
94% of researchers rate our articles as excellent or good
Learn more about the work of our research integrity team to safeguard the quality of each article we publish.
Find out more
ORIGINAL RESEARCH article
Front. Manuf. Technol.
Sec. Sustainable Life Cycle Engineering and Manufacturing
Volume 5 - 2025 | doi: 10.3389/fmtec.2025.1439429
The final, formatted version of the article will be published soon.
You have multiple emails registered with Frontiers:
Please enter your email address:
If you already have an account, please login
You don't have a Frontiers account ? You can register here
The exact closed-form formulas for all performance measures (i.e., throughput, maximum utilization, work in process, blocking probability for the second station, probability of the third station being idle, etc.) of short serial production lines with two, three, and four stages without buffers are presented for the first time in literature. Markov chains model these production lines. An Algorithm is used to construct their state transition diagram, from which the steady-state probabilities are extracted in the symbolic form of two polynomial ratios, using a recently introduced method that assigns probabilities on the graph anti-arborescences. Then, the underlying Markov chain can obtain every performance measure via its known definition from the literature by simple algebraic operations. The proposed Algorithm's results shed light on the well-known bowl phenomenon of production lines, and understanding the exact formula structure is used to create a simple model for throughput estimation of fully balanced short serial production lines through genetic programming. The enormous size of the exact formulas highlights the problem of the need for more computational support for production lines larger than four stages without buffers.
Keywords: Short serial production lines1, Performance measures2, Closed form formulas3, throughput5, Bowl phenomenon6, Spanning trees7, Genetic programming8
Received: 27 May 2024; Accepted: 24 Mar 2025.
Copyright: © 2025 Boulas, Dounias and Papadopoulos. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence:
Chrissoleon T Papadopoulos, Aristotle University of Thessaloniki, Thessaloniki, Greece
Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.
Research integrity at Frontiers
Learn more about the work of our research integrity team to safeguard the quality of each article we publish.