Mathematical modeling for a multiproduct manufacturing system featuring postponement, external suppliers, overtime, and scrap

Yuan Shyi P. Chiu, Jian Hua Lian, Victoria Chiu, Yunsen Wang, Hsiao Chun Wu

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Manufacturing firms operating in today’s competitive global markets must continuously find the appropriate manufacturing scheme and strategies to effectively meet customer needs for various types of quality of merchandise under the constraints of short order lead-time and limited in-house capacity. Inspired by the offering of a decision-making model to aid smooth manufacturers’ operations, this study builds an analytical model to expose the influence of the outsourcing of common parts, postponement policies, overtime options, and random scrapped items on the optimal replenishment decision and various crucial system performance indices of the multiproduct problem. A two-stage fabrication scheme is presented to handle the products’ commonality and the uptime-reduced strategies to satisfy the short amount of time before the due dates of customers’ orders. A screening process helps identify and remove faulty items to ensure the finished lot’s anticipated quality. Mathematical derivation assists us in finding the manufacturing relevant total cost function. The differential calculus helps optimize the cost function and determine the optimal stock-replenishing rotation cycle policy. Lastly, a simulated numerical illustration helps validate our research result’s applicability and demonstrate the model’s capability to disclose the crucial managerial insights and facilitate manufacturing-relevant decision making.

Original languageEnglish
Pages (from-to)1-12
Number of pages12
JournalInternational Journal of Industrial Engineering Computations
Issue number1
StatePublished - 2022


  • Batch production
  • External supplier
  • Mathematical modelling
  • Multiproduct fabrication
  • Overtime
  • Postponement
  • Rotation cycle
  • Scrap


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