Analysis of a production-inventory system with unreliable production facility

M. J.M. Posner, M. Berg

Research output: Contribution to journalArticlepeer-review


The general purpose of this research is to incorporate the element of machine imperfection into production-inventory models. Most existing production-inventory models simply ignore the reliability factor, thereby tacitly assuming perfectly reliable systems. Machine failures, however, do occur and could be very disruptive-particularly in a highly automated production environment. In the model studied in this work, we consider a relatively simplified production situation: one machine, constant production rate, and a compound Poisson demand process for the product; but we superimpose the reliability feature comprising the machine failure process and the ensuing repair actions. For this situation we derive an explicit closed form solution for the steady-state distribution of the inventory level, and this result is then used to compute system performance indices of interest related to service level to customers and machine utilization. Some numerical results demonstrate the effect of the reliability parameters on these performance indices.

Original languageEnglish
Pages (from-to)339-345
Number of pages7
JournalOperations Research Letters
Issue number6
StatePublished - Dec 1989
Externally publishedYes

Bibliographical note

Funding Information:
The authors appreciateth e financial support provided by ResearchC ouncilof Canadau nderg rantsA 4374and GP4084.


  • inventory
  • level crossings
  • production
  • reliability

ASJC Scopus subject areas

  • Software
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Applied Mathematics


Dive into the research topics of 'Analysis of a production-inventory system with unreliable production facility'. Together they form a unique fingerprint.

Cite this