**4. Numerical example**

This part of the chapter demonstrates a short numerical example of the application of the above-mentioned methodology from an assignment problems point of view. In our analyzed distribution system there are four suppliers, two distribution centers, and four customers, as **Figure 10** shows.

The input data of the scenario are shown in the Appendix, as follows:



In the case of a conventional supply chain solution the optimized material handling (transportation) cost is 54,837 EUR, which can be divided into two main parts: the cost among suppliers and distribution centers is 15,537 EUR and the cost among distribution centers and customers is 39,300 EUR. In the case of a cyber-physical system, where all three levels of the supply chain are integrated through the Internet of Things technologies, the material-handling (transportation cost) is 51,929 EUR, which can be divided into two main parts: the cost among suppliers and distribution centers is 21,557 EUR and the cost among distribution centers and customers is 30,372 EUR. It means, that in the case of this simple scenario the total material handling cost can be decreased by 5.30%.

The optimal assignment of supplier and distribution centers with related material flow intensity is shown in **Table 1**, while the optimal assignment of distribution centers and customers is shown in **Table 2**.


#### **Table 1.**

*The optimal assignment of suppliers and distribution centers with related material flow intensity [TEU/time window].*


#### **Table 2.**

*The optimal assignment of distribution centers and customers with related material flow intensity in [TEU/time window].*

The simplified numerical example shows, that the optimal solution of the integrated system does not lead to decreased costs at all levels of the supply chain, which means that the cyber-physical system focuses on the optimization of the whole system, while in the case of conventional supply chain solutions, the part systems of the supply chain are separately optimized.

## **5. Discussion and conclusions**

The globalization of market processes requires the development of supply chains to meet the increasingly dynamic needs of individual customers with the efficiency of mass production. This means not only increasing the efficiency and flexibility of production processes but also improving related processes such as purchasing and distribution. In addition to increasing efficiency, there is a growing emphasis on the development of "green" systems and "green" solutions to reduce the environmental impact of processes related to meeting market needs.

In this chapter, a systematic literature review is carried out to identify the main lines of research, emphasizing the importance of product development, competitive distribution networks, risk evaluation, application of Industry 4.0 technologies, emission measuring and emission management, and optimization.

Based on the results of this systematic literature review, it is concluded, that using Industry 4.0 technologies, it is possible to transform conventional distribution systems into cyber-physical networks, where smart sensors, edge computing solutions, digital twinning, and discrete event simulation make it possible to coordinate the hyperconnected distribution network based on real-time data and perform a more sophisticated decision-making process. Within the frame of this chapter, a potential approach is described including both the functional model of a cyber-physical distribution network and the mathematical model to optimize the operation from environmental impact point of view.

The described method makes it possible to support managerial decisions, because depending on the results of the optimization different purchasing portfolios can be generated. The described methodology can be used to analyze the potentials of the potential transformation of conventional supply-chain solutions into a cyber-physical supply-chain.

The resources of manufacturing companies and third-party logistics providers are not taken into consideration and the parameters of the distribution network are given as deterministic parameters. These limitations show the directions for further research. In further studies, the model can be extended to a more complex model including resource optimization for manufacturing and logistics services. Second, this study only considered time, capacity, and energy consumption as deterministic parameters. Fuzzy models can be also suitable for the description of a stochastic environment, where capacities and time windows can be taken into consideration as uncertain parameters. This should be also considered in future research.

## **Conflict of interest**

The authors declare no conflict of interest.
