Solving a hybrid batch production problem with unreliable equipment and quality reassurance

Singa Wang Chiu, Hua Yao Wu, Tsu Ming Yeh, Yunsen Wang

Research output: Contribution to journalArticlepeer-review

4 Scopus citations


A hybrid batch fabrication plan involving an outsourcing option is often established to deal with the in-house capacity constraint and/or meet timely demand with a reduced cycle time. Besides, the occurrences of unpredictable equipment malfunction and imperfect product quality should also be effectively managed during in-house fabrication to meet the production schedule and the required quality level. To address these concerns, we examine a hybrid economic production quantity (EPQ) problem with an unreliable machine and quality reassurance; wherein, an outside provider helps supply a portion of the batch at a requested timing and desirable quality, but at the price of a higher than in-house unit cost. Corrective action is performed immediately when a Poisson-distributed breakdown occurs. Once the equipment repairing task completes, the interrupted lot’s fabrication resumes. Random nonconforming products are identified, and the re-workable items among them are separated from the scraps. A rework task follows the regular process in each cycle at an extra cost. A portion of reworked items fails and are scrapped. A model portraying the problem’s characteristics is built, and an optimization methodology is utilized to find the optimal runtime solution to the problem. A numerical example reveals our result’s applicability, and specific managerial implications are suggested.

Original languageEnglish
Pages (from-to)235-248
Number of pages14
JournalInternational Journal of Industrial Engineering Computations
Issue number3
StatePublished - 2021


  • Hybrid economic production quantity
  • Outsourcing
  • Poisson-distributed breakdown
  • Production planning
  • Random scrap
  • Rework


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