Optimal lot sizing with maintenance actions and imperfect production processes

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.