## 2 Brief Literature Review and Research Gaps
### Metaheuristic Solution Approach  
As a result of their efficiency and ability to be used in real-world production environments, metaheuristics as approximation methods have made breakthroughs in solving various complex optimization problems in the industry and become the main methods used to solve large-scale scheduling problems [47]. Nonetheless, it is worth noting that few studies in the literature have proposed metaheuristics to solve scheduling problems with learning and/or deteriorating effects [1; 2].  
The existing literature can be placed into three main streams according to the considered effect, namely the learning effect, the deteriorating effect, and finally, the combined effects. [PERSON] [48] proposed a tabu search algorithm to solve the single-machine scheduling problem with a time-dependent learning effect. [PERSON]. [49] developed four meta-heuristics, namely the genetic algorithm (GA), simulated annealing, ABC, and iterated greedy algorithms to solve a two-stage, three-machine assembly scheduling problem with a position-dependent learning effect. On the other hand, [PERSON]. [41] proposed an ABC algorithm to solve the flexible flowshop scheduling problem with a step deteriorating effect, while [50] proposed three metaheuristics including dynamic differential evolution, the simulated annealing algorithm, and the cloud-theory-based simulated annealing algorithm, to solve the two-stage assembly scheduling problem under a time-dependent deteriorating effect. In practical settings, combined effects (learning and deteriorating) are also considered. In this regard, we can quote the work of [51], which developed a GA to solve parallel machine scheduling problems under the effects of position-dependent learning and time-dependent deteriorating effects.  
Joint planning of production and maintenance activities, taking into account learning and/or deteriorating effects has also been studied in the literature. However, works in this area are even more scarce. From the learning perspective, [PERSON]. [52] solved the joint flowshop scheduling problem with a hybrid metaheuristic algorithm based on the simulated annealing algorithm and firefly algorithm. For the deteriorating effect, [PERSON]. [53] developed a GA to deal with the joint single-machine scheduling problem taking into account the deteriorating effect. Finally, considering the case of combined effects, [PERSON]. [54] proposed an ABC algorithm to solve the joint flowshop scheduling problem under the time-dependent deteriorating effect and position-dependent learning effect. [PERSON]. [55] studied the joint parallel batching scheduling problem under a combined position-dependent learning effect and time-dependent deteriorating effect. A hybrid algorithm combining GA and differential evolution (DE) was proposed for resolution.  
Based on the findings of the literature, it has been observed that scheduling problems frequently feature position-dependent learning effects and/or time-dependent deteriorating effects [2]. Furthermore, variable maintenance durations due to learning or deteriorating effects is also an important research stream in the scheduling literature. While variable maintenance durations due to the deterioration effect have most often been considered [56; 57; 58], variable maintenance durations due to the learning effect have scarcely been studied [54; 59].