Economic lot sizing in a production system with random demand

Abstract

An extended economic production quantity model that copes with random demand is developed in this paper. A unique feature of the proposed study is the consideration of transient shortage during the production stage, which has not been explicitly analysed in existing literature. The considered costs include set-up cost for the batch production, inventory carrying cost during the production and depletion stages in one replenishment cycle, and shortage cost when demand cannot be satisfied from the shop floor immediately. Based on renewal reward process, a per-unit-time expected cost model is developed and analysed. Under some mild condition, it can be shown that the approximate cost function is convex. Computational experiments have demonstrated that the average reduction in total cost is significant when the proposed lot sizing policy is compared with those with deterministic demand.

Keywords:

• economic production quantity
• lot sizing policy
• Poisson process
• inventory control

Acknowledgements

The authors thank the three anonymous referees and the associate editor, for their constructive input and comments, which served to improve the manuscript.

Additional information

Funding

This work was supported in part by the National Science Council of Taiwan [grant number NSC95-2416-H006-025-MY2].

Notes on contributors

Shine-Der Lee

Shine-Der Lee received his PhD degree from the School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, GA, USA. He is currently a professor in the Department of Industrial and Information Management, National Cheng Kung University, Tainan, Taiwan. His research interests are in the areas of mathematical modelling of complex production/inventory problems, and design and analysis of logistic/supply chain systems. His publications have appeared in Computers and Operations Research, European Journal of Operational Research, International Journal of Production Research, International Journal of Production Economics, and Transportation Research, among others. He is a frequent reviewer for over 20 SCI/SSCI journals.

Chin-Ming Yang

Chin-Ming Yang is a doctoral candidate in the Graduate School and Department of Industrial and Information Management, National Cheng Kung University, Tainan, Taiwan. His primary research interests are the applications of operation research techniques to model and analyse the production and inventory management problems. He has published papers in Applied Mathematical Modeling and Asia Pacific Journal of Operational Research.

Shu-Chuan Lan

Shu-Chuan Lan received her PhD degree from the Graduate School and Department of Industrial and Information Management, National Cheng Kung University, Tainan, Taiwan. Her research interests have focused on the modelling of production and operation management problems via stochastic process and statistical models. Her publications have appeared in Asia Pacific Journal of Operational Research and International Journal of Production Economics.