*5.2.1.1 Determination of Production process secondary KPI indicators Consideration no. 3*

The previous section deals with initial KPI indicator generation and determination of primary KPI indicators for strategic management level. In that section, we shall discuss the KPI indicator decomposition for tactic level, which is based on the following consideration. The outgoing linguistic sets and KPI indicators for KPI decomposition related to tactic level are quantified via formulas (26, 27, 28, 29 and 30). With respect to the above-mentioned issues the following clause might be postulated:

*At the strategic management level, the Production main process might be quantified via {[PROD (i, j1)]} linguistic set and two KPI indicators could be postulated, which indicate that process functionality (performance) (see also formulas (28) and (29) and (30).*

However, the similar sequence of steps (algorithm) might be applied when quantifying and generating KPI indicators for further main processes, sales and distribution, HR, technological and financial management at the strategic management level.

The KPI indicators postulated for strategic management level are represented by formulas (25, 26, (28, 29) and (30) create basis for their further decomposition related to tactic management level.

Let us select the [Mark\_res\_assets\_mat \_ires(0)] subset from {[Tbex (i, j)]} and assign it to market required output products quantified via {[MROP (i, j)]}, while formulas (28 and 29) might be postulated:

$$[\text{Mark\\_res\\_assets\\_mat\\_ires}(\mathbf{0})] \subseteq \{ [\text{Tbx} \ (\mathbf{i}, \mathbf{j})] \} \tag{49}$$

$$[\text{Mark\\_res\\_assets\\_mat\\_ires}(\mathbf{0})] = \{[\text{MROP}\ (\mathbf{i}, \mathbf{j})]\},\tag{50}$$

The {[MROP (i, j)]} contains subsets applied for quantification market required output products classes, e.g. utility glass article classes – bowls, bottles, vases, etc.

$$\{ [\text{MROP} \ (\mathbf{i}, \mathbf{j})] \} = \{ [\text{MROP} \ (\mathbf{i}, \mathbf{1})], [\text{MROP} \ (\mathbf{i}, \mathbf{2})] \dots \{ [\text{MROP} \ (\mathbf{i}, \mathbf{m}\_1)] \} \tag{51}$$

Where.

Index m1 is a number of article classes.

Furthermore, let us create a selected linguistic set {[MROPsel (i, j)]}, a content of which is created by selected classes of [MROPsel (i, j)], [MROP (i, 1)], [MROP (i, 2)], [MROP (i,3)], as for instance (see also formula (53)).

$$\{ [\text{MROP}\_{\text{sel}}(\mathbf{i}, \mathbf{j})] \}, = \{ [\text{MROP}\,(\mathbf{i}, \mathbf{1})], [\text{MROP}\,(\mathbf{i}, \mathbf{2})], [\text{MROP}\,(\mathbf{i}, \mathbf{3})] \} \tag{52}$$

*Business Process Linguistic Modeling: Theory and Practice Part I: BPLM Strategy Creator DOI: http://dx.doi.org/10.5772/intechopen.95096*

and let us postulate the {CUST (i, j2)]} linguistic set, the content of which create data concerned with the customers.

$$\{\left[\text{CUST}\left(\mathbf{i},\mathbf{j}\_2\right)\right]\} = \{\left[\text{CUST}\left(\mathbf{i},\mathbf{1}\right)\right], \left[\text{CUST}\left(\mathbf{i},\mathbf{2}\right)\right], \dots, \left[\text{CUST}\left(\mathbf{i},\mathbf{m}\_{2\parallel}\right)\right] \}\tag{53}$$

where Index m2 means a number of customers.

In the next step, an appropriate {[MROPsel (i, j)]} set for each customer will be assigned, while formula (19) might be postulated.

$$\forall \{ \left[ \text{CUST } (\mathbf{i}, \mathbf{j}\_2) \right] \} \,\exists \, \{ \left[ \text{MROP}\_{\text{sel}} (\mathbf{i}, \mathbf{j}) \right] \} \Rightarrow \{ \left[ \text{CUST } (\mathbf{i}, \mathbf{j}\_2) \right] \} \,\Leftrightarrow \{ \left[ \text{MROP}\_{\text{sel}} (\mathbf{i}, \mathbf{j}) \right] \} \quad \{ \mathbf{54} \}$$

In the next step we shall assign to each {[MROPsel (i, j)]} set a {[MROPselfinass (i, j3)]} and {[MROPselcosts (i, j4)]}, where {[MROPselfinass (i, j)]} set quantifies the financial assets related to selected class of any market required output products.

{[MROPselfincosts (i, j)]} set quantifies the material costs related to selected class of any market required output products.

$$\begin{array}{l} \{ \left[ \text{CUST} \left( \mathbf{i}, \mathbf{j}\_2 \right) \right] \} \otimes \{ \left[ \text{MROP}\_{\text{sel}} \left( \mathbf{i}, \mathbf{j} \mathfrak{Z} \right) \right] \} \otimes \{ \left[ \text{MROP}\_{\text{sel} \text{fmaxs}} \left( \mathbf{i}, \mathbf{j} \mathfrak{A} \right) \right] \} \otimes \{ \left[ \text{MROP}\_{\text{sel} \text{fmaxs}} \left( \mathbf{i}, \mathbf{j} \mathfrak{Z} \right) \right] \} \\\ = \{ \left[ \text{Thexc} \left( \mathbf{i}, \mathbf{j} \right] \right] \} \otimes \{ \left[ \text{Return} \left( \mathbf{i}, \mathbf{j} \right] \right] \} \end{array}$$

(55)

(58)

$$\{\left[\text{TDecx}\left(\mathbf{i},\mathbf{j}\right)\right]\} = \{\left[\text{CUST }\left(\mathbf{i},\mathbf{j}\_2\right)\right], \{\left[\text{MROP}\_{\text{sel}}\left(\mathbf{i},\mathbf{j}\mathbf{2}\right)\right]\}\tag{56}$$

$$\{\left[\text{CONTRACTB}\left(\mathbf{i}\right)\right]\} = \Pi\left\{\left[\text{CUST}\left(\mathbf{i}, \mathbf{j}\_2\right)\right], \left\{\left[\text{MROP}\_{\text{sel}}\left(\mathbf{i}, \mathbf{j}\right)\right]\right\}\tag{57}$$

j=1 …m3

appropriate decomposition of primary KPI indicators related to performance of those processes to should be done. However, the KPI indicator decomposition for tactic level will be explained based on Consideration 3 and the KPI indicator decomposition for operational level will be explained based on Consideration 4 as well, while the Consideration no. 3 results the **secondary KPI indicators** and the Consideration no. 4 results the **tertiary KPI indicators** and both considerations are

*5.2.1.1 Determination of Production process secondary KPI indicators*

The previous section deals with initial KPI indicator generation and determination of primary KPI indicators for strategic management level. In that section, we shall discuss the KPI indicator decomposition for tactic level, which is based on the following consideration. The outgoing linguistic sets and KPI indicators for KPI decomposition related to tactic level are quantified via formulas (26, 27, 28, 29 and 30). With respect to the above-mentioned issues the following clause might be

*At the strategic management level, the Production main process might be quantified via {[PROD (i, j1)]} linguistic set and two KPI indicators could be postulated, which indicate that process functionality (performance) (see also formulas (28) and (29)*

However, the similar sequence of steps (algorithm) might be applied when quantifying and generating KPI indicators for further main processes, sales and distribution, HR, technological and financial management at the strategic manage-

formulas (25, 26, (28, 29) and (30) create basis for their further decomposition

The KPI indicators postulated for strategic management level are represented by

Let us select the [Mark\_res\_assets\_mat \_ires(0)] subset from {[Tbex (i, j)]} and assign it to market required output products quantified via {[MROP (i, j)]}, while

The {[MROP (i, j)]} contains subsets applied for quantification market required output products classes, e.g. utility glass article classes – bowls, bottles, vases, etc.

f g ½ � MROP ið Þ *;* j ¼ f½ � MROP ið Þ *;* 1 , MROP i ½ � ð Þ *;* 2 … *:*f g ½ � MROP ið Þ *;* m1 (51)

Furthermore, let us create a selected linguistic set {[MROPsel (i, j)]}, a content of which is created by selected classes of [MROPsel (i, j)], [MROP (i, 1)], [MROP

MROPsel f g ½ � ð Þ i*;* j , ¼ f g ½ � MROP ið Þ *;* 1 *;* ½ � MROP ið Þ *;* 2 *;* ½ � MROP ið Þ *;* 3 (52)

½ � Mark\_res\_assets\_mat\_ires 0ð Þ ⊆f g ½ � Tbex ið Þ *;* j (49) ½Mark\_res\_assets\_mat\_ires 0ð Þ� ¼ f g ½ � MROP ið Þ *;* j , (50)

described within subsequent sections.

*Operations Management - Emerging Trend in the Digital Era*

*5.2.1 KPI decomposition related to tactic level*

**5.2 KPI indicator decomposition**

*Consideration no. 3*

related to tactic management level.

formulas (28 and 29) might be postulated:

Index m1 is a number of article classes.

(i, 2)], [MROP (i,3)], as for instance (see also formula (53)).

postulated:

*and (30).*

ment level.

Where.

**174**

j2 = 1 …m2

The {[CONTRACTB (i)]} linguistic set quantifies the basic contract, which indicates relations among customers and selected market required output products, incl. Financial costs and financial assets.

$$\{\{\text{Rotor}\ (\mathbf{i}, \mathbf{j})\}\} = \{\{\text{CUST (i, j\_2)}\}, [\text{MROP}\_{\text{sel}}\ (\mathbf{i}, \mathbf{j})], [\text{MROP}\_{\text{selfinstas}}\ (\mathbf{i}, \mathbf{j})], [\text{MROP}\_{\text{selfinstas}}\ (\mathbf{i}, \mathbf{j})]\}$$

$$\{\{\text{CNOT}\text{RACTC}(\mathbf{i})\}\} == \Pi\left\{\{\text{CUST (i, j\_2)}\}, [\text{MROP}\_{\text{sel}}\ (\mathbf{i}, \mathbf{j}\_3)], [\text{MROP}\_{\text{selfinstas}}\ (\mathbf{i}, \mathbf{j}\_4)]\right\},$$

$$\{\text{MROP}\_{\text{selfinstos}}\ (\mathbf{i}, \mathbf{j}\mathbf{5})\}$$

j=1 …m3 j3 = 1 …m3 j4 = 1 …m4 j5 = 1 …m5 j2 = 1 …m2

Before, we make the final step we have to assign an appropriate group of business processes to each group of selected market required output products, while formula (70) might be postulated.

$$\forall \{ \text{[MROP}\_{\text{sel}} \,(\text{i}, \text{j})] \} \,\exists \left\{ \begin{bmatrix} \text{BP (I}, \text{j}\_6) \end{bmatrix} \right\} \Rightarrow \{ \text{[MROP}\_{\text{sel}} \,(\text{i}, \text{j})] \,, \Leftrightarrow \{ \text{[} \text{[BP (I}, \text{j}\_6)] \} \} \qquad \text{(59)}$$

$$\{\left[\text{MROP}\_{\text{sel}}\left(\mathbf{i},\mathbf{j}\right)\right], \left[\text{BP}\left(\mathbf{I},\mathbf{j}\_{\text{6}}\right)\right]\} = \{\left[\text{Tberdp}\left(\mathbf{i},\mathbf{j}\right)\right]\} \otimes \{\left[\text{Retxbp}\left(\mathbf{i},\mathbf{j}\right)\right]\}\tag{60}$$

{[Tbexbp (i, j)]} = {[[BP (I, j6)]} – list of BP groups needed for production of market required output products quantified via {[MROPsel (i, j)],

$$\{ [\text{Rectbp}\ (\text{i}, \text{j})] \} = \{ [\text{MROP}\_{\text{sel}}\ (\text{i}, \text{j})], \{ [[\text{BP}\ (\text{I}, \text{j}\_6)] \ ] \} \tag{61}$$

Formula (24) indicates a list of relations among BP groups and market required output product group.

$$\{\left[\text{CONTRACTD}\left(\text{i}\right)\right]\}=\Pi\left\{\left[\text{CUST}\left(\text{i},\text{j}\_2\right)\right],\left\{\left[\text{MROP}\_{\text{sel}}\left(\text{i},\text{j}\_3\right)\right],\left[\text{MROP}\_{\text{sel}\text{fmass}}\left(\text{i},\text{j}\_4\right)\right]\right\},$$

$$\left[\text{BP}\left(\text{I},\text{j}\_6\right)\right]\}$$

j=1 …m3, j2 = 1 …..m2, j3 = 1 ….m3, j4 = 1 ….m4, j5 = 1 ….m5, j6 = 1 ….m6, Finally, adequate KPI indicators will be defined.

$$\text{KPI}\left(\mathbf{i}, \mathbf{1}\right) = \{ \left[ \text{CONTRACTB}\left(\mathbf{i}\right) \right] \}\tag{63}$$

(62)

Where the linguistic [[MROP1selfincosts (i, j)] subset quantifies financial costs and

3 (69)

(70)

(71)

(73)

(74)

(75)

f½ MROP1selfincosts ½ � ð Þ <sup>i</sup>*;* <sup>j</sup> , MROPselfinass ½ � ð Þ <sup>i</sup>*;* <sup>j</sup>

9 

the [MROP2selmatcosts (i, j)] subset quantifies material costs and create basis for preparation that subset which contains material data needed for production of the

*Business Process Linguistic Modeling: Theory and Practice Part I: BPLM Strategy Creator*

3 ⊆ MROPsel\_bp i*;* j

3

ality and performance might be derived, while the modified PBPL Equation is

8 ⊗ Retx i*;* j

When applying the PBPL Equation, KPI indicator for the selected BP function-

f MROP2selmatcosts ½ � ð Þ i*;* j , MROP1selfincosts ½ � ð Þ i*;* j , MROPselfinass ½ � ð Þ i*;* j , MROPselmatass ½ ð Þ i*;* j �g

<sup>¼</sup> MROPselmatass ½ � ð Þ <sup>i</sup>*;* <sup>j</sup> *;* MROP2selmatcosts <sup>ð</sup> ½ � ð Þ <sup>i</sup>*;* <sup>j</sup> <sup>g</sup> (72)

g¼f MROP2selmatcosts ½ � ð Þ <sup>i</sup>*;* <sup>j</sup> , MROP1selfincosts ½ � ð Þ <sup>i</sup>*;* <sup>j</sup> , MROPselfinass ½ � ð Þ <sup>i</sup>*;* <sup>j</sup> ,

When dealing with BP External metrics KPI Indicators, so called basic and

MROPselfinass ½ � ð Þ i*;* j MROPselmatass ½ ð Þ i*;* j �g

The similar algorithm might be applied, when deriving BP Internal metrics KPI

<sup>¼</sup> MROPselmatass ½ � ð Þ <sup>i</sup>*;* <sup>j</sup> *;* MROP2selmatcosts <sup>ð</sup> ½ � ð Þ <sup>i</sup>*;* <sup>j</sup> <sup>g</sup>

¼ f MROP2selmatcosts ½ � ð Þ <sup>i</sup>*;* <sup>j</sup> , MROP1selfincosts ½ � ð Þ <sup>i</sup>*;* <sup>j</sup> ,

KPIem ¼ KPIemb ið Þ *;* 3 ⊗ KPIemb ið Þ *;* 3 (76)

MROP1sel\_bp i*;* j

above-mentioned products

*Step 4*

*Step 5*

f Retx i*;* j

*Step 6*

*Step 7*

Indicators.

**177**

⊗ MROPsel\_bp i*;* j

MROP2selmatcosts ½ � ð Þ i*;* j MROPsel\_bp i*;* j

*DOI: http://dx.doi.org/10.5772/intechopen.95096*

*5.2.2.3 Applying of PBPL equation solutions*

postulated with respect to formula (61).

3 <sup>¼</sup> Tbex i*;* <sup>j</sup>

*5.2.2.4 PBPL equation solution results*

8

*5.2.2.5 BP external metrics KPI indicators*

external KPI indicators will be defined.

*5.2.2.6 BP Internal metrics KPI Indicators*

KPIemb ið Þ¼ *;* 3 Tbex i*;* j

KPIemext ið Þ¼ *;* 3 Retx i*;* j

MROPselmatass ½ ð Þ i*;* j �g

8

8

Tbex i*;* j

8

$$\text{KPI} \left( \mathbf{i}, \mathbf{2} \right) = \{ \left[ \mathbf{CONTRACTC} \left( \mathbf{i} \right) \right] \}\tag{64}$$

$$\text{KPI}\left(\mathbf{i}, \mathbf{3}\right) = \{ \left[ \text{CONTRACTD}\left(\mathbf{i}\right) \right] \}\tag{65}$$

KPI (i, 3) indicator creates basis for decomposition related to operational level.
