Title

Existence and properties of optimal production and inventory policies

Document Type

Journal article

Source Publication

Mathematics of Operations Research

Publication Date

11-1-2004

Volume

29

Issue

4

First Page

923

Last Page

934

Keywords

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

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.

DOI

10.1287/moor.1040.0097

Print ISSN

0364765X

Publisher Statement

Copyright © 2004 INFORMS. Access to external full text or publisher's version may require subscription.

Full-text Version

Publisher’s Version

Language

English

Recommended Citation

Sun, D. (2004). Existence and properties of optimal production and inventory policies. Mathematics of Operations Research, 29(4), 923-934. doi: 10.1287/moor.1040.0097

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