# Analysis of Factors Influencing the Prices of Tourist Offers
## 4 Model of the Price Change Process
### Process Model  
Process models can be discovered based on the entire Event Log or filtered by attributes. It allows for analyzing the data at different levels of detail or dividing it into groups in relation to one of the constant factors. Filtering can be conducted on the level of whole traces or individual events. There are many process mining tools that could be used to analyze the Event Logs. There were mainly four methods used:  
1. Directly-Follows Graph (DFG)--a simple representation of the process models. Each node represents an activity with the frequency of occurrences and the arcs describe the relationship between various activities. The weight of the edges is the number of transitions from one activity to the next. The MAX_NO_EDGES_IN_DIAGRAM parameter allows for adjusting the detail of the graph. 2. Heuristics Miner--use a representation similar to DFG with frequencies of events and sequences, called a heuristics net. The basic idea is that infrequent paths are omitted from the model. Whether an arc will be added to the model is determined by the dependency value greater than the value of the DEPENDENCY_THRESH parameter. 3. Transition Matrix (SM)--from the heuristics net object, the activities_occurrences and dfg_matrix can be read. Based on these data, Transition Matrices were calculated. In the matrix cells, there are values corresponding to the problem: what percentage are the situations in which the change of one factor immediately precedes the change of the other factor. The formula is: \[TM_{A,B}=\frac{n(A\to B)}{n(A)}\cdot 100\%\] (2) where: \[A\], \[B\] --activities denoting the change of the factor, e.g., OPEC up \[n(A)\] --number of occurrences of an activity \[A\] \[n(A\to B)\] --number of direct transitions from an activity \[A\]  to \[B\] 4. Cortado Variant Explorer [32] is one of the views generated by the Cortado tool. It clearly presents variants of the occurrence of activities with their actual sequence preserved. This tool also allows for generating process models based on sequences of activities, but in the problem under consideration, these models did not give the expected results. Using the above-mentioned methods, tourist data were analyzed in many different variants, and thus many models were generated that cannot be discussed in detail in this paper. One changing factor was chosen to demonstrate the process mining example: the barrel of oil price (OPEC). Other Event Log settings are presented in Table 7. The Event Log was created for one tour operator. Figure 13: The simplified UML diagram of the Event Log. The fuel price change factor is recorded when the absolute value of the difference of the last two prices is greater than 0.5$. The activity \"OPEC up\" means a fuel price increase and similarly \"OPEC down\" means a fuel price decrease. The same naming rule has been applied to the trip prices. For trips, every price change is recorded, without any thresholds. Figure 14 presents two DFGs with different levels of detail. Figure 14 shows the number of occurrences of a given change and the transitions between them. It is quite general, with no dates or individual sequences. It can noticed that the vast majority of trip prices have increased in the last 30 days before departure and considering the relation from OPEC to PRICE, the most numerous transitions are from \"OPEC up\" to \"PRICE up\". This model is used to compute the Transition Matrix shown in \[A\]0 Figure 14 shows a fragment of DFG with dates. It can be observed that the decline in OPEC prices took place on 17 June and 18 June, while on 19 June, 707 trip prices dropped. On the other hand, on 22 June and on 23 June, the fuel prices increased, while on 30 June, the prices of 1215 trips increased. Table 8 shows that after the increase in OPEC prices, about 15% of trip prices increased, and this is the greatest relationship. However, also after the decline in OPEC prices, around 9% of the trip prices rose.