## 1 Introduction  
Scheduling is an important tool for manufacturers and production engineers since it deals with the allocation of human and machine resources to satisfy consumer demand. The objective is to monitor and optimize workloads, as well as to reduce production time and costs while adhering to all production constraints. In traditional scheduling problems and models, job processing times are assumed to be a constant value. However, this hypothesis is not suitable for many realistic situations in which the job processing time may change owing to job deterioration and/or learning effect phenomena. Indeed, when the employees execute the same task repeatedly, they learn how to perform more efficiently. On the other hand, machines wear out after long periods of processing. Therefore, recent trends in scheduling theory have focused on modeling real-world production scheduling problems where human learning, as well as machine deteriorating effects, are taken into account when studying scheduling problems [1, 2]. The learning effect [3] is a natural human-oriented phenomenon appearing among operators after repeating similar tasks frequently. They gain experience and the execution time decreases accordingly. Ref. [4] proposed the first modeling of this phenomenon with a learning curve and since then, multiple models have been proposed in the literature. [PERSON]. [3, 5] were among the pioneers that investigated the learning effect in scheduling problems, and this was continued in the literature in hundreds of studies with different machine configurations [6; 7]. On the other hand, the deteriorating effect [8; 9] is a machine-oriented phenomenon appearing after processing tasks are conducted on machines for a long time. The machine performances wear out and therefore additional delays are required to execute the production schedule. [PERSON]. [8; 10] seem to be the first to have investigated this effect in production scheduling. The interested reader can find extensive surveys of different scheduling models and problems involving deteriorating jobs in [11; 12]. More recently, [PERSON]. [13] presented an updated survey of the results on scheduling problems with deteriorating jobs and time-dependent processing times. As for learning and/or deterioration effects, [PERSON]. [7] reviews the mathematical models for scheduling problems. It is worth noting that most proposed learning or deteriorating effects functions are either position-dependent, time-dependent, or sum-of-processing-times-dependent [6; 13; 14]. To counter the deteriorating effect, increase machines' availability, and reduce the overall production costs, maintenance activities should be planned along the production process [15]. However, unavailability periods for machines appear since the maintenance activities may take up a potential production time that could otherwise be allocated to completing production tasks. Therefore, to compensate for this deficiency, maintenance tasks should be scheduled in an effective way to improve machine availability and minimize disruption to the production process [16]. [PERSON]. [17] established that appropriate maintenance planning can preserve machine performance and save 20-30% of total operating costs. Recently, maintenance strategies have moved towards a smart aspect. In fact, modern sensor, diagnosis, and prognostic and health management (PHM) technologies allow the ideal planning of interventions and reduce inopportune spending. Simply put, signals gathered from embedded sensors (or inspection information) are analyzed in order to continuously (or periodically) monitor the health state of the production system. Following that, the current state is inferred and the future progression till failure is predicted in order to estimate the time left before the occurrence of failure, known as the remaining useful life (RUL) [18]. Then, the PHM outputs (i.e, RUL) are exploited in the decision making that concerns maintenance planning.