An optimal common production cycle time for imperfect production processes with scrap

This paper considers the effects of imperfect production processes and the decision on whether and when to implement a screening process for defective items generated during a production run on the Economic Lot Scheduling Problem (ELSP). It is assumed that a process is in control at the beginning of a production run. After a period of production, the process may shift to an out-of-control state at a random time, and consequently produces a fixed percentage of defective items. These defective items cannot be repaired or reworked, and thus must be scrapped with an additional cost. The objective is to determine an optimal common production cycle time that minimizes the expected average cost per unit of time. The bisection method is employed to obtain a near-optimal solution. A closed-form solution is also derived after using an approximation to an exponential function involved in the objective function. Numerical examples are provided to illustrate the derivation of the optimal common production cycle time.