Economic Production Quantity Model with Scrapped Items and Limited Production Capacity


1 Department of Industrial Engineering,Sharif University of Technology

2 Department of Industrial Engineering,Iran University of Science and Technology

3 Department of Industrial Engineering,Qazvin Islamic Azad University


In this paper, an Economic Production Quantity (EPQ) model is studied, in which the
production defective-rate follows either a uniform or a normal probability distribution. Shortages are
allowed and take a backorder state, and the existence of only one machine causes a limited production
capacity for the common cycle length of all products. The aim of this research is to determine the
optimal production quantity of each product, such that the expected total cost including holding, shortage,
production, setup and defective items cost is minimized. The mathematical model of the problem is derived,
for which the objective function is proved to be convex. Then, a derivative approach is utilized to obtain
the optimal solution. At the end, two numerical examples are provided to illustrate the practical usage of
the proposed method.