# Time and Cost Schedule Dynamic-Hidden Trojan Horses
## 6 Case Study-Extension
### Logistics Function of Resource Distribution  
The volatility shown in Figure 5 is higher for the logistic nonlinear resource distribution than for the resource distribution by the linear function. The time series of H indices is created from the data of the simulated production speed courses in Figure 8. The linear variants show persistent behavior and have a long-term memory. The presence of chaotic behavior in some simulations cannot be eliminated. In the representation of Figure 8, there are noticeable, especially more pronounced, slumps from the deterministic state than in the case of the linear resources distribution.  
The linear variant shows almost half the difference (0.056) between the minimal and maximal value of the H coefficient compared to the logistic variant (0.092). The graphic representation is presented in Figure 9. The non-linear function of resource distribution--the Hurst logistic--shows higher differences between the minimal and maximal values of H  
Figure 8: Value under- and above-average Hurst coefficient (logistic variant). (Source: authors).  
Figure 7: Value under- and above-average of Hurst coefficient (linear variant). (Source: authors).  
coefficients than the linear course of H-coefficients. Through interpretation, it was found that logistic functions are more suitable for practical applications of resource distribution.  
Relatively small differences are given by masking the positive and negative deviations in the calculation of the arithmetic mean. The sum of the distances measured from the maximal limit of the Hurst coefficient means a more expressive description of the difference between the logistic and linear distribution of resources in production process activities. The higher the value is, the greater the total distance from the maximum H-coefficient, i.e., the extreme of deflection in the model of the implementation process (Table 3).  
The use of a linear distribution of resources in the activities of individual production processes has a closer connection to the limit of deterministic behavior--value 1. It is closer to deterministic behavior. The distance for the logistic distribution function increases to 4.0644 in an illustrative example, according to Tab. 3. In individual stages, it significantly becomes more distant from the deterministic limit of 1.00. A separate issue is the detection of long-term memory of time series data and the indication of chaotic states in their factual structure, for example, the links between activities, durations, proposed production rates, and more. This creates a prerequisite for creating suitable software.  
The entire simulation process, including the evaluation, can be seen in Figure 10. The upper part examines the original reference project up to the phase of obtaining the evaluation characteristics. If the project proposal is accepted but does not carry out the feasibility conditions, it is stopped as unsuitable for implementation (Stopping of the project). Otherwise, a cycle of the project proposal correction with simulation (Proposal revision) is started, which ends with a comparison with the reference state (Comparison with reference project). When it shows improvement, it can be assumed that there may not be hidden chaotic conditions in the project and a recommendation for its implementation is expected. The opposite case returns the project proposal in the cycle to the state of correction (Proposal revision) and its further evaluation.  
\begin{table}
\begin{tabular}{l l} \hline \hline \multicolumn{1}{c}{**Sum of Distances from Max. Hurst**} \\ \hline Distances Logistic & 4.0644 \\ Distances Linear & 0.9041 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Sum of distances from max. Hurst coefficient. (Source: authors).  
Figure 9: Min and max values of Hurst coefficient (logistic and linear variant). (Source: authors).