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.
Bibliographical noteThe author would like to thank Professor M. Queyranne, the anonymous referees, and the area editor for their valuable suggestions. This research was partially supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, Hong Kong, SAR China (Project No. LU 3108/03H). It was partially
supported by an internal grant from Lingnan University, Vancouver, Canada (DR03A8).
- Existence theory
- Optimal policy
- Production and inventory policy
- Property of optimal policy