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Asymptotic Optimality of Base-Stock Policies for Perishable Inventory Systems
- Source :
- Management Science. 69:846-864
- Publication Year :
- 2023
- Publisher :
- Institute for Operations Research and the Management Sciences (INFORMS), 2023.
-
Abstract
- We consider periodic review perishable inventory systems with a fixed product lifetime. Unsatisfied demand can be either lost or backlogged. The objective is to minimize the long-run average holding, penalty, and outdating cost. The optimal policy for these systems is notoriously complex and computationally intractable because of the curse of dimensionality. Hence, various heuristic replenishment policies are proposed in the literature, including the base-stock policy, which raises the total inventory level to a constant in each review period. Whereas various studies show near-optimal numerical performances of base-stock policies in the classic system with zero replenishment lead time and a first-in-first-out issuance policy, the results on their theoretical performances are very limited. In this paper, we first focus on this classic system and show that a simple base-stock policy is asymptotically optimal when any one of the product lifetime, demand population size, unit penalty cost, and unit outdating cost becomes large; moreover, its optimality gap converges to zero exponentially fast in the first two parameters. We then study two important extensions. For a system under a last-in-first-out or even an arbitrary issuance policy, we prove that a simple base-stock policy is asymptotically optimal with large product lifetime, large unit penalty costs, and large unit outdating costs, and for a backlogging system with positive lead times, we prove that our results continue to hold with large product lifetime, large demand population sizes, and large unit outdating costs. Finally, we provide a numerical study to demonstrate the performances of base-stock policies in these systems. This paper was accepted by Victor Martinez de Albéniz, operations management. Funding: J. Bu was partially supported by a Hong Kong Polytechnic University Start-up Fund for New Recruits [Grant P0039585]. X. Gong was partially supported by a Chinese University of Hong Kong (CUHK) Direct Grant [Grant 4057147] and the Hong Kong Research Grants Council (RGC) General Research Fund [Grant CUHK14500120]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/mnsc.2022.4400 .
- Subjects :
- History
Asymptotic analysis
Mathematical optimization
Polymers and Plastics
Heuristic (computer science)
Computer science
Strategy and Management
Management Science and Operations Research
Industrial and Manufacturing Engineering
Rate of convergence
Business and International Management
Constant (mathematics)
Lead time
Average cost
Stock (geology)
Curse of dimensionality
Subjects
Details
- ISSN :
- 15265501 and 00251909
- Volume :
- 69
- Database :
- OpenAIRE
- Journal :
- Management Science
- Accession number :
- edsair.doi.dedup.....bb430f878af8a5c90cf9c8f0437fc139