The paper deals with an economic manufacturing quantity (EMQ) model for the selling price and the time dependent demand pattern in an imperfect production process. Due to long-run, machine breakdown may occur, as a result, the system may shift to out-of-control state from in-control state and production systems begin to produce imperfect quality items. The production of imperfect items increases with time. All imperfect quality items are reworked at a fixed cost to restore these to its original quality. To reduce the production of the imperfect quality items, we consider reliability as a decision variable along with the development cost and the production cost as a function of reliability. The profit function is maximized by Euler-Lagrange formula. The numerical example, sensitively analysis, and graphical illustrations are given to illustrate the model.
Bibliographical noteFunding Information:
The authors are grateful to three anonymous referees for their useful comments on earlier versions of the paper. This work was financially supported by University Grants Commission (Minor Research Project, File No. 41-1433/2012(SR)). The first author expresses his heartfelt gratitude to his parents, wife, and Arnesh Sarkar. This research comes to reality with their help and inspiration. The 1st author dedicates this research to Prof. Kripasindhu Chaudhuri, Department of Mathematics, Jadavpur University, Kolkata, West Bengal, India and Dr. Shib Sankar Sana, Department of Mathematics, Bhangar Mahavidyalaya, West Bengal, India. The second author dedicates her research to her son Upayan Adak.
All Science Journal Classification (ASJC) codes
- Computational Mathematics
- Applied Mathematics