## 3 Materials and Methods
The procedure presented in Figure 6 was developed by the authors, combining established AHP methodology with novel applications specific to network coordination in omni-channel distribution systems and the role of logistics operators. While grounded in the standards of the AHP method and drawing upon research by other scholars, the procedure's uniqueness lies in its tailored application to these specific areas. This innovative approach builds on the traditional AHP framework, which decomposes complex \begin{table}
\begin{tabular}{c c c} \hline \hline
**Forms of Network** & & **Coordination Mechanisms** \\
**Coordination** & & \\ \hline \multirow{3}{*}{market} & \(\bullet\) & Price. \\  & \(\bullet\) & Formal relationships. \\  & \(\bullet\) & Bilateral security. \\ \hline \multirow{3}{*}{hierarchical} & \(\bullet\) & Control structures and systems resulting from management style. \\  & \(\bullet\) & Organisational integration. \\  & \(\bullet\) & Bureaucratic allocation of resources. \\ \hline \multirow{3}{*}{social} & \(\bullet\) & Trust. \\  & \(\bullet\) & Social standards. \\  & \(\bullet\) & Significant exchange of information. \\ \hline \multirow{3}{*}{logistical} & \(\bullet\) & Network participants’ resources management from the logistics \\  & \(\bullet\) & operator level. \\  & \(\bullet\) & Forecasting network flows. \\ \cline{1-1}  & \(\bullet\) & Organisation of transport and extraordinary transport. \\ \cline{1-1}  & \(\bullet\) & Logistical information management from the logistics \\ \cline{1-1}  & \(\bullet\) & Operator level. \\ \cline{1-1}  & \(\bullet\) & Demand management. \\ \cline{1-1}  & \(\bullet\) & Management of human resources and infrastructure in the network. \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The network coordination mechanisms considered in the AHP method. problems into hierarchical components for pairwise comparison using expert judgments. By adapting these principles to focus on omni-channel strategies and logistics operators, we extended the AHP method's applicability, addressing the unique challenges and dynamics of these domains. In summary, the novelty of our procedure is its specific adaptation of the well-established AHP methodology to the context of network coordination, omni-channel distribution, and logistics operators, providing new insights and enhancing the method's relevance to these fields. The selection of experts was determined by the narrow research area requiring knowledge of both omni-channel and the role of logistics operators in building customer satisfaction and enhancing distribution network reliability. Twenty-four experts were invited to participate in the study. The expert self-assessment sheet included both knowledge and experience criteria. It was assumed that an expert is a person who works within the structures of a logistics operator in an independent decision-making position that is related to the implementation of warehouse or transport processes in a multi-channel and has professional experience in this area of more than 5 years. We determined the expert's degree of familiarity with the problem in question on the basis of the expert's self-assessment on a 10-point scale. The expert's task was to objectively indicate their own familiarity with the problem, scoring themself from 0 to 10, where 0 meant that the expert had no familiarity with the problem and 10 meant that familiarity with the problem belonged to the expert's narrow specialisation. On the basis of the competence index (according to the assumption made, it had to exceed 0.5), we qualified 8 experts for further research. The experts' panel included only senior managers working in 3 PL companies. The chosen experts are as follows:  
* Expert 1: Senior Logistics Manager, 12 years of experience, specializing in warehouse and transport management including e-commerce operation. * Expert 2: Operations Director, 15 years of experience, responsible for 3 PL strategies, also omni-channel implementation.