Multiple lot-sizing decisions with an interrupted geometric yield and variable production time

Hsi M. Hsu*, Tai Sheng Su, Muh-Cherng Wu, Liang Chuan Huang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


This study examines a multiple lot-sizing problem for a single-stage production system with an interrupted geometric distribution, which is distinguished in involving variable production lead-time. In a finite number of setups, this study determined the optimal lot-size for each period that minimizes total expected cost. The following cost items are considered in optimum lot-sizing decisions: setup cost, variable production cost, inventory holding cost, and shortage cost. A dynamic programming model is formulated in which the duration between current time and due date is a stage variable, and remaining demand and work-in-process status are state variables. This study then presents an algorithm for solving the dynamic programming problem. Additionally, this study examines how total expected costs of optimal lot-sizing decisions vary when parameters are changed. Numerical results show that the optimum lot-size as a function of demand is not always monotonic.

Original languageEnglish
Pages (from-to)699-706
Number of pages8
JournalComputers and Industrial Engineering
Issue number3
StatePublished - 1 Oct 2009


  • Dynamic programming
  • Interrupted geometric distribution
  • Lot-sizing
  • Production lead-time
  • Production/inventory system

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