# Taxonomy of Scheduling Problems with Learning and Deterioration Effects
## 1 Introduction  
Scheduling is defined as the assignment of a set of jobs to a set of resources (machines, workers) over time in order to minimize one or more objective functions [1]. In classical scheduling problems, the job processing time is considered constant and known in advance, while in stochastic scheduling models, the processing time is modeled as a probability function also known in advance. However, these assumptions are a simplification of real contexts in which the inclusion of workers' behavior impacts job processing times and system performance. [PERSON] [1] acknowledged that human characteristics thus have an impact, particularly in cases where manual operations are involved. In manual operations, the time to complete tasks may increase when resources deteriorate due to fatigue or may decrease when resources improve workers' productivity. Hence, in general terms, human characteristics can be grouped into two categories, depending on the effect on the execution of the job: learning or deterioration effects [2]. The scheduling problems with learning a deteriorating effect is part of the family of scheduling problems with time-changing effects. Since the 1990s, authors have expressed their interest in such problems where the job processing times are affected by their locations in the sequence. While it is true that the first idea that arises from learning processes relates to the tasks carried out only by humans, it is also relevant in mixed environments (interaction between machines and humans) because human expertise in activities such as maintenance and monitoring are determined in system performance. In the same way, machines and devices managed by artificial intelligence can take advantage of the learning process [2]. Similarly, when we talk about deterioration processes, we usually think of them as affecting mainly machines, but this can happen in the case of humans such as fatigue oraging. Consequently, it is relevant to take into account these adaptations to the traditional scheduling problem. Finally, they have come closer to real production systems. In scheduling theory, the inclusion of human factors dates back to the work of [PERSON] et al. [3], who presented one of the first contributions on this subject, adding behavior and workload when operators are confronted with multiple tasks. [PERSON] et al. [4] subsequently concluded that some human characteristics and behaviors may affect human performance at work and thereby impact the job processing time. The phenomenon of learning effects in industrial environments had already been introduced by [PERSON] [5], but [PERSON] [6] was the first author to introduce the learning effect in a single-machine scheduling problem, while [PERSON] and [PERSON] [7] were pioneers in the study of deterioration effects on a single machine scheduling problem. In recent years, the number of publications addressing scheduling problems with learning or deterioration effects has increased. Some of the published literature reviews focus mainly on the learning effect. For instance, [PERSON] [8] reviewed the progress of the learning effect on scheduling problems and formally distinguished between position-based and time-based learning. [PERSON] and [PERSON] [9] presented the state-of-the-art related to learning and forgetting curves, describing each model and showing their opportunities and limitations for applications in industrial settings. [PERSON] et al. [10] presented a framework for scheduling and the integration of human factors (physical and/or cognitive human characteristics and behaviors). While they emphasized the importance of interdisciplinary cooperation, [PERSON] et al. [11] reviewed several learning models and proposed categories to classify the most common approaches. Recently, [PERSON] and [PERSON] [12] presented a review of fatigue forecasting and measurement methods, as well as the integration of fatigue forecasting into work-rest scheduling, shift scheduling and personnel scheduling.