Fabrication runtime decision for a hybrid system incorporating probabilistic breakdowns, scrap, and overtime

Yuan Shyi Peter Chiu, Yunsen Wang, Tsu Ming Yeh, Singa Wang Chiu

Research output: Contribution to journalArticlepeer-review

3 Scopus citations


Manufacturers today need to optimize their fabrication runtime decision by meeting short customer order due dates externally and managing the potentially unreliable machines and manufacturing processes internally. Outsourcing and overtime are commonly utilized strategies to expedite fabricating time. Additionally, detailed analyses and necessary actions on inevitable product defects (i.e., removal of scraps) and equipment breakdowns (such as machine repairing) are prerequisites to fabrication runtime planning. Motivated by assisting today’s manufacturers decide the best batch runtime plan under the situations mentioned above, this study applies mathematical modeling to a hybrid fabrication problem that incorporates partial overtime and outsourcing, inevitable product defects, and a Poisson-distributed breakdown. We develop a model to accurately represent the problem’s characteristics. Formulations and detailed model analyses allow us to find the cost function first. Differential equations and algorithms help us confirm the gain function’s convexity and find the best runtime decision. Lastly, we use numerical illustrations to show our study’s applicability by revealing in-depth crucial managerial information of the studied problem.

Original languageEnglish
Pages (from-to)293-308
Number of pages16
JournalInternational Journal of Industrial Engineering Computations
Issue number3
StatePublished - 1 Jun 2022


  • Fabricating runtime
  • Outsourcing
  • Overtime
  • Probabilistic breakdowns
  • Scrap


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