Maximising profits for an EPQ model with unreliable machine and rework of random defective items

Abstract

This article deals with an economic production quantity (EPQ) model in an imperfect production system. The production system may undergo in ‘out-of-control’ state from ‘in-control’ state, after a certain time that follows a probability density function. The density function varies with reliability of the machinery system that may be controlled by new technologies, investing more costs. The defective items produced in ‘out-of-control’ state are reworked at a cost just after the regular production time. Occurrence of the ‘out-of-control’ state during or after regular production-run time is analysed and also graphically illustrated separately. Finally, an expected profit function regarding the inventory cost, unit production cost and selling price is maximised analytically. Sensitivity analysis of the model with respect to key parameters of the system is carried out. Two numerical examples are considered to test the model and one of them is illustrated graphically.

Keywords:

• imperfect production process
• reliability
• defective items
• inventory
• in-control state
• out-of-control state
• rework

Acknowledgements

The authors would like to thank to the editors and referees for their constructive suggestions and corrections to improve the clarity of the article. The first author expresses his gratitude to the Council of Scientific & Industrial Research, New Delhi, for funding to carry out the research.