Kirsch operator

Delivery Performance (DP) is a broadly used standard KPI measurement in supply chains to measure the fulfillment of a customers demand to the wish date. Following the nomenclature of the DR-DP-Matrix three main approaches to measure DR can be distinguished:

• $D{P}_T^V$
• $D{P}_S^D$
• $D{P}_S^T$

Type of measurement: volume (V)/singular(S)

Type of view: on time (T)/ delivery (D)

Volume/On Time

Formula

If ($(Deman{d}_{p,c}+Backlo{g}_{p-1,c})>0$)

$D{P}_T^V$ = $\frac{Delivere{d}_{p,c}+Predeliver{y}_{p-1,c}}{Deman{d}_{p,c}+Backlo{g}_{p-1,c}}$

Else

NULL

Demand:= customers wish c:= product identifier p:= Time period e.g. a day, a week, a month ...

The cumulation over a period and a group of product identifiers c is done as follows: $D{P}_{p,c}=\frac{\sum _{p,c}(D{P}_T^V)}{coun{t}_{p,c}(D{P}_T^V<>NULL)}$

whereas p is determined by demand period

Singular/Delivery and Singular/On Time

Singular case definition

To fit to the needs of the environment, the granularity of a singular case ($D{P}_{*}^S$) has to be defined. In general a singular case is described by a n-Tuple consisting of a set of the following order and delivery details:

• order number
• customer identifier
• product identifier
• wish date of customer
• confirmed date of supplier
• ship to information
• delivery date
• delivery note number

Formula

• $D{P}_S^D$

After a singular case has been delivered to the customer its DP is measured as follows:

If (wish date = arrival date) then

DP_{singular case}=1

else

DP_{singular case}=0

arrival date = delivery date + transit time

By cumulating the results of singular cases over a certain period p and, if necessary, additional criteria c (e.g. customer, product, ...) the delivery performance is calculated as follows:

$D{P}_{p,c}=\frac{\sum _{p,c}(DP)}{coun{t}_{p,c}(singularcases)}$

whereas p is determined by the arrival date

• $D{P}_S^T$

After a period has elapsed all singular cases with wish date within period are considered and their DP is measured as follows:

If (wish date = arrival date) then

DR_{singular case}=1

else

DR_{singular case}=0

arrival date = delivery date + transit time

By cumulating the results of singular cases over a certain period p and, if necessary, additional criteria c (e.g. customer, product, ...) the delivery performance is calculated as follows:

$D{P}_{p,c}=\frac{\sum _{p,c}(DP)}{coun{t}_{p,c}(singularcases)}$

whereas p is determined by the first confirmed date

Result

0%≤$D{P}_{T/D}^{S/V}$≤100%