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

Published

Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Shang, KH; Song, JS

Published Date

  • October 9, 2006

Published In

Volume / Issue

  • 8 / 4

Start / End Page

  • 394 - 406

Electronic International Standard Serial Number (EISSN)

  • 1526-5498

International Standard Serial Number (ISSN)

  • 1523-4614

Digital Object Identifier (DOI)

  • 10.1287/msom.1060.0114

Citation Source

  • Scopus