Optimal Batch Production for a Single Machine System with Accumulated Defectives and Random Rate of Rework

In this paper we consider an imperfect production system which produces good and defective items and assume that defective items can be reworked. Due to the nature of rework process we do not restrict the rework rate to be equal to normal production rate or constant and assume that it is a random variable with an arbitrary distribution function. We also assume as it is true in most real world situation that the unit rework processing cost need not to be equal to unit normal processing cost. We consider the case in which during a specified period of time consisting of several cycles the rework process takes place only in its last cycle. For practical reasons such as the ease of production scheduling and resource planning we require that the length of the last cycle must have the same length as the other cycles of this period. For this purpose we assume in the last cycle of this period first the normal production starts after which the rework of all defective units produced in the period begins. After the end of the last cycle of the period the whole process will start all over again. Further we assume that, for reduction of set up cost for rework per unit time, the total number of setups for rework must be as small as possible. For this system we derive the expected total cost function consisting of inventory holding, waiting time of defectives for rework, setup, and processing costs per unit time. Then we obtain the economic batch quantity which minimizes this expected cost.