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The nature of optimal policies for deterministic finite-horizon inventory models
- Source :
- International Journal of Systems Science: Operations & Logistics; January 2022, Vol. 9 Issue: 1 p39-60, 22p
- Publication Year :
- 2022
-
Abstract
- This paper concerns a general formulation for a longstanding problem. This is the problem of determining a replenishment schedule that minimises the total cost of stocking and holding an inventory in a deterministic finite-horizon inventory model. The formulation permits the treatment of seemingly unrelated models in a single framework. These include classical lot-size models, batching models, repair models, recovery models and others. Admissible control policies are restricted to a partition of some closed interval on the real line. The solution of a mixed integer nonlinear programming problem (MINLP) delivers the optimal partition. It is shown that the MINLP possesses an optimal solution under very mild conditions. The theory of submodular functions on a lattice is the key to handling the integer variable. This theory permits the recovery and generalisations of earlier results on the interleaving property of optimal partitions and a convexity property of the value of the objective function. Past intractable inventory models with demand driven by a general differential equation and in the absence and in the presence of shortages and inflation are solved. This generalises a number of existing results in the literature.
Details
- Language :
- English
- ISSN :
- 23302674 and 23302682
- Volume :
- 9
- Issue :
- 1
- Database :
- Supplemental Index
- Journal :
- International Journal of Systems Science: Operations & Logistics
- Publication Type :
- Periodical
- Accession number :
- ejs59091243
- Full Text :
- https://doi.org/10.1080/23302674.2020.1803435