## 1 Introduction  
Nowadays, competition between production companies is very strong. They must constantly develop new solutions that will allow them to stand out from the competition and attract new customers. The trends observed include offering customers innovative products with the possibility of personalization. Offering a dedicated and innovative product in a competitive market requires a short response time to customer inquiries and the rapid fulfillment of customer orders [1]. The most efficient way to meet these requirements is through effective production scheduling that fully utilizes the potential of the production resources owned by the company. The development of a complex schedule, especially for small series production, taking into account many types and parameters of technological operations at the same time with a relatively short duration of order fulfillment, is often a challenge for planners using analytical methods. Dynamically developed advanced planning and scheduling systems (APSs) are designed to support the production management team by automating the production scheduling process, often using very advanced algorithms. These solutions are to ensure the feasibility of the generated schedule and allow for its optimization, in particular, with regard to minimizing the total time of executing all production orders or minimizing the costs. Currently, we can observe a growing interest in the development of production scheduling systems. The results of thousands of studies in the area of innovative algorithmic solutions are published. These solutions are probably based on all known optimization algorithms. Examples of such algorithms are simulated annealing [2], genetic [3, 4] and mmetic [5] algorithms, TSP methods [6], particle swarm optimization [7], gray wolf optimization [8], or branch-and-bound algorithms [9]. In addition to purely algorithmic solutions, new, more general scheduling methodologies are also being developed. Currently, in the context of determining the planned execution time of production operations, there are many new proposals for methods to include the setup time in the schedule [10; 11]. An interesting methodological solution is the inclusion of the learning effect in the scheduling [12]. The phenomenon is understood as the process of gaining experience by the staff, which leads to a reduction in the time required to perform subsequent tasks. Taking into account the learning effect in production scheduling is expressed by determining the dependence between the duration of a production operation and the number of previous executions of identical operations or their total duration time. The solution works well when planning the production of a large series of products, but it does not take into account the individual characteristics of the employees and the tools used in the operation. A similar issue is the aging effect, which consists of the dependence between the deterioration of the task execution time and the number of its previous executions [13]. Another issue related to the variable duration of production tasks is the job deterioration problem, in which processing times increase according to the waiting time of the job [14]. An interesting area of research is methodologies for auxiliary resources [15; 16; 17; 18]. When multiple units (employees, tools) can be used, the execution time of technological operations can be controlled and reduced by allocating additional resources. Time is functionally related to the number of units allocated. Currently, much of the research in the area of production scheduling is focused on optimizing production plans in terms of the size of the production batch [19; 20; 21; 22; 23; 24; 25; 26], ensuring the minimization of energy consumption [27; 28; 29], optimization of the buffer size to ensure resistance to production disturbances [30; 31], multi-criteria optimization [32], and global approaches of Industry 4.0 [33; 34].