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
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
