## 2 Materials and Methods
### The OEE Model
#### 2.1.1 Factors That Make up OEE and Their Application to LUZ  
Availability  
Drawing an analogy with the manufacturing sector, this factor reflects the time that a machine, in our case, a LUZ, is actively in use compared to the total time it could be producing. Considering a 24-hour day, only a fraction is reserved for loading and unloading. From those reserved hours, scheduled downtime must be deducted, such as reserving the LUZ for removals, diesel supplies to communities, or external city events. Therefore, this factor reflects the measurement of the time that the LUZ is in use, i.e., occupied within the reserved time, excluding scheduled downtimes. In addition to the KPIs or variables currently used to evaluate loading and unloading areas, and in order to characterise this availability factor, it has been necessary to define a new KPI that will be called weighted occupancy time (t\({}_{\text{p}}\)). It is calculated as follows for a vehicle i:  
Lt = total length of the LUZ  
Lt = length of the vehicle occupying the area  
Tt = Total time reserved for loading and unloading in the area  
tj = time that is occupying the zone  
Ltj /Lj = % zone occupation  
Ltj + tj = weighted occupation time (t\({}_{\text{p}}\))  
\[\sum_{\text{j=1}}^{\text{N}}t_{\text{p}}=\text{total occupation of the area}\]  
The interpretation of this new weighted time indicator is that its sum reflects the spatial-temporal contribution of each vehicle to the LUZ, i.e., how much time the vehicle's length occupies the area, and its sum is compared with the Total Time available to assess the availability of the area. To calculate the indicator, standard lengths have been taken for each type of vehicle: private car (4 m), small van (4 m), delivery van (4.5 m), large volume van (5.8 m), light truck with a maximum authorised mass (MAM) of 3.5 tons (6.2 m), and light truck with a MAM of 7.5 tons (7.7 m). An availability indicator close to 1 means that it has been permanently occupied during that time, either legally or illegally. On the other hand, a low result would indicate a long period of non-occupation. \[\text{Availability}=\frac{\sum\limits_{\text{j=1}}^{\text{N}}\text{t}_{\text{p}} }{\text{T}_{\text{t}}}\]  
Efficiency  
This factor measures the time that the area has actually been occupied by commercial DUM vehicles, i.e., the weighted occupancy time of non-commercial and unauthorised vehicles is discounted, leaving only goods delivery vehicles to be considered. The calculation of this indicator takes into account the reduction in the weighted time of use of unauthorised vehicles \(\text{t}_{\text{x}}\) over the total time \(\text{T}_{\text{t}}\)  
\[\text{Efficiency}=1-\frac{\text{t}_{\text{x}}}{\text{T}_{\text{t}}}\]  
A value close to 1 would indicate that there has been no illegal occupation in the area, while a low value would indicate abuse by unauthorised vehicles. The indicator shows the length of time the area has been occupied by commercial vehicles. Quality  
In cities, there are rules and regulations regarding the time allowed for loading and unloading operations. To correctly quantify the time exceeded, the first 30 min are considered correct use, as indicated in the Zaragoza City Council's Urban Mobility Ordinance, and the excess time is considered illegal occupation of the LUZ. This factor quantifies the excess time that the area has been occupied by commercial vehicles that have exceeded the time allowed by the city authorities, i.e., the weighted occupancy time of commercial vehicles is subtracted, which, once the legal time has been exceeded, becomes illegal occupation (\(\text{t}_{\text{oil}}\)). The calculation of this indicator takes into account the reduction in the weighted time of illegal occupation due to exceeding the time allowed. \[\text{Quality}=1-\frac{\text{t}_{\text{oi}}}{\text{T}_{\text{t}}}\]  
A value close to 1 would reveal that commercial vehicles comply with the time allowed for loading or unloading, while a low value would indicate abuse by commercial vehicles which use the LUZ as a free parking space.