PPI Repository

Expected Total Cost and Lead Time Ratio

\mathit{e}\mathit{TCLTR}\mathit{^{\times}}(g)

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

Dimension:

Cost

Granularity:

Group of cases

Description

Ratio between the expected total cost of a case belonging to a group of cases and the expected lead time of a case belonging to a group of cases.

Potential use

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

Assumptions

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

Desired Value:

MINIMIZE

Required attributes

actinst
case
tc
time
type

Equations

Formula for practitioners

$\frac{\mathit{TC}(g)}{\sum _{c \in g} \mathit{LT}(c)}$

$\mathit{TC}(g)$ returns the total cost of case group $g$ .
$\mathit{LT}(c)$ returns the total lead time of case $c$ .

Formal Definition

$\frac{\mathit{TC}\mathit{^{\times}}(g)}{\sum _{c \in g} \mathit{LT}(c)}$
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.groups.expected_total_cost_and_lead_time_ratio

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