Existence and properties of optimal production and inventory policies

Daning SUN

Research output: Journal PublicationsJournal Article (refereed)Researchpeer-review

6 Citations (Scopus)

Abstract

It is an important and fundamental question whether an optimal inventory policy exists for a general deterministic multi-item, multistage (GDMM) production and inventory model. We show that an inventory model with a nonsubadditive ordering cost function could have no optimal policy over a finite horizon. However, when the ordering cost is a subadditive function an optimal policy exists for a GDMM production and inventory model over both a finite horizon and an infinite horizon. Properties of optimal inventory policies are crucial to investigating an inventory problem. We present four properties of optimal policies: (1) nonpositive inventory ordering, (2) last-minute ordering, (3) extended last-minute ordering, and (4) nonnegative filling properties. They have been explicitly or implicitly used in analyzing many different inventory models. The last two properties have been used but not proved before.
Original languageEnglish
Pages (from-to)923-934
Number of pages12
JournalMathematics of Operations Research
Volume29
Issue number4
DOIs
Publication statusPublished - 1 Nov 2004

Fingerprint

Inventory Model
Optimal Policy
Finite Horizon
Subadditive Function
Infinite Horizon
Cost functions
Cost Function
Non-negative
Policy
Inventory policy
Inventory model
Costs
Optimal policy
Finite horizon

Keywords

  • Existence theory
  • Optimal policy
  • Production and inventory policy
  • Property of optimal policy

Cite this

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title = "Existence and properties of optimal production and inventory policies",
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Existence and properties of optimal production and inventory policies. / SUN, Daning.

In: Mathematics of Operations Research, Vol. 29, No. 4, 01.11.2004, p. 923-934.

Research output: Journal PublicationsJournal Article (refereed)Researchpeer-review

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AU - SUN, Daning

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N2 - It is an important and fundamental question whether an optimal inventory policy exists for a general deterministic multi-item, multistage (GDMM) production and inventory model. We show that an inventory model with a nonsubadditive ordering cost function could have no optimal policy over a finite horizon. However, when the ordering cost is a subadditive function an optimal policy exists for a GDMM production and inventory model over both a finite horizon and an infinite horizon. Properties of optimal inventory policies are crucial to investigating an inventory problem. We present four properties of optimal policies: (1) nonpositive inventory ordering, (2) last-minute ordering, (3) extended last-minute ordering, and (4) nonnegative filling properties. They have been explicitly or implicitly used in analyzing many different inventory models. The last two properties have been used but not proved before.

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