Analysis of lead time correlation under a base-stock policy

Tim Hellemans*, Robert Boute, Benny Van Houdt

*Corresponding author for this work

Research output: Contribution to journalArticle

Abstract

We analyze the impact of lead time correlation on the inventory distribution, assuming a periodic review base-stock policy. We present an efficient method to compute the shortfall distribution for any Markovian lead time process, and we provide structural results when lead times are characterized by a 2-state Markov-modulated process. The latter reveals how lead time correlation increases the inventory variance and enables a closed form for the asymptotic behavior of the shortfall's variance in case the two possible lead time values are sufficiently different. We also establish upper and lower bounds on the inventory variance, which hold for any general time-homogeneous lead time process. Our results are complemented by a numerical experiment that indicates how commonly used approximations of the shortfall distribution mis-specify base-stock levels in the presence of lead time correlation. Not only does the inventory distribution increase in variance as the lead time correlation increases, it also becomes multi-modal.

Original languageEnglish (US)
Pages (from-to)519-535
Number of pages17
JournalEuropean Journal of Operational Research
Volume276
Issue number2
DOIs
StatePublished - Jul 16 2019

    Fingerprint

Keywords

  • Base-stock policy
  • Inventory
  • Order crossovers
  • Stochastic correlated lead-times

ASJC Scopus subject areas

  • Computer Science(all)
  • Modeling and Simulation
  • Management Science and Operations Research
  • Information Systems and Management

Cite this