# Material Flow Optimization as a Tool for Improving Logistics Processes in the Company
## 3 Methodology
The checkerboard table provides extensive insights into interactions between entities. While simple tables usually cover only two parameters--material flow per time unit--it is possible to extend them with additional data, such as transport frequency, loading times, and packaging sizes. This allows for a more precise analysis of material flows. The key advantage of this method lies in its ability to provide a detailed and measurable description of relationships within a company's logistics infrastructure. Its flexibility makes it highly adaptable to various needs, ensuring universal applicability. By implementing the checkerboard table, analysts gain a simple yet effective tool for collecting data, which can later be utilized for more complex evaluations. Ultimately, the goal of this method is to standardize the description of relationships between workstations, thereby improving material flow analysis and optimization [51]. The checkerboard table was applied as a visual and analytical tool to evaluate material flow in comparison with the selected optimization variants. This approach provided a clear representation of material movements under existing conditions and after the application of optimization, considering the following factors:  
* The number of material handling operations before final processing;
* The frequency of transportation and the average distance between logistics points;
* The time required for individual operations throughout the entire process;
* The impact on overall production flow and the elimination of inefficient movements. The checkerboard table methodology involves dividing the material flow into discrete elements, which are then evaluated based on predefined efficiency parameters. The analysis results enabled the identification of critical points in the logistics chain and the modeling of their optimal solutions within the new internal transport system. The cost model formulas were developed based on actual recorded operational costs within the company, considering the key components. The costs of external transport, \(C_{ext}\), are calculated according to Formula (1), as follows:  
\[C_{ext}=P_{transp}\times N_{transp}+C_{handl}\left[\epsilon\right] \tag{1}\]  
where  
\(P_{transp}\)--average cost per unit of material transport [EUR/unit];  
\(N_{transp}\)--number of transport operations in each period [operations/time];  
\(C_{handl}\)--handling costs associated with external transport [EUR]. The cost of internal transport, \(C_{int}\), is calculated according to Formula (2):  
\[C_{int}=P_{fuel}\times S+P_{maint}+P_{staff}\left[\epsilon\right] \tag{2}\]  
where  
\(P_{fuel}\)--average fuel costs per unit of distance [EUR/km];  
\(S\)--total distance traveled by internal transport vehicles [km];  
\(P_{maint}\)--maintenance and repair costs of the internal transport system [EUR];  
\(P_{staff}\)--personnel costs for operating internal transport vehicles [EUR]. **Step 2: Calculation of Material Flow Costs**  
The costs associated with material flow between workstations are calculated using Formula (3). This formula enables the precise calculation of the financial impact of material movements within the company's logistics network. By applying this approach, businesses can identify costly inefficiencies and optimize the allocation of resources in material handling and transport. \[C_{flow}=\sum_{i=1}^{n}\sum_{j=1}^{m}\left(d_{ij}*f_{ij}*c_{transfer}\right) \tag{3}\]  
where  
_Cflow_--total material flow costs;  
_dij_--distance between workstations i and j (meters);  
_fij_--frequency of transfers between workstations i and j;  
_ctransfer_--unit transfer cost (EUR/m). **Step 3: Identification of Deficiencies**  
Workstations with the highest cost values in the checkerboard table are identified as critical nodes within the material flow.