Optimal lot sizing with maintenance actions and imperfect production processes

Abstract

Porteus (1986) explored an economic order quantity model with imperfect production processes that the approximate lot size is derived. Basically, he dealt with the lot size problem is rather meaningful. However, for mathematical simplicity, he adopted a truncated Taylor series expansion to present the approximate expected total cost function that results in overvalue of expected total cost. In this paper, we extend Porteus (1986) to present the optimal lot size model for defective items with a constant probability when the system is out-of-control and taking the maintenance cost into account. We show that there exists a unique optimal lot size such that the expected total cost is minimised. In addition, the bounds of optimal lot size are provided to develop the solution procedure. Finally, numerical examples are given to illustrate the theoretical results and compare optimal solutions obtained by using our approach and Porteus's approach. Numerical results show that our approach is better.

Keywords:

• lot sizing
• EOQ
• imperfect production processes
• maintenance

Additional information

Funding

This study was partially supported by the National Science Research Council of the ROC [grant number NSC 98-2410-H-240-004-MY3].

Notes on contributors

Kuo-Lung Hou

Kuo-Lung Hou is a Professor in the Department of Industrial Engineering and Management, Overseas Chinese University. Dr Hou received his PhD in Industrial Management from the National Taiwan University of Science and Technology. His articles have appeared in Applied Mathematical Modelling, European Journal of Operational Research, Computer & Operations Research, International Journal of Information and Management Sciences, ICIC Express Letters, Journal of Information & Optimization Sciences, Journal of Statistics & Management Systems, OPSEARCH, Journal of the Operational Research Society, Mathematical and Computer Modelling and International Journal of Systems Science. His current research interests include operations research, production planning and inventory control.

Li-Chiao Lin

Li-Chiao Lin is an Associate Professor of the Department of Business Administration in National Chin-Yi University of Technology. She received her MSc in Industrial Management from the National Taiwan University of Science and Technology. Her articles have appeared in International Journal of Information and Management Sciences, Journal of Information & Optimization Sciences, Journal of Statistics & Management Systems, OPSEARCH, Journal of the Operational Research Society and International Journal of Systems Science. Her current research interests include the fields of production–inventory control and investment management.

Tien-Yu Lin

Tien-Yu Lin is an Assistant Professor in the Department of Marketing and Supply Chain Management at Overseas Chinese University, Taiwan. He received his PhD degrees in Department of Business Administration from the National Chung Cheng University. His articles have appeared in Computers & Industrial Engineering, Applied Mathematical Modelling, Asia-Pacific Journal of Operational Research, Journal of Marine Science and Technology, Journal of the Operations Research Society of Japan, Journal of the Chinese Institute of Industrial Engineers and Journal of Information and Optimization Sciences. His research activities include supply chain management, inventory control, decision analysis and consumer behaviour.