# Taxonomy of Scheduling Problems with Learning and Deterioration Effects
## 4 Discussion  
This literature review provides an overview of studies related to scheduling problems with learning and deteriorating effects. The discussion is offered in two phases. The first one answers the questions put forward in Section 2.1, which enable us to understand the progress in this field. The second one, identifying opportunities and challenges. Giving the answer to \(RQI\), the findings suggest that research related to the scheduling problem with learning and deteriorating effects has generated much interest in recent years. It was noted that the number of articles has increased significantly since 1999. The majority of short-listed articles focused on managing the problem by studying the complexity and developing algorithms that can be comparable in their performance with others already proposed. This implied continuing to maintain classic objective functions, which are sometimes far from being the criteria of interest for stakeholders today. Thus, interaction with business partners would allow us to bring the problems closer to reality, thus ensuring sustainability, taking into account economic, social, and environmental dimensions. In terms of _RQ2_, various types of configurations have been studied, with the most studied one being the single machine system. However, more recently, authors have been exploring more complex configurations such as the flowshop and the hybrid flowshop [144; 145]. They involve multiple types of resources (machines, workers, etc. ), which must be managed as well as possible [146], in addition to the fact that they correspond to the most common and realistic configurations in the industry [42; 147]  
Regarding _RQ3_, in most cases, the approach considered a single objective, with only 28.8% combining two or more criteria in the objective function. The most recurrent categories of criteria are those involving TRO--work in progress and TRO--utilization of resources, as per the taxonomy of [PERSON] [42], [PERSON] [43], and [PERSON] [44]. This shows the authors' preference to orient towards economic objectives. In this category, the makespan is the most well-studied criterion. In the sustainable category, social orientation criteria are not often included, but they have begun to emerge on a large scale (e.g., noise levels). In the matter of _RQ4_, findings show that the learning effect has been modeled primarily by the equation in terms of the number of jobs previously processed or the sum of the processing times. These basic models have been improved by adding truncation parameters, for example. Another important finding is the treatment of the deterioration effect in the literature. This term is typically used for job deterioration (111 articles) but has also been used by some authors for deteriorating resources. In the latter case, the effect may result from the number of jobs previously processed or the cumulative effect of the deterioration. Recently, the combination of learning and deterioration has become increasingly common in the literature. Concerning _RQ5_, this present study has shown that the solution method employed to solve the problem is highly dependent on the type of configuration under study. The development of algorithms for the optimal solution in polynomial time is regularly applied in single machine systems. For other configurations such as job shops, flowshops, hybrid flowshops and flexible job shops, methods such as heuristic and metaheuristics become relevant. There is a trend towards proposing novel methods for optimization [98] or using hybrid metaheuristics, in response to the computational complexity that these problems involve, by taking advantage of the characteristics of different metaheuristics operating simultaneously [148]. In recent years, tools such as simulation and multi-agents have garnered increasing interest, particularly when parameter uncertainty is included. Extensive use has also been made of the competitive agent approaches, where two or more criteria need to be optimized.