PPI Repository

Direct Cost

\mathit{DC}\mathit{^{\times}}(c)

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

Dimension:

Cost

Granularity:

Case

Description

Total cost associated with all instantiations of activities that have a direct effect on the outcome of a case.

Potential use

Event log in which activities can be categorized based on whether they directly contribute to the outcome of the process or not.

Assumptions

Minimizing total cost is desirable.

Desired Value:

MINIMIZE

Required attributes

act
actinst
case
tc
type

Equations

Formula for practitioners

$\sum _{i \in \mathit{inst}(c), \mathit{act}(i) \in \mathit{DCl}} \mathit{TC}(i)$

$\mathit{inst}(c)$ returns the set of all activity instances in case $c$ .
$\mathit{act}(i)$ returns the activity of activity instance $i$ .
$\mathit{DCl}$ returns the set of direct cost activities.
$\mathit{TC}(i)$ returns the cost of activity instance $i$ .

Formal Definition

$\sum _{i \in \mathit{inst}(c), \mathit{act}(i) \in \mathit{DCl}} \mathit{TC}\mathit{^{\times}}(i)$
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.cases.direct_cost

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