## 2 Literature Review  
Current computer technologies and artificial intelligence (AI) approaches have become essential for small- and medium-sized enterprises (SMEs) that wish to thrive in the modern business market in order to accomplish the lowest costs and maximize resource utilization and activity scheduling [8; 9]. Consequently, the method of resource use and schedule optimization will be explored. The first problem recognized is setting up a model that fits service production with a daily varying volume in the metalworking industry. The second is to determine and apply an appropriate methodology for solving the problem. The optimization criteria are represented by an objective function functionally related to a set of control variables. The choice of the objective function is the most crucial step in solving an optimization problem. According to [PERSON] [10] and [PERSON] [11], there is no developed efficient or accurate algorithm for the solution of the NP-complete optimization problem, at least so far, so various authors who have dealt with this problem in recent years have used modern methods or metaheuristic algorithms to solve it. Unlike classical methods, all metaheuristic methods give results that are not accurate but converge to an optimum. Classical methods give results which with certainty represent a local extreme within the given precision. However, classical methods are applicable to solve NP-completeness only for smaller-scale problems. The JSSP has been segmented into different categories according to the number of machines and jobs. The smaller issues can range from nine to twenty jobs and can use anywhere from four to ten machines. Medium-sized issues might range anywhere from 25 to 40 jobs and use anywhere from 15 to 20 machines. When dealing with large-scale issues, the number of jobs can range anywhere from 45 to 60, and the number of machines can range anywhere from 25 to 30 [12]. Over the course of the years, academics have suggested both accurate and heuristic approaches for solving the JSSP. These methods have many aims, such as lowering makespan, completion time variance (CTV), and the number of tardy jobs [13]. Because of the complexity of the computations involved, it is difficult to find ideal solutions for large-scale JSSPs. Instead, it is preferable to obtain near-optimal solutions through the use of heuristic methods [13; 14]. [PERSON] et al. [15] offer a unique proactive-reactive strategy to adapt to dynamic changes in working environments and to tackle the joint scheduling problem for machine tools and transportation resources. To adapt to dynamic events and construct the reschedule plan in a timely manner, the same authors developed a unique particle swarm optimization technique with an integrated ge netic algorithm (GA). A multiagent manufacturing system that takes into account dynamic events such as stochastic job insertions and unpredictable machine failures was presented by [PERSON] et al. [16]. This system was based on deep reinforcement learning and integrated the self-organization mechanism and self-learning strategy with the multiagent manufacturing system testbed. [PERSON] and [PERSON] [17] investigated numerous aspects and suggested a knowledge-based cooperative memetic algorithm for energy-aware distributed flow shop scheduling. Because it has the potential to improve resource utilization and production efficiency while simultaneously lowering production costs, research on the flexible job shop scheduling problem (FJSP) has emerged as a topic of interest over the course of the past decade. To increase the scope of the JSSP, it should take into account the fact that each operation can be carried out on one of the machines that are a part of a subset of the machines in the production workshop [3; 18]. Therefore, the FJSP is more difficult to solve than traditional scheduling problems.