## 4 Case Study and Results
### Event Log and Process Discovery  
Once the activities are identified, activity profiles are created for each of the dump trucks where it shows the activities with corresponding timestamps as shown in Figure 8. This was done to create an event log from the activity profile. This activity profile is then converted into an event log with timestamps and the name of activities. During the event log generation, idle activities were further divided into several categories based on their relevance in the operation. For example, if the truck is idle before loading, it is assumed that there is a queue in the loading zone and the truck is waiting for the excavator to be loaded. Similarly, if the truck is idle before the dumping, the truck is assumed to be waiting in a queue to get into the dump zone. Moreover, two excavators were operating on the site, so based on the GPS data, it was also categorized if the truck was waiting for one excavator or another (e.g., \(WtExc1\) means waiting for excavator 1). There was a total of 32 cases, 149 events, and 9 event classes. A case is defined  
Figure 8: Activity profile of three trucks. Figure 7: Count of identified activities. as a complete operational cycle, which typically follows as the truck is loaded, then hauled to the dumpsite, dumped the soil, and returned to the loading zone, as well as all the wait time in between those activities. The 9 event classes were _WtExc1_ (i.e., waiting for excavator 1), _WtExc2_ (i.e., waiting for excavator 2), _LdExc1_ (i.e., loading under excavator 1), _LdExc2_ (i.e., loading under excavator 2), _Haul_, _Wt2 Dmp_ (i.e., waiting to enter the dump zone), _Dump_, _Wt2 Ret_ (i.e., waiting to return from the dump zone), and _Return_. Table 1 summarizes the event log in terms of cases and events. Once the event log is created, the underlying operational process is discovered using the process discovery algorithm. Several process discovery algorithms such as alpha++, alpha#, heuristic miner, and inductive miner were implemented to discover the process model of the operation. As the earthmoving process is relatively simple and there are no short-loops, self-loops, and frequency-related issues, the output from all the mining algorithms presented a very similar process model. These mining algorithms and variations were primarily derived from the alpha algorithm. The alpha algorithm is based on abstracting certain relationships between activities, such as direct succession, causality, parallel, and choice. A footprint was drawn from the event logs using these relationships which is shown in Table 2.  
Table 2 shows that all the activities are related to each other by one of those relations. For example, _WtExc1_ is directly followed by _LdExc1_, denoted by the arrow (\(\rightarrow\)) sign. _WtExc1_ activity also happens in parallel with _WtExc2_ activity which is denoted by the \(\mid\mid\) sign. Except for these two, there is no other activity that follows or is followed by the _WtExc1_ activity, denoted by the # sign. This footprint is used to draw the Petri net shown in Figure 9 which demonstrates the process model of the earthmoving operation. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Class** & **Absolute Occurrence** & **Relative Occurrence** \\ \hline _Haul_ & 32 & 21.5\% \\ _Return_ & 32 & 21.5\% \\ _Dump_ & 32 & 21.5\% \\ _LdExc1_ & 16 & 10.7\% \\ _LdExc2_ & 16 & 10.7\% \\ _WtExc1_ & 8 & 5.4\% \\ _WtExc2_ & 7 & 4.7\% \\ _Wt2 Dmp_ & 4 & 2.7\% \\ _Wt2 Ret_ & 2 & 1.3\% \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Summary of the event classes with their absolute and relative occurrence.