a given cost/revenue structure, we can thus determine the long-run average profit.

Original languageEnglish
Number of pages21
JournalAnnals of Operations Research
DOIs
Publication statusE-pub ahead of print - 2020

Fingerprint

Compound Poisson
EOQ model
Perishable items
Revenue
Profit
Expected value
Performance measures
Compound Poisson process
Shortage
Costs

Keywords

  • Compound Poisson process
  • EOQ model
  • Outdatings
  • Perishable inventory
  • Regenerative process
  • Unsatisfied demands

Cite this

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abstract = "We consider a stochastic EOQ-type model, with demand operating in a two-state random environment. This environment alternates between exponentially distributed periods of high demand and generally distributed periods of low demand. The inventory level starts at some level q, and decreases according to different compound Poisson processes during the periods of high demand and of low demand. Refilling of the inventory level to level q is required when level 0 is hit or when an expiration date is reached, whichever comes first. If such an event occurs during a high demand period, an order is instantaneously placed; otherwise, ordering is postponed until the beginning of the next high demand period. We determine various performance measures of interest, like the distribution of the inventory level at time t and of the inventory demand up to time t, the distribution of the time until refilling is required, the expected time between two refillings, the expected amount of discarded material and the expected total amount of material held in between two refillings, and the expected values of various kinds of shortages. For a given cost/revenue structure, we can thus determine the long-run average profit.",
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A compound Poisson EOQ model for perishable items with intermittent high and low demand periods. / Boxma, O.; Perry, D. (Corresponding author); Stadje, W.; Zacks, S.

In: Annals of Operations Research, 2020.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Boxma, O.

AU - Perry, D.

AU - Stadje, W.

AU - Zacks, S.

PY - 2020

Y1 - 2020

N2 - We consider a stochastic EOQ-type model, with demand operating in a two-state random environment. This environment alternates between exponentially distributed periods of high demand and generally distributed periods of low demand. The inventory level starts at some level q, and decreases according to different compound Poisson processes during the periods of high demand and of low demand. Refilling of the inventory level to level q is required when level 0 is hit or when an expiration date is reached, whichever comes first. If such an event occurs during a high demand period, an order is instantaneously placed; otherwise, ordering is postponed until the beginning of the next high demand period. We determine various performance measures of interest, like the distribution of the inventory level at time t and of the inventory demand up to time t, the distribution of the time until refilling is required, the expected time between two refillings, the expected amount of discarded material and the expected total amount of material held in between two refillings, and the expected values of various kinds of shortages. For a given cost/revenue structure, we can thus determine the long-run average profit.

AB - We consider a stochastic EOQ-type model, with demand operating in a two-state random environment. This environment alternates between exponentially distributed periods of high demand and generally distributed periods of low demand. The inventory level starts at some level q, and decreases according to different compound Poisson processes during the periods of high demand and of low demand. Refilling of the inventory level to level q is required when level 0 is hit or when an expiration date is reached, whichever comes first. If such an event occurs during a high demand period, an order is instantaneously placed; otherwise, ordering is postponed until the beginning of the next high demand period. We determine various performance measures of interest, like the distribution of the inventory level at time t and of the inventory demand up to time t, the distribution of the time until refilling is required, the expected time between two refillings, the expected amount of discarded material and the expected total amount of material held in between two refillings, and the expected values of various kinds of shortages. For a given cost/revenue structure, we can thus determine the long-run average profit.

KW - Compound Poisson process

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KW - Perishable inventory

KW - Regenerative process

KW - Unsatisfied demands

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