Job sizing and sequencing in additive manufacturing to control process deterioration

The term Additive Manufacturing (AM) describes a set of novel manufacturing technologies in which successive layers of matter are formed to create an object, e.g., three-dimensional (3D) printing. These technologies have several major advantages that have led to their rapidly increasing involvement in mass production. However, due to their unique properties they are subject to deterioration, which is expressed in the aging of different components followed by random maintenance requirements. Additionally, they are all preemptive-repeat; namely, if a failure occurs during the printing of an object, then its printing will have to recommence from the start as the work is resumed. This article addresses the problem of sequencing an AM process while referring to its relevant properties. It also addresses a more complicated environment in which the work may arrive over time. We adopt a stochastic preemptive-repeat scheduling model, generalize it to incorporate the process age, and develop the formalization of two main measures of a given schedule: the expected completion time, i.e., the time duration required to complete the printing of all jobs, and the total expected flow time, i.e., the expected time a job spends in the system. Our formalization enables the determination of a schedule that minimizes these measures. In particular, we formulate and solve a constrained continuous optimization problem to determine the optimal size of the designed jobs to be printed. This challenge, which relates to the unique flexibility of these technologies, currently hinders the practice of dental 3D printing manufacturing lines.