# A New Approach to the Allocation of Multidimensional Resources in Production Processes
## 1 Introduction  
The modern economy is characterized by high competitiveness of producers and distributors, global supply chains, fast capital flow, high degree of automation and robotization, etc. On the other hand, an individual approach to the customer and his/her needs is required. All this means that producers and distributors from high-wage countries are under constant pressure to adjust production to the changing and individual customer requirements while minimizing costs, especially labor costs.  
The first problem they have to solve is the dichotomy between the scale and scope of production resulting from the diverse needs of customers. Due to the constant increase in labor costs, investments in new technologies and the need to shorten production cycles, it is difficult to be competitive in terms of price and assortment at the same time. This is due to the fact that the economy of scale is based on the production of a large number of products with little diversity, while the economy of scope focuses on providing customized products. Another emerging problem is a clear contradiction between planning and value orientation in production [1]. An answer to the above problems can be the emergence of self-optimization and self-organization production systems. Such systems offer the potential of enhancing flexibility, productivity and reliability of production. The above-mentioned solutions, together with modern technologies such as cyber-physical systems,RFID, IoT, cloud computing, machine learning, etc., constitute the basis of Industry 4.0 [2; 3]. The use of the aforementioned modern technologies in the concept of Industry 4.0 [4] makes it possible to deal with situations of dichotomy related to the quantity and variety of the production assortment. Moreover, it enables adjustment of the configuration and production capacity to the changing external conditions (changing demand, absenteeism, changing distribution conditions, changing legal conditions, etc.).  
One of the elements that can be the basis for self-optimization and self-organization production systems [5] is the appropriate approach to the allocation and configuration of modern production resources [6]. This is due to the fact that modern production resources have many functions, can be configured, remotely controlled, etc.  
This paper presents the problem of a proactive and reactive approach to the allocation and control of multidimensional resources in production processes.  
The structure of the article is as follows. Section 2 contains a literature review on resource allocation problems in production systems. Section 3 presents a description of the problem of multi-dimensional resource allocation under consideration. Section 4 is devoted to the presentation of the proprietary model of multi-dimensional resource allocation, which can be the basis for building a decision support system in the field of modern production systems. Section 5 presents the implementation of the model with the use of two environments, i.e., mathematical programming and constraint logic programming, the so-called hybrid approach [7; 8] data structure and an innovative procedure for reducing the size of the modeled problem. Section 6 contains a series of computational experiments that were carried out using multiple data instances differing in the number of workstations, resources, orders, tasks, etc. The last Section is a summary and conclusions.