Some single-machine scheduling problems with aging effect

This paper considers single machine scheduling with an aging effect. This phenomenon appears in many realistic production processes. Thus, it is important to consider the phenomenon in scheduling problems. We show that the problems to minimize the sum of completion times and the quadratic cost function of completion times can be solved in polynomial time under the proposed model. We further show that the problem to minimize the the weighted sum of completion times has polynomial-time solution under some agreeable conditions.