Optimal batch quantity in a cleaner multi-stage lean production system with random defective rate

Muhammad Tayyab, Biswajit Sarkar

Research output: Contribution to journalArticlepeer-review

86 Citations (Scopus)


Optimal batch size reduces variability in the lean manufacturing process with minimized system costs. It simplifies the scheduling, enhances the quality, reduces inventories, and improves the production process continuously. On account of this, determining optimal batch size is the area of interest for the researchers with the objective of reducing inventories and related system costs. Products of the textile sector are produced generally in a multi-stage production setup, and it consists of random defective rate within the long-run production systems. In this context, this paper revisits an economic production quantity (EPQ) model with an imperfect multi-stage production system and analyzes an inventory model by considering a random defective rate in a cleaner multi-stage lean manufacturing system. These defective items are reworked and converted into perfect quality items by incurring additional processing costs. The proportion of defective items can be reduced through continuous improvements in the production process reliability by performing various lean manufacturing techniques, enlisting the total productive maintenance at the highest rank. A mathematical model is developed using a familiar beta distribution density function for the random defective rate. Then, the total cost of the system is minimized through analytical technique, where the batch size is a decision variable. Outcomes through analytical and numerical study confirm that optimum batch size is obtained by this model and it has a direct relationship with number of production stages.

Original languageEnglish
Pages (from-to)922-934
Number of pages13
JournalJournal of Cleaner Production
Publication statusPublished - 2016 Dec 15

Bibliographical note

Funding Information:
The authors of this research work are thankful to three anonymous reviewers and the Honorable Editor-In-Chief and Honorable Associate Editor for their important and helpful comments and suggestions for the required improvements in the previous manuscript of this paper. This work was supported by the research fund of Hanyang University ( HY-2016-N , Project number 201600000001706) for new Faculty member. The first author is extremely grateful to Mr. Azhar Sadiq (Director Operations, Master Lean Sensie), and Mr. Latif Zaib (GM Operations, Executive Lean Coach), for their continuous help.

Publisher Copyright:
© 2016 Elsevier Ltd

All Science Journal Classification (ASJC) codes

  • Renewable Energy, Sustainability and the Environment
  • Environmental Science(all)
  • Strategy and Management
  • Industrial and Manufacturing Engineering


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