PPI Repository

Total Cost and Service Time Ratio

\mathit{TCSTR}\mathit{^{\times}}(i)

\mathit{\times} \in \{\mathit{sgl}, \mathit{sum}\}

Dimension:

Cost

Granularity:

Activity instance

Description

Ratio between the total cost associated with an activity instance, and the service time of an activity instance.

Potential use

Event log in which the total cost in relation to the time taken for conducting activity instances is of relevance.

Assumptions

Ratio between total cost and service time should be as close to 0 as possible.

Desired Value:

MINIMIZE

Required attributes

actinst
tc
time
type

Equations

Formula for practitioners

$\frac{\mathit{TC}(i)}{\mathit{ST}(i)}$

$\mathit{TC}(i)$ returns the total cost of activity instance $i$ .
$\mathit{ST}(i)$ returns the service time of activity instance $i$ .

Formal Definition

$\frac{\mathit{TC}\mathit{^{\times}}(i)}{\mathit{ST}(i)}$
The $\mathit{\times}$ indicates that the PPI can take multiple forms, in this case, $\mathit{\times} \in \{\mathit{sgl}, \mathit{sum}\}$ . If $\mathit{\times} = \mathit{sgl}$ , then the function considers single events of activity instances for cost calculations, i.e., it uses $\mathit{TC}\mathit{^{sgl}}$ ; if $\mathit{\times} = \mathit{sum}$ , then the function considers the sum of all events of activity instances for cost calculations, i.e., it uses $\mathit{TC}\mathit{^{sum}}$ .

Python implementation

This indicator is implemented in the process_performance_indicators Python library.

process_performance_indicators.indicators.cost.instances.total_cost_and_service_time_ratio

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