The throughput rate of multistation unreliable production lines

C. Heavey, H. T. Papadopoulos, J. Browne

Research output: Contribution to journalArticle

63 Citations (Scopus)

Abstract

This paper is concerned with unreliable multistation series production lines. The first station is never starved and the last station is never blocked. The processing times at each station i is Erlang type Pi distributed with Pi, the number of phases, allowed to vary for each station. Buffers of nonidentical capacities are allowed between successive stations. A station maybe reliable or unreliable. Time to failure is exponentially distributed and repair times are Erlang type Ri distributed with Ri allowed to vary, at each station. In this paper a methodology for generating the associated set of linear equations is presented. These set of linear equations are solved via the use of the Successive Over-Relaxation (SOR) method with a dynamically adjusted relaxation factor as used by Seelen [25]. Referring to the throughput rate of the production lines, many numerical cases are solved and documented. These exact results are of use for comparison purposes against approximate results which exist in the literature. Although many new results are obtained, the size of the system which can be solved is inherently limited by the technique being used. This is due to the curse of dimensionality.

Original languageEnglish
Pages (from-to)69-89
Number of pages21
JournalEuropean Journal of Operational Research
Volume68
Issue number1
DOIs
Publication statusPublished - Jul 9 1993
Externally publishedYes

Fingerprint

Production Line
Linear equations
Throughput
Pi
Linear equation
Vary
Repair
Curse of Dimensionality
Relaxation Method
Exact Results
Buffer
Processing
Series
Methodology
methodology
time
Production line

Keywords

  • Finite buffers
  • Iterative SOR method
  • Production
  • Quasi-birth-death process
  • Queues
  • Reliability

ASJC Scopus subject areas

  • Information Systems and Management
  • Management Science and Operations Research
  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Modelling and Simulation
  • Transportation

Cite this

The throughput rate of multistation unreliable production lines. / Heavey, C.; Papadopoulos, H. T.; Browne, J.

In: European Journal of Operational Research, Vol. 68, No. 1, 09.07.1993, p. 69-89.

Research output: Contribution to journalArticle

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