A memetic algorithm for minimizing the total weighted completion time on a single machine under step-deterioration

In this paper, we consider minimizing total weighted completion time criteria on a single machine. Jobs processing times are step function of its starting time and all jobs have a common due date. First, we present some new lemmas and dominance properties for this NP-hard problem, and then a memetic algorithm using these properties is developed. We compare the solutions of the memetic algorithm with optimal solutions obtained from complete enumeration. The results show that the average percentage error of the proposed algorithm from optimal solutions is about 2% and as the variance of processing time increase, the percentage errors decrease.