**5. Consideration no.1 Determination of KPI initial indicators**

When considering a top core business process (hereinafter known as CB Process), a vertical structure of which is quantified via linguistic set {[CBS (i, j)]}, where.

i = 0,1, 2,3 …. n is a serial number of the actual business process (BP) within BP vertical structure set.

j = 0,1,2,3 ….m1 is a serial number of business process function (BPF) within selected BP.

Because the core BP is at the top of BP vertical structure index i = 0 and j = 0 the top business process is being quantified via {[CBS (0, 1)]} linguistic set its performance quantified via KPI indicator with respect to formula (4).

f g KPI 0ð Þ <sup>¼</sup> <sup>X</sup>Totfin Costs ð Þ <sup>0</sup> *;* <sup>X</sup>Totmat Costs ð Þ <sup>0</sup> *;* YTotfin Assetst *;* YTotmat Assetst (4)

Where

In general, any business process (BP) is characterized via its own internal and external metrics, while the BP external metrics deals with BP inputs and outputs and the internal metrics deals with appropriate human resources, production technological devices and tools. However, the BP external metrics KPI indicators include BP material input costs, BP financial input cost, BP production output material assets and production output financial assets as well, while the internal metrics KPI indicators include human resources theoretical knowledge and practical skill data together with adequate financial costs and assets. On the other hand, the internal metrics technological resources include production technological devices and tools (material aspects) and production technological devices and tools (finan-

*Operations Management - Emerging Trend in the Digital Era*

**4.2 BPLM strategy creator – structure and functionality – quantitative view**

The BPLM Strategy Creator (BPLM SC) application represent a relatively independent system, which consist of several subsystems, components and modules

• the first subsystem should provide selecting of adequate documents closely related to BS qualitative and quantitative aspects and their semantic analysis together with the data storage and processing, which has been generated as a result of the above-mentioned semantic analysis while it is denoted as the

• This subsystem contains two components, while the BPLM SC 01–01 component should enable involving the data and document segments concerned with BS qualitative aspects to adequate BS qualitative documents and the BPLM SC 01–02 component enable converting the data and document

segments concerned with BS quantitative aspects to adequate BS KPI

• the second subsystem should provide investigation of the core business

• the third subsystem should provide BS quantitative aspect simulation and optimization and consists of two components BPLM SC 03–01 component, which should provide the BS KPI indicator and core process simulation and BPLM SC 03–02 component, which should provide the BS KPI indicator and

In general, the BP performance is being quantified via key performance indicators (hereinafter known as KPI indicators), which might have a very heterogeneous

**4.3 KPI indicator quantification, generation and decomposition**

process, which create an integral part BS creation and generation of initial KPI indicators and a decomposition of them for tactic and operational management level, while it consists of BPLM SC 02–01 component, which should provide investigation of the core business process from functional point of view, where the core business process (CBP) metrics plays a role of principle importance and the BPLM SC 02–02 component should provide the KPI indicator decomposition related to tactic and operation management level

BPLM SC 01 Data and document preparation subsystem

cial costs and asset aspects).

*4.2.1 General overview*

postulated as follows:

indicators.

core process optimization.

*4.3.1 KPI indicator quantification*

**168**

[XTotfin Costs (0)] is a linguistic subset, which contains elements closely related to CB Process functionality input financial costs

[XTotmat Costs (0)] is a linguistic subset, which contains elements closely related to CB Process functionality entire input material quantity

[XTotmat Assets (0)] is a linguistic subset, which contains elements closely related to CB Process functionality entire output material quantity

[XTotfin Assets (0)] is a linguistic subset, which contains elements closely related to CB Process functionality entire output financial assets

However, a content of linguistic subsets, which create an integral part for {KPI (0)} represents data closely related to market research and the firm or company internal resources analysis as well.

The above-mentioned quantification of the core BP is being done at the strategic management level, while a similar quantification of business processes (BPs) should be done at tactic and operational management levels too.

Let us consider the PBPL equation in a general form with respect to formula (3) and let us assign the linguistic sets with respect to formula (3), while formulas (5) up to (8) might be postulated.

$$\{\left[\mathbf{Petx}\left(\mathbf{i},\mathbf{j}\right)\right]\} = \{\left[\mathbf{X}^{\mathbf{Totfin}}\_{\mathbf{Custs}}\left(\mathbf{0}\right)\right], \left[\mathbf{X}^{\mathbf{Totmat}}\_{\mathbf{Costs}}\left(\mathbf{0}\right)\right]\}\tag{5}$$

$$\{ [\text{Pe}\ (\mathbf{i}, \mathbf{j})] \} = \{ [\text{CBS}\ (\mathbf{0}, \mathbf{1})] \} \tag{6}$$

$$\{\left[\mathbf{T}\mathbf{b}\mathbf{x}\left(\mathbf{i},\mathbf{j}\right)\right]\} = \left\{\left[\mathbf{X}^{\text{Totmat}}{}\_{\text{Assets}}\left(\mathbf{0}\right)\right], \left[\mathbf{X}^{\text{Totfin}}{}\_{\text{Assets}}\left(\mathbf{0}\right)\right]\right\}\tag{7}$$

where

The [[XTotfin Costs (0)] and [XTotmat Costs (0)]} linguistic sets represent initial inputs for core BP quantified via {[CBS (0, 1)]} linguistic set and the {[XTotmat Assets (0)], [XTotfin Assets (0)]} linguistic sets represent subsequent outputs from BP quantified via {[CBS (0, 1)]} linguistic set.

The {[Retx (i, j)]} linguistic set represents relations among the above-mentioned linguistic sets with respect to formula (2d).

$$\{\left[\text{Rect}\left(\dot{\mathbf{u}},\dot{\mathbf{j}}\right)\right]\} = \{\left[\mathbf{X}^{\text{Totmat}}\_{\text{Assets}}\left(\mathbf{0}\right)\right], \left[\mathbf{X}^{\text{Totfin}}\_{\text{Assets}}\left(\mathbf{0}\right)\right], \left[\text{CBS }\left(\mathbf{0},\mathbf{1}\right)\right], \left[\mathbf{X}^{\text{Totfin}}\_{\text{Counts}}\left(\mathbf{0}\right)\right],\tag{8}$$
 
$$\left[\mathbf{X}^{\text{Totmat}}\_{\text{Counts}}\left(\mathbf{0}\right)\right]$$

With respect to the above-mentioned formulas the **Primary KPI indicators** might be postulated and have a nature of linguistic sets as well (see also formulas 9, 10).

$$\{\text{KPI}\left(\mathbf{1}\right)\} = \left[\mathbf{X}^{\text{Totfin}}\_{\text{Assets}}\left(\mathbf{0}\right)\right] / \left[\left[\mathbf{X}^{\text{Totfin}}\_{\text{Costs}}\left(\mathbf{0}\right)\right] \tag{9}\right]$$

f g KPImanp 2ð Þ <sup>¼</sup> <sup>X</sup>TotmatmanpAssets ð Þ <sup>0</sup> *<sup>=</sup>*<sup>½</sup> <sup>X</sup>TotmatmanpCosts ð Þ <sup>0</sup> (15)

When looking at formula (11), we might see that the initial KPI (0) indicator is closely related to the glass utility production process (GUP process), which seems to be the core process and is being quantified via {[GUPC (0, 1)]} linguistic set and

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

Costs ð Þ <sup>0</sup> , YTotfin

However, the core process denoted as GUP process consists of main process

Now, let us analyze appropriate main processes denoted as **Production** quantified via {[PROD (i, j1)]} linguistic set in order to determine the partial KPI indicators, while the initial KPI indicator value could create basis for those purposes. It

Before providing KPI indicator quantification several auxiliary linguistic subset

<sup>Y</sup>TotfinmanpAssetst ð Þ <sup>0</sup> <sup>¼</sup> f g ½ � Mark\_res\_assets\_fin 0ð Þ *;* ½ � Mark\_res\_costs\_fin 0ð Þ

YTotfmatmanpAssetst ð Þ <sup>0</sup> <sup>¼</sup> f g ½ � Mark\_res\_assets\_mat 0ð Þ *;* ½ � Mark\_res\_costs\_mat 0ð Þ

A word Mark\_res, which creates basis of an appropriate linguistic set name indicates that items and values contained in there are initial input data acquired as a

Determination of {[PCPFin (i, j)], [PCPMat (i, j)]} linguistic sets, which are closely related to the firm or company real internal material and financial resources. The normalized internal resource values are postulated within the firm technical and economic standards (Int\_res\_fin\_val\_act (0), Int\_res\_fin\_mat \_act (0), while based on those values a value of Int\_res\_fin\_koef (0) koeficient, which indicates what about a quantity of financial and material assets might be achieved, when applying real firm or company internal resources (see also formulas (19–22).

½ �¼ PCPFin ið Þ *;* j ½ � Int\_res\_fin\_val\_req 0ð Þ*;*Int\_res\_fin\_val\_act 0ð Þ*;*Int\_res\_fin\_koef 0ð Þ

½PCPMat ið Þ *;* j � ¼ ½ � Int\_res\_mat\_val\_req 0ð Þ*;*Int\_res\_mat\_val\_act 0ð Þ*;*Int\_res\_mat\_koef 0ð Þ

For {[Petx (i, j1)]} linguistic set content see also formula (2a) and for {[Pe

(i,j2)]} linguistic set content see also formula (24).

f g ½ � PCP ið Þ *;* j ¼ f g ½ � PCPFin ið Þ *;* j *;* ½ � PCPMat ið Þ *;* j (19)

f g ½ � Pe ið Þ *;* j2 ¼ f g ½ � PCP ið Þ *;* j (22)

content should be determined. It might be done within Step 1 and Step 2.

quantified via appropriate linguistic sets postulated as follows as well.

*5.1.2 Determination of Production process primary KPI indicators*

<sup>½</sup>GUPC 0ð Þ *;* <sup>1</sup> �gg (16)

Assetst , YTotmat

Assetst

(17)

(18)

(20)

(21)

formula (11) is converted to formula (16).

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

Costs ð Þ <sup>0</sup> , XTotmat

f g KPI 0ð Þ ¼ f XTotfin

might be done via following steps:

result of market research.

Step 2

**171**

Step 1

$$\{\text{KPI}\left(2\right)\} = \left[\mathbf{X}^{\text{Totmat}}{}\_{\text{Assets}}\left(\mathbf{0}\right)\right] / \left[\left[\mathbf{X}^{\text{Totmat}}{}\_{\text{Costs}}\left(\mathbf{0}\right)\right] \tag{10}$$

However, those KPI indicators create basis for generation of further KPIs and their decomposition as well, while they have a linguistic set nature. As mentioned above the initial KPI indicators are being quantified via linguistic sets with respect to formulas (9) and (10). However, they are generated at strategic management level and are closely related to core BP quantified via linguistic set {[CBS (0, 1)]} as well, while formula (3) is extended about {[CBS (0, 1)]} linguistic set and formula (11) might be postulated.

$$\{\text{KPI}\left(\mathbf{0}\right)\} = \left\{ \left[ \mathbf{X}^{\text{Toffin}}\_{\text{Cats}}\left(\mathbf{0}\right) \right], \left[ \mathbf{X}^{\text{Toffmat}}\_{\text{Cats}}\left(\mathbf{0}\right) \right], \left[ \mathbf{Y}^{\text{Toffin}}\_{\text{Aasest}}\right], \left[ \mathbf{Y}^{\text{Toffmat}}\_{\text{Aasest}}\right], \left[ \mathbf{CBS}\left(\mathbf{0}, \mathbf{1}\right) \right] \right\} \tag{11}$$

#### **5.1 Determination of KPI primary indicators**

#### *5.1.1 Consideration no. 2*

With respect the above-mentioned issues two types of KPI initial indicators are being postulated (see also formula):

$$\begin{aligned} \left\{ \text{KPI}\_{\text{mamp}} \left( \mathbf{0} \right) \right\} &= \left\{ \left[ \mathbf{X}^{\text{Toffinnamp}}\_{\text{Cots}} \left( \mathbf{0} \right) \right], \left[ \mathbf{X}^{\text{Toffmanamp}}\_{\text{Cots}} \left( \mathbf{0} \right) \right], \left[ \mathbf{Y}^{\text{Toffinnamp}}\_{\text{Asetst}} \right], \mathbf{0} \right\} \\ & \left[ \mathbf{Y}^{\text{Toffmatamp}}\_{\text{Asetst}} \right] \left\{ \mathbf{0} \right\} \end{aligned} \tag{12}$$
 
$$\left\{ \mathbf{KPI}\_{\text{machp}} \left( \mathbf{0} \right) \right\} = \left\{ \left[ \mathbf{X}^{\text{Toffinnachp}}\_{\text{Cots}} \left( \mathbf{0} \right) \right], \left[ \mathbf{X}^{\text{Toffmanachp}}\_{\text{Cots}} \left( \mathbf{0} \right) \right], \left[ \mathbf{Y}^{\text{Toffinnachp}}\_{\text{Asetst}} \right]\_{\text{Asetst}} \right\}. \tag{13}$$

$$\begin{aligned} \{\mathbf{K} \mathbf{P} \mathbf{I}\_{\text{machp}} \left( \mathbf{0} \right) \} &= \{ \left[ \mathbf{X}^{\text{roundman.up}} \left( \mathbf{0} \right) \right], \left[ \mathbf{X}^{\text{roundman.up}} \left( \mathbf{0} \right) \right], \left[ \mathbf{Y}^{\text{roundman.up}} \mathbf{A} \mathbf{s} \mathbf{t} \mathbf{t} \right], \\ & \qquad \left[ \mathbf{Y}^{\text{Tomat} \text{machp}} \mathbf{A}\_{\text{Asest}} \right] \} \end{aligned} \tag{13}$$

where

the manp index is concerned with utility glass manually oriented production and the manchp index is concerned with utility glass machinery oriented production.

We shall discuss the KPI indicator quantification; generation and decomposition problems for glass utility manual production, while the derived formulas and algorithms might be applied for machinery oriented utility glass production as well.

The partial KPI indicators (see also formulas 14 and 15) indicate financial (Totfinmanp) and material (Totmatmanp) assets and costs and they considered to be results of market and the firm or company internal resources and they might represent initial manual inputs.

$$\{\text{KPImanp} \left(\mathbf{1}\right)\} = \left[\mathbf{X}^{\text{Totifinsmnp}}\_{\text{Assets}} \left(\mathbf{0}\right)\right] / \left[\left[\mathbf{X}^{\text{Totifinamp}} \mathbf{C}\_{\text{Costs}} \left(\mathbf{0}\right)\right] \tag{14}$$

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

$$\{\text{KPImanp} \left(2\right)\} = \left[\mathbf{X}^{\text{Totmatmanp}}\_{\text{Assets}} \left(\mathbf{0}\right)\right] / \left[\left[\mathbf{X}^{\text{Totmatmanp}}\_{\text{Costs}} \left(\mathbf{0}\right)\right] \right.\tag{15}$$

When looking at formula (11), we might see that the initial KPI (0) indicator is closely related to the glass utility production process (GUP process), which seems to be the core process and is being quantified via {[GUPC (0, 1)]} linguistic set and formula (11) is converted to formula (16).

$$\{\text{KPI}\left(\mathbf{0}\right)\} = \{\left[\mathbf{X}^{\text{Toffin}}\_{\text{Costs}}\left(\mathbf{0}\right)\right], \left[\mathbf{X}^{\text{Toffmat}}\_{\text{Costs}}\left(\mathbf{0}\right)\right], \left[\mathbf{Y}^{\text{Toffin}}\_{\text{Assets}}\right], \left[\mathbf{Y}^{\text{Toffmat}}\_{\text{Assets}}\right] \quad \text{(16)}$$

$$\left[\mathbf{G}\text{UPC}\left(\mathbf{0}, \mathbf{1}\right)\right] \}$$

However, the core process denoted as GUP process consists of main process quantified via appropriate linguistic sets postulated as follows as well.

#### *5.1.2 Determination of Production process primary KPI indicators*

Now, let us analyze appropriate main processes denoted as **Production** quantified via {[PROD (i, j1)]} linguistic set in order to determine the partial KPI indicators, while the initial KPI indicator value could create basis for those purposes. It might be done via following steps:

Step 1

f g¼f ½ � Retx ið Þ *;* <sup>j</sup> <sup>X</sup>Totmat

(11) might be postulated.

*5.1.1 Consideration no. 2*

where

**170**

being postulated (see also formula):

represent initial manual inputs.

formulas 9, 10).

XTotmat Costs ð Þ <sup>0</sup> <sup>g</sup>

Assets ð Þ <sup>0</sup> , XTotfin

*Operations Management - Emerging Trend in the Digital Era*

f g KPI 1ð Þ <sup>¼</sup> XTotfin

f g KPI 2ð Þ <sup>¼</sup> <sup>X</sup>Totmat

f g KPI 0ð Þ <sup>¼</sup> <sup>X</sup>TotfinCosts ð Þ <sup>0</sup> *;* XTotmatCosts ð Þ <sup>0</sup> *;* YTotfinAssetst

YTotmatmanpAssetst <sup>g</sup>

YTotmatmachpAssetst <sup>g</sup>

**5.1 Determination of KPI primary indicators**

With respect to the above-mentioned formulas the **Primary KPI indicators**

Assets ð Þ <sup>0</sup> *<sup>=</sup>*<sup>½</sup> XTotfin

Assets ð Þ <sup>0</sup> *<sup>=</sup>*<sup>½</sup> <sup>X</sup>Totmat

*;* ½ � CBS 0ð Þ *;* <sup>1</sup>

With respect the above-mentioned issues two types of KPI initial indicators are

KPImanp ð Þ <sup>0</sup> ¼ f <sup>X</sup>TotfinmanpCosts ð Þ <sup>0</sup> , XTotmamanptCosts ð Þ <sup>0</sup> , YTotfinmanpAssetst

KPImachp ð Þ <sup>0</sup> ¼ f <sup>X</sup>TotfinmachpCosts ð Þ <sup>0</sup> , XTotmamachpCosts ð Þ <sup>0</sup> , YTotfinmachpAssetst

the manp index is concerned with utility glass manually oriented production and the manchp index is concerned with utility glass machinery oriented production. We shall discuss the KPI indicator quantification; generation and decomposition problems for glass utility manual production, while the derived formulas and algorithms might be applied for machinery oriented utility glass production as well. The partial KPI indicators (see also formulas 14 and 15) indicate financial (Totfinmanp) and material (Totmatmanp) assets and costs and they considered to be results of market and the firm or company internal resources and they might

f g KPImanp 1ð Þ <sup>¼</sup> <sup>X</sup>TotfinmsnpAssets ð Þ <sup>0</sup> *<sup>=</sup>*<sup>½</sup> XTotfinmanpCosts ð Þ <sup>0</sup> (14)

However, those KPI indicators create basis for generation of further KPIs and their decomposition as well, while they have a linguistic set nature. As mentioned above the initial KPI indicators are being quantified via linguistic sets with respect to formulas (9) and (10). However, they are generated at strategic management level and are closely related to core BP quantified via linguistic set {[CBS (0, 1)]} as well, while formula (3) is extended about {[CBS (0, 1)]} linguistic set and formula

might be postulated and have a nature of linguistic sets as well (see also

Assets ð Þ <sup>0</sup> , CBS 0 ½ � ð Þ *;* <sup>1</sup> , <sup>½</sup> <sup>X</sup>Totfin

*;* YTotmatAssetst

Costs ð Þ <sup>0</sup> ,

Costs ð Þ <sup>0</sup> (9)

Costs ð Þ <sup>0</sup> (10)

(8)

g (11)

,

,

(12)

(13)

Before providing KPI indicator quantification several auxiliary linguistic subset content should be determined. It might be done within Step 1 and Step 2.

$$\{\left[\mathbf{Y}^{\text{Tofffnmap}}\_{\text{Assets}}\left(\mathbf{0}\right)\right]\} = \{\left[\mathbf{Mark\\_res\\_assets\\_fin}\left(\mathbf{0}\right)\right], \left[\mathbf{Mark\\_res\\_costs\\_fn}\left(\mathbf{0}\right)\right]\}\tag{17}$$

$$\{\left\{\mathbf{Y}^{\text{Totfmatmap}}\_{\text{Assets}}\left(\mathbf{0}\right)\right\}\} = \{\left[\mathbf{Mark\\_res\\_assets\\_mat\left(\mathbf{0}\right)}\right], \left[\mathbf{Mark\\_res\\_cost\\_mat\left(\mathbf{0}\right)}\right]\}\tag{18}$$

A word Mark\_res, which creates basis of an appropriate linguistic set name indicates that items and values contained in there are initial input data acquired as a result of market research.

Step 2

Determination of {[PCPFin (i, j)], [PCPMat (i, j)]} linguistic sets, which are closely related to the firm or company real internal material and financial resources. The normalized internal resource values are postulated within the firm technical and economic standards (Int\_res\_fin\_val\_act (0), Int\_res\_fin\_mat \_act (0), while based on those values a value of Int\_res\_fin\_koef (0) koeficient, which indicates what about a quantity of financial and material assets might be achieved, when applying real firm or company internal resources (see also formulas (19–22).

$$\{ [\text{PCP } (\mathbf{i}, \mathbf{j})] \} = \{ [\text{PCPFin } (\mathbf{i}, \mathbf{j})], [\text{PCPMat } (\mathbf{i}, \mathbf{j})] \} \tag{19}$$

$$\left[ \text{PCPFin} \left( \mathbf{i}, \mathbf{j} \right) \right] = \left[ \text{Int\\_res\\_fin\\_val\\_req} \left( \mathbf{0} \right), \text{Int\\_res\\_fin\\_act\\_0} \left( \mathbf{0} \right), \text{Int\\_res\\_fin\\_koef} \left( \mathbf{0} \right) \right] \tag{20}$$

$$[\text{PCP} \,(\text{i}, \text{j})] = [\text{Int\\_res\\_mat\\_val\\_req} \,(\text{0}), \text{Int\\_res\\_mat\\_val\\_act} \,(\text{0}), \text{Int\\_res\\_mat\\_koef} \,(\text{0})] \tag{21}$$

$$\{ [\text{Pe } (\mathbf{i}, \mathbf{j} \mathbf{2})] \} = \{ [\text{PCP } (\mathbf{i}, \mathbf{j})] \} \tag{22}$$

For {[Petx (i, j1)]} linguistic set content see also formula (2a) and for {[Pe (i,j2)]} linguistic set content see also formula (24).

$$\{\left[\mathbf{Petx}\left(\mathbf{i},\mathbf{j1}\right)\right]\} = \left\{\left[\mathbf{Y}^{\text{Toffmann}}\_{\text{Assets}}\left(\mathbf{0}\right)\right], \left[\mathbf{Y}^{\text{Toffmatman}}\_{\text{Assets}}\left(\mathbf{0}\right)\right]\right\}\tag{23}$$

distribution, HR, technological and financial management at the strategic manage-

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

At strategic management level, a set of core BP are implemented and operated and quantified via appropriate linguistic sets, e.g. the Sales and Distribution BP is quantified via {[SAD (i, j)]}, where the *main frame customer*s play a role of principle importance and are being quantified via [MFRC (i, j)]. When applying PBPL equa-

f g ½ � PROD ið Þ *;* j1 ⊗ f g ½ � MFRC ið Þ *;* j ⊗ f g ½ � SAD ið Þ *;* j ¼ f g ½ � Tbex ið Þ *;* j ⊗ f g ½ � Retx ið Þ *;* j

However, at strategic management level, a set of core BP are implemented and operated and quantified via appropriate linguistic sets, e.g. Human resources (HR} management is quantified via {[HR (i, j)]} as well where the *main frame human resources* play a role of principle importance and are being quantified via [HRC (i, j)]. When applying PBPL equation adequate KPI indicators might be derived.

f g ½ � PROD ið Þ *;* j1 ⊗ f g ½ � HRC ið Þ *;* j ⊗ f g ½ � HR ið Þ *;* j ¼ f g ½ � Tbex ið Þ *;* j ⊗ f g ½ � Retx ið Þ *;* j (37)

Finally, at strategic management level, a set of core BP are implemented and operated (see also **Table 1**) and quantified via appropriate linguistic sets, e.g. Technological TECH management is quantified via {[TECHN (i, j)]} as well where the *main frame technological devices and tools* play a role of principle importance and are being quantified via [TECHNC (i, j)]. When applying PBPL equation adequate

f g ½ � PROD ið Þ *;* j1 ⊗ f g ½ � TECNC ið Þ *;* j ⊗ f g ½ � TECH ið Þ *;* j ¼ f g ½ � Tbex ið Þ *;* j ⊗ f g ½ � Retx ið Þ *;* j

f g ½ � Retx ið Þ *;* j ¼ f g ½ � PROD ið Þ *;* j1 *;* ½ � TECHNC ið Þ *;* j *;* ½ � TECH ið Þ *;* j (45)

In order to create a complex set of KPI indicators related to business processes

implemented and operated at tactic and operational management level, an

f g ½ � Tbex ið Þ *;* j ¼ f g ½ � PROD ið Þ *;* j1 *;* ½ � MFRC ið Þ *;* j (32)

fKPIsad ð0g ¼ f g KPIsad 0ð Þ *;* 1 ⊗ f g KPIsad 0ð Þ *;* 2 (36)

f g ½ � Tbex ið Þ *;* j ¼ f g ½ � PROD ið Þ *;* j1 *;* ½ � HRC ið Þ *;* j (38)

fKPIhr ð0g ¼ f g KPIsad 0ð Þ *;* 1 ⊗ f g KPIsad 0ð Þ *;* 2 (42)

f g ½ � Tbex ið Þ *;* j ¼ f g ½ � PROD ið Þ *;* j1 *;* ½ � TECHNC ið Þ *;* j (44)

fKPItech ð0g ¼ f g KPItech 0ð Þ *;* 1 ⊗ f g KPItech 0ð Þ *;* 2 (48)

f g KPItech 0ð Þ *;* 1 ¼ ½ �g Tbex ið Þ *;* j (46) f g KPItech 0ð Þ *;* 2 ¼ f g ½ � Retx ið Þ *;* j (47)

f g KPIhr 0ð Þ *;* 1 ¼ f g ½ � Tbex ið Þ *;* j (40) f g KPIhr 0ð Þ *;* 2 ¼ f g ½ � Retx ið Þ *;* j (41)

f g ½ � Retx ið Þ *;* j ¼ f g ½ � PROD ið Þ *;* j1 *;* ½ � MFRC ið Þ *;* j *;* ½ � HR ið Þ *;* j (39)

f g KPIsad 0ð Þ *;* 1 ¼ ½ �g Tbex ið Þ *;* j (34) f g KPIsad 0ð Þ *;* 2 ¼ f½ � Retx ið Þ *;* j � (35)

f½ � Retx ið Þ *;* j � ¼ f g ½ � PROD ið Þ *;* j1 *;* ½ � MFRC ið Þ *;* j *;* ½ � SAD ið Þ *;* j (33)

(31)

(43)

ment level.

tion adequate KPI indicators might be derived.

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

KPI indicators might be derived.

**173**

When applying the PBPL Equation its general form, (see also formula (24)) formula (25) might be postulated.

$$\{ [\text{Petx} \ (\text{i}, \text{j1})] \} \otimes \{ [\text{Pe} \ (\text{i}, \text{j2})] \} = \{ [\text{Tbex} \ (\text{i}, \text{j})] \} \otimes \{ [\text{Ret} \ (\text{i}, \text{j})] \} \tag{24}$$

After installment of previous relations into formula (24) formula (25) might be postulated.

$$\{\left[\mathbf{Y}^{\text{Torfinnnan}}\_{\text{Assets}}\left(\mathbf{0}\right)\right], \left[\mathbf{Y}^{\text{Torfmatman}}\_{\text{Assets}}\left(\mathbf{0}\right)\right]\} \otimes \{\left[\mathbf{PCP}\left(\mathbf{i}, \mathbf{j}\right)\right]\} = \{\left[\mathbf{Tbes\ (i, j)}\right]\} \otimes \{\left[\mathbf{Ret\ (i, j)}\right]\}\tag{25}$$

where

the {[Tbex (i, j)]} linguistic contains data closely related to quantity of financial and material asset generated based on the actual firm or company internal resources.

$$\{ [\text{"Dax } (\text{i}, \text{j})] \} = \{ [\text{Mark\\_res\\_assets\\_fin\\_ires}(0)], [\text{Mark\\_res\\_assets\\_mat\\_res}(0)], \} \tag{26}$$

$$\{ | \text{Rect}\left( \mathbf{i}, \mathbf{j} \right) | \} = \{ | \text{Mark\\_res\\_assets\\_fin\\_ires}(0) |, | \text{Mark\\_res\\_costs\\_fins}(0) |, \} \tag{27}$$
 
$$[ \text{Mark\\_res\\_assets\\_fin\\_ire}(0) ], [ \text{Mark\\_res\\_costs\\_fins}(0) ] ]$$

the {[Retx (i, j)]} linguistic contains data closely related to quantity of financial and material asset generated based on the actual firm or company internal resources with respect to appropriate financial and material costs.

In general, the above-mentioned algorithm enables determining KPIprod (0, 1)} and KPIprod (0, 2)}, while formulas (28) and (29) might be postulated.

$$\{\text{KPIprod} \,(\mathbf{0}, \mathbf{1})\} = \{\text{[Tbxx } (\mathbf{i}, \mathbf{j1})] \}\tag{28}$$

$$\{\text{KPIprod} \,(\mathbf{0}, \mathbf{2})\} = \{\text{[Retx (i, j2)]}\} \tag{29}$$

where

{KPIprod (0, 1)} = {[Tbex (i, j1)]} –the first Primary KPI indicator, which indicates real possibilities of the firm or company business represented by financial and material assets with respect to the firm or company production internal resources.

{KPIprod (0, 2)} = {[Retx (i, j2)]} – the second Primary KPI indicator, which indicates real possibilities of the firm or company business represented by financial and material assets with respect to the firm or company production financial and material cost. 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).

f½ � PROD ið Þ *;* j1 g ¼ fKPIprod 1ð Þ *;* 2 g ¼ f g KPIprod 0ð Þ *;* 1 ⊗ f g KPIprod 0ð Þ *;* 2 (30)

However, the similar sequence of steps (algorithm) might be applied when quantifying and generating KPI indicators for further main processes, sales and *Business Process Linguistic Modeling: Theory and Practice Part I: BPLM Strategy Creator DOI: http://dx.doi.org/10.5772/intechopen.95096*

distribution, HR, technological and financial management at the strategic management level.

At strategic management level, a set of core BP are implemented and operated and quantified via appropriate linguistic sets, e.g. the Sales and Distribution BP is quantified via {[SAD (i, j)]}, where the *main frame customer*s play a role of principle importance and are being quantified via [MFRC (i, j)]. When applying PBPL equation adequate KPI indicators might be derived.

$$\{\left[\text{PROD}\left(\mathbf{i},\mathbf{j}\mathbf{1}\right)\right]\} \otimes \{\left[\text{MFRC}\left(\mathbf{i},\mathbf{j}\right)\right]\} \otimes \{\left[\text{SAD}\left(\mathbf{i},\mathbf{j}\right)\right]\} = \{\left[\text{Tbes}\left(\mathbf{i},\mathbf{j}\right)\right]\} \otimes \{\left[\text{Return }\left(\mathbf{i},\mathbf{j}\right)\right]\}$$

(31)

$$\{ [\text{Tberx } (\mathbf{i}, \mathbf{j})] \} = \{ [\text{PROD } (\mathbf{i}, \mathbf{j1})], [\text{MFRC } (\mathbf{i}, \mathbf{j})] \} \tag{32}$$

$$\{ [\text{Retx} \ (\mathbf{i}, \mathbf{j})] \} = \{ [\text{PRED } (\mathbf{i}, \mathbf{j} \mathbf{1})], [\text{MFRC } (\mathbf{i}, \mathbf{j})], [\text{SAD } (\mathbf{i}, \mathbf{j})] \} \tag{33}$$

$$\{\text{KPIsad}(0, \mathbf{1})\} = [\text{Tber } (\mathbf{i}, \mathbf{j})] \}\tag{34}$$

$$\{\text{KPIsad}\left(\mathbf{0},\mathbf{2}\right)\} = \{\left[\text{Retx}\left(\mathbf{i},\mathbf{j}\right)\right]\}\tag{35}$$

$$\{\text{KPIsad}\,(\text{0}) = \{\text{KPIsad}(\text{0}, \text{1})\} \otimes \{\text{KPIsad}(\text{0}, \text{2})\}\tag{36}$$

However, at strategic management level, a set of core BP are implemented and operated and quantified via appropriate linguistic sets, e.g. Human resources (HR} management is quantified via {[HR (i, j)]} as well where the *main frame human resources* play a role of principle importance and are being quantified via [HRC (i, j)]. When applying PBPL equation adequate KPI indicators might be derived.

$$\{ \{ \text{PROD } (\text{i}, \text{j1}) \} \} \otimes \{ \{ \text{HRC } (\text{i}, \text{j}) \} \} \otimes \{ \{ \text{HR} \left( \text{i}, \text{j} \right) \} \} = \{ \{ \text{Thex } (\text{i}, \text{j}) \} \} \otimes \{ \{ \text{Return } (\text{i}, \text{j}) \} \} \quad \{ \text{37} \}$$

$$\{ [\text{Tber}\ (\mathbf{i}, \mathbf{j})] \} = \{ [\text{PROD}\ (\mathbf{i}, \mathbf{j}\mathbf{1})], [\text{HRC}\ (\mathbf{i}, \mathbf{j})] \}\tag{38}$$

$$\{ [\text{Retx}\ (\mathbf{i}, \mathbf{j})] \} = \{ [\text{RODU}\ (\mathbf{i}, \mathbf{j}\mathbf{1})], [\text{MFRC}\ (\mathbf{i}, \mathbf{j})], [\text{HR}\ (\mathbf{i}, \mathbf{j})] \} \tag{39}$$

$$\{\text{KPlhr}(\mathbf{0}, \mathbf{1})\} = \{\text{[Tber } (\mathbf{i}, \mathbf{j})\text{]}\} \tag{40}$$

$$\{\text{KPIhr}\left(\mathbf{0}, \mathbf{2}\right)\} = \{\left[\text{Retx}\left(\mathbf{i}, \mathbf{j}\right)\right]\}\tag{41}$$

$$\{\text{KPIhr} \,(\mathbf{0})\} = \{\text{KPIsad}(\mathbf{0}, \mathbf{1})\} \otimes \{\text{KPIsad}(\mathbf{0}, \mathbf{2})\} \tag{42}$$

Finally, at strategic management level, a set of core BP are implemented and operated (see also **Table 1**) and quantified via appropriate linguistic sets, e.g. Technological TECH management is quantified via {[TECHN (i, j)]} as well where the *main frame technological devices and tools* play a role of principle importance and are being quantified via [TECHNC (i, j)]. When applying PBPL equation adequate KPI indicators might be derived.

$$\{\{\text{PROD (i,j1)}\}\} \otimes \{\{\text{TECNC(i,j)}\}\} \otimes \{\{\text{TECH (i,j)}\}\} = \{\{\text{TECx (i,j)}\}\} \otimes \{\{\text{Retx (i,j)}\}\} \tag{43}$$

$$\{ [\text{Tbx} \ (\mathbf{i}, \mathbf{j})] \} = \{ [\text{PROD} \ (\mathbf{i}, \mathbf{j} \mathbf{1})], [\text{TECHNC} \ (\mathbf{i}, \mathbf{j})] \} \tag{44}$$

$$\{ [\text{Retx (i,j)}] \} = \{ [\text{PRED (i,j1)}], [\text{TECHNC (i,j)}], [\text{TECH (i,j)}] \} \tag{45}$$

$$\{\text{KPlitch}(\mathbf{0}, \mathbf{1})\} = [\text{Tbx}\ (\mathbf{i}, \mathbf{j})] \,\text{\AA} \tag{46}$$

$$\{\text{KPItech } (0, 2)\} = \{\text{[Retx } (\mathbf{i}, \mathbf{j})]\} \tag{47}$$

$$\{\text{KPlitch }(\mathbf{0})\} = \{\text{KPlitch}(\mathbf{0}, \mathbf{1})\} \otimes \{\text{KPlitch}(\mathbf{0}, \mathbf{2})\} \tag{48}$$

In order to create a complex set of KPI indicators related to business processes implemented and operated at tactic and operational management level, an

f g¼ ½ � Petx ið Þ *;* j1 YTotfinmanpAssetst ð Þ <sup>0</sup> *;* YTotfmatmanpAssetst ð Þ <sup>0</sup> (23)

f g ½ � Petx ið Þ *;* j1 ⊗ f g ½ � Pe ið Þ *;* j2 ¼ f g ½ � Tbex ið Þ *;* j ⊗ f g ½ � Ret ið Þ *;* j (24)

(25)

(26)

After installment of previous relations into formula (24) formula (25) might be

<sup>Y</sup>TotfinmanpAssetst ð Þ <sup>0</sup> *;* YTotfmatmanpAssetst ð Þ <sup>0</sup> <sup>⊗</sup> f g¼ ½ � PCP ið Þ *;* <sup>j</sup> f g ½ � Tbex ið Þ *;* <sup>j</sup> <sup>⊗</sup> f g ½ � Ret ið Þ *;* <sup>j</sup>

the {[Tbex (i, j)]} linguistic contains data closely related to quantity of financial

f g ½ � Tbex ið Þ *;* j ¼ f g ½ � Mark\_res\_assets\_fin\_ires 0ð Þ *;* ½ � Mark\_res\_assets\_mat\_ires 0ð Þ *;*

the {[Retx (i, j)]} linguistic contains data closely related to quantity of financial and material asset generated based on the actual firm or company internal resources

In general, the above-mentioned algorithm enables determining KPIprod (0, 1)}

{KPIprod (0, 1)} = {[Tbex (i, j1)]} –the first Primary KPI indicator, which indicates real possibilities of the firm or company business represented by financial and material assets with respect to the firm or company production internal

{KPIprod (0, 2)} = {[Retx (i, j2)]} – the second Primary KPI indicator, which indicates real possibilities of the firm or company business represented by financial and material assets with respect to the firm or company production financial and material cost. With respect to the above-mentioned issues the following clause

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

f½ � PROD ið Þ *;* j1 g ¼ fKPIprod 1ð Þ *;* 2 g ¼ f g KPIprod 0ð Þ *;* 1 ⊗ f g KPIprod 0ð Þ *;* 2 (30)

However, the similar sequence of steps (algorithm) might be applied when quantifying and generating KPI indicators for further main processes, sales and

½ � Mark\_res\_assets\_fin\_ires 0ð Þ , Mark\_res\_costs\_fin 0 <sup>½</sup> ð Þ�g (27)

fKPIprod 0ð Þ *;* 1 g ¼ f g ½ � Tbex ið Þ *;* j1 (28) f g KPIprod 0ð Þ *;* 2 ¼ f g ½ � Retx ið Þ *;* j2 (29)

and material asset generated based on the actual firm or company internal

f g ½ � Retx ið Þ *;* j ¼ f½ � Mark\_res\_assets\_fin\_ires 0ð Þ , Mark\_res\_costs\_fin 0 ½ � ð Þ ,

and KPIprod (0, 2)}, while formulas (28) and (29) might be postulated.

with respect to appropriate financial and material costs.

When applying the PBPL Equation its general form, (see also formula (24))

formula (25) might be postulated.

*Operations Management - Emerging Trend in the Digital Era*

postulated.

where

resources.

where

resources.

might be postulated:

(29) and (30).

**172**

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 described within subsequent sections.

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

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

¼ f½ � CUST ið Þ *;* <sup>1</sup> , CUST i ½ � ð Þ *;* <sup>2</sup> , … *::*½CUST <sup>ð</sup>i, m2Þ�g (53)

In the next step, an appropriate {[MROPsel (i, j)]} set for each customer will be

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

<sup>⊗</sup> MROPsel f g ½ � ð Þ <sup>i</sup>*;* j3 <sup>⊗</sup> MROPselfinass f g ½ � ð Þ <sup>i</sup>*;* j4 <sup>⊗</sup> MROPselfincosts f g ½ � ð Þ <sup>i</sup>*;* j5

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

> 2 , MROPsel i*;* j

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

) f MROPsel ½ � ð Þ <sup>i</sup>*;* <sup>j</sup> , <sup>⇔</sup> f½ BP I*;* <sup>j</sup>

<sup>¼</sup> f g ½ � Tbexbp ið Þ *;* <sup>j</sup> <sup>⊗</sup> f g ½ � Retxbp ið Þ *;* <sup>j</sup> (60)

{[Tbexbp (i, j)]} = {[[BP (I, j6)]} – list of BP groups needed for production of

Formula (24) indicates a list of relations among BP groups and market required

f g ½ � Retxbp ið Þ *;* j ¼ f MROPsel ½ � ð Þ i*;* j , f½ BP I*;* j

MROPselfincosts ½ ð Þ i*;* j5 �g

6

market required output products quantified via {[MROPsel (i, j)],

6

2

2

, MROPsel ½ � ð Þ i, j , MROPselfinass ½ � ð Þ i, j , MROPselfincosts ½ � ð Þ i, j

2

<sup>⇔</sup> MROPsel f g ½ � ð Þ <sup>i</sup>*;* <sup>j</sup> (54)

, MROPsel f g ½ � ð Þ <sup>i</sup>*;* j2 (56)

, MROPsel f g ½ � ð Þ <sup>i</sup>*;* <sup>j</sup> (57)

3 , MROPselfinass i*;* j

(55)

4

(58)

,

6 <sup>g</sup> (59)

6

<sup>g</sup> (61)

data concerned with the customers.

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

2

2

of any market required output products.

¼ f g ½ � Tbexc ið Þ *;* j ⊗ f g ½ � Retxc ið Þ *;* j

incl. Financial costs and financial assets.

f g ½ � CONTRACTC ið Þ ¼¼ Π f CUST i*;* j

formula (70) might be postulated.

∀ MROPsel f g ½ � ð Þ i*;* j ∃ BP I*;* j

MROPsel ½ � ð Þ i*;* j *;* BP I*;* j

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

f g¼ ½ � Retxc i, j ð Þ CUST i, j2

where Index m2 means a number of customers.

<sup>∃</sup> MROPsel f g ½ � ð Þ <sup>i</sup>*;* <sup>j</sup> ) CUST i*;* <sup>j</sup>

f g ½ � Tbexc ið Þ *;* j ¼ f CUST i*;* j

f g ½ � CONTRACTB ið Þ ¼ Π f CUST i*;* j

assigned, while formula (19) might be postulated.

CUST i*;* j

∀ CUST i*;* j

CUST i*;* j

j=1 …m3 j2 = 1 …m2

j2 = 1 …m2

output product group.

**175**

2
