# Taxonomy of Scheduling Problems with Learning and Deterioration Effects
## 3 Results
### Classification of Papers Related to Problem Characteristics
#### 3.2.2 Objective Function  
Our findings show that most short-listed research papers (71.2%) focus on a single optimization criterion, while 28.8% deal with the optimization of multi-criteria objective functions. We see that 59.5% of total contributions, including two or more objective functions, use the weighted sum of criteria as a solution approach. In recent years, scheduling problems dealing with multi-criteria objective functions have become popular because of the more complex industrial environments [41].  
Related to the classical criteria considered in scheduling problems, the most studied objective functions are the minimization of makespan (279 articles), the minimization of total completion time (170 articles), and the minimization of weighted completion time (87 articles). As the authors consider workers, machines, or both as resources, some objective function criteria such as machine hiring costs, maintenance costs and total energy consumption could be found.  
Since more than 30 objective functions criteria were identified in the short-listed articles, a grouping is proposed, taking as a reference the taxonomies suggested by [42; 43; 44]. The objective functions are classified as time-related objectives (TRO), job-related objectives (JRO), cost-related, and environmental objectives. The first category includes the utilization of resources and work-in-process. The second category covers objectives related to customer satisfaction and work balancing. The third and fourth categories, respectively, group together functions that evaluate costs and sustainability criteria (which include environmental and social criteria). Appendix A shows the objective functions; however, variations concerning the original equations may occur depending on the configuration of the system studied.  
The criteria that belong to the category TRO--work in progress are more frequent, appearing 389 times. Then comes TRO--utilization of resources criteria appear 313 times.  
Figure 5: Distribution of short-listed articles according to the system configuration and year of publication. SM: single machine; PM: parallel machine; FS: flowshop; JS: job shop; HFS: hybrid flowshop; FJS: flexible job shop.  
In third, fourth and fifth place are JRO--customer-related, JRO--balancing-related, and cost-related, with 122, 97 and 87, respectively. Finally, sustainable objectives are rarely considered (8 times). As shown in Figure 6, most studies have been oriented towards traditional scheduling criteria, as these mean an economic benefit to the system.  
In recent years, there has, however, been growing interest in working with sustainable systems, which has led to the integration of sustainability criteria into objective functions. In this last category, we include the criteria aimed at minimizing energy consumption [45; 46; 47; 48], as well as criteria pertaining to socially-oriented objective functions such as minimization of the average rate of workers' deterioration [49] and of the noise levels to which workers are exposed [50].