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A closed-form approximation for serial inventory systems and its application to system design

Publication ,  Journal Article
Shang, KH; Song, JS
Published in: Manufacturing and Service Operations Management
October 9, 2006

We analyze a serial base-stock inventory model with Poisson demand and a fill-rate constraint. Our objective is to gain insights into the linkage between the stages to facilitate optimal system design and decentralized system control. To this end, we develop a closed-form approximation for the optimal base-stock levels. The development consists of two key steps: (1) convert the service-constrained model into a backorder cost model by imputing an appropriate backorder cost rate, and then adapt the single-stage approximation developed for the latter, and (2) use a logistic distribution to approximate the lead-time demand distribution in the single-stage approximation obtained in (1) to yield closed-form expressions. We then use the closed-form expressions to conduct sensitivity analyses and establish qualitative properties on system design issues, such as optimal total system stock, stock positioning, and internal fill rates. The closed-form approximation and most of the qualitative properties apply equally to the model with a backorder cost, although some differences do exist. Other results of this study include a bottom-up recursive procedure to evaluate any given echelon base-stock policy and lower bounds on the optimal echelon base-stock levels. © 2006 INFORMS.

Duke Scholars

Published In

Manufacturing and Service Operations Management

DOI

EISSN

1526-5498

ISSN

1523-4614

Publication Date

October 9, 2006

Volume

8

Issue

4

Start / End Page

394 / 406

Related Subject Headings

  • Operations Research
  • 4901 Applied mathematics
  • 3509 Transportation, logistics and supply chains
  • 1505 Marketing
  • 1503 Business and Management
  • 0102 Applied Mathematics
 

Citation

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Shang, K. H., & Song, J. S. (2006). A closed-form approximation for serial inventory systems and its application to system design. Manufacturing and Service Operations Management, 8(4), 394–406. https://doi.org/10.1287/msom.1060.0114
Shang, K. H., and J. S. Song. “A closed-form approximation for serial inventory systems and its application to system design.” Manufacturing and Service Operations Management 8, no. 4 (October 9, 2006): 394–406. https://doi.org/10.1287/msom.1060.0114.
Shang KH, Song JS. A closed-form approximation for serial inventory systems and its application to system design. Manufacturing and Service Operations Management. 2006 Oct 9;8(4):394–406.
Shang, K. H., and J. S. Song. “A closed-form approximation for serial inventory systems and its application to system design.” Manufacturing and Service Operations Management, vol. 8, no. 4, Oct. 2006, pp. 394–406. Scopus, doi:10.1287/msom.1060.0114.
Shang KH, Song JS. A closed-form approximation for serial inventory systems and its application to system design. Manufacturing and Service Operations Management. 2006 Oct 9;8(4):394–406.

Published In

Manufacturing and Service Operations Management

DOI

EISSN

1526-5498

ISSN

1523-4614

Publication Date

October 9, 2006

Volume

8

Issue

4

Start / End Page

394 / 406

Related Subject Headings

  • Operations Research
  • 4901 Applied mathematics
  • 3509 Transportation, logistics and supply chains
  • 1505 Marketing
  • 1503 Business and Management
  • 0102 Applied Mathematics