**5. Numerical Results**

*5.1. Overview of Computation Times*

Table 5 shows the average computation times (¯*t*), the median value (*t median*), the minimum computation time (*t min*) and the maximum computation time (*t max*) for each instance graph. Each row of the table gives the aggregate results over 81 different instances stemming from the systematic combination of the parameter entries in Table 4.

As expected, the computing time increases for larger instance classes, up to the maximum of 48 h allowed for the Gurobi solution process. Thus, the size of the network has a significant influence on the computation time. However, even within an instance class, the computing times vary remarkably. Structure C has significantly higher computing times in all instance classes, although the graph size is similar to the other structures. In addition, even within a instance graph, the computing times fluctuate enormously, as indicated by the wide range between minimum and maximum values.

Further, we observe that the median value is significantly smaller than the average for the small and medium instance classes. This is because, within an instance graph, many instances can be solved to proven optimality within seconds, minutes or a few hours, and some instances could not be solved in the given time limit (48 h). The outliers lead to high median values for these instance classes.

However, for large instances, the mean value is always smaller than the median value. This is because most instances could not be solved to optimality within the time limit and consequently have a reported computation time of 48 h.


**Table 5.** Computation Times.
