**5.3 Case study**

### *5.3.1 Determination of production process KPI indicators*

The case study aim is to show how the derived math formulas and relations should be applied in a practice, when calculating actual data. The algorithm proposed within previous sections is passing through the following main phases:

After having applied formulas (77–80), we shall get values for primary KPI

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

f g KPI 0ð Þ ¼ f½ � 1*;* 000*;* 000 Euros , 200 ½ � *;* 000 Euros , 100 ½ *;* 000 pp�g, 50½ � *;* 000 Euros ,

This expression means that the primary KPI indicator s closely related to the production core process quantified via [PROD (i, j1)]}. However, that KPI indicator does not consider the firm or company real possibilities related to its internal

As a result of that adequate coefficient should be determined. They might be calculated based on data contained within appropriate technical and economic

However our disposals are 170,000 Euros only and an appropriate coefficient

Subsequently, we shall get s appropriate values related to {KPI (1)} and {KPI (2)} with the use of formula (8a) (8b). It means 1,000,000 x 0, 85, 200,000 x 0,85, 100,000 x 0,85 and 50,000 x0,85 and we get correct values for {KPI (1)} and {KPI (2)} indicators. Those indicators are denoted **as primary indicators** and they are closely related to core production process running at strategic management level and create bases for determination of the secondary KPI indicator values.

Let us consider the {KPI (2)} indicator values, which indicates that costs for production of [100,000 pp]} are [50,000 Euros]}. Now, we shall try decomposing the {KPI (2)} related to actual contracts and groups of business processes assigned to those contracts. However, before we start doing that, we have to manage several auxiliary actions. The first one is closely related to market required output products

*Step 1* Determination of product number with respect to adequate Coef value.

½Mark\_res\_assets\_mat\_ires 0ð Þ�¼f½ � 100*;* 000 pp x 0, 85 ¼ 85*;* 000 pp (86)

Step 2 The {[MROP (i, j)]} content will be divided into subordinated product

f g ½ � MROP ið Þ *;* j ¼ 85*;* 000 pp (87)

½ �¼ MROP ið Þ *;* 1 ½ � bowls ¼ 30*;* 000 pp (88) ½ �¼ MROP ið Þ *;* 2 ½ � bottles ¼ 30*;* 000 pp (89) ½ �¼ MROP ið Þ *;* 3 ½ � vases ¼ 25*;* 000 pp (90)

quantified via {[MROP (i, j)]}. We shall do it within following steps:

Coef ¼ 170, 000*=*200000 ¼ 0, 85 (85)

f g KPI 1ð Þ ¼ f g ½ � 1*;* 000*;* 000 Euros *;* ½ � 200*;* 000 Euros (82) f g KPI 2ð Þ ¼ f g ½ � 100*;* 000 pp , 50½ *;* 000 Euros�g (83)

(84)

indicators, with respect to formulas (82) and (83).

1 <sup>g</sup>

norms with the use of the following consideration.

*5.3.3 Determination of primary KPI indicators*

*5.3.4 Determination of secondary KPI indicators*

might be calculated based on formula

PROD i*;* j

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

resources.

classes.

**179**


Furthermore, appropriate phases will be explained in more details.

### *5.3.2 Determination of initial KPI indicators*

Before that phase is being activated a set of adequate data should be prepared, while the data are categorized as the market research results and the firm or company internal resources. The market research results inform us about possibilities how to apply our production in market and give us information how many products is the market able to accept and in which structure and what about financial assets might be generated as a result of that acceptance. However, the information related to adequate costs plays a role of principle importance as well. It means, we are able to answer the question related to the linguistic set content postulated within formulas (77–80)2, 3, 4, 5.

$$\{\mathbf{Y}^{\text{Totmat}}\_{\text{Assets}}\} = [\mathbf{100000}\ \mathbf{pp}],\tag{77}$$

$$\mathbf{\dot{x}}\begin{bmatrix} \mathbf{Y}^{\text{Totfin}} \\ \text{Assetst} \end{bmatrix} = \begin{bmatrix} \mathbf{10000000} \ \mathbf{Euros} \end{bmatrix} \tag{78}$$

$$\begin{bmatrix} \mathbf{X}^{\text{Totfin}} \text{Cats} \ (\mathbf{0}) \end{bmatrix} = \begin{bmatrix} \mathbf{200000} \ \text{Euros} \end{bmatrix} \tag{79}$$

$$\begin{bmatrix} \mathbf{X}^{\text{Totmat}} \, \_{\text{Cotts}} \begin{pmatrix} \mathbf{0} \end{pmatrix} \end{bmatrix} = \begin{bmatrix} \mathbf{50000} \, \mathbf{E} \mathbf{u} \mathbf{ros} \end{bmatrix} \tag{80}$$

With respect to those issues, the initial KPI indicator postulated via formula one might be indicated as follows:

$$\begin{aligned} \{\text{KPI} \left( \mathbf{0} \right) \} &= \left\{ \left[ \mathbf{X}^{\text{Totfin}}\_{\text{Cots}} \left( \mathbf{0} \right) \right], \left[ \mathbf{X}^{\text{Totmat}}\_{\text{Cots}} \left( \mathbf{0} \right) \right], \left[ \mathbf{Y}^{\text{Totfin}}\_{\text{Assets}} \right], \left[ \mathbf{Y}^{\text{Totmat}}\_{\text{Assets}} \right] \right\} \\ &= \{ \left[ \mathbf{100000} \, \mathbf{pp} \right], \left[ \mathbf{10000000} \, \mathbf{Euros} \right], \left[ \mathbf{2000000} \, \mathbf{Euros} \right], \left[ \mathbf{500000} \, \mathbf{Euros} \right] \} \end{aligned} \tag{81}$$

<sup>2</sup> Pp – number of products, which might be accepted in the market in pieces

<sup>3</sup> Financial assets, which could be achieved based on acceptance of the product piece amount at the market

<sup>4</sup> A need of total financial costs needed for production of products, while that number includes material, technological HR and operational costs

<sup>5</sup> This value represents costs for recruitment of adequate material inputs

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

After having applied formulas (77–80), we shall get values for primary KPI indicators, with respect to formulas (82) and (83).

f g KPI 1ð Þ ¼ f g ½ � 1*;* 000*;* 000 Euros *;* ½ � 200*;* 000 Euros (82)

f g KPI 2ð Þ ¼ f g ½ � 100*;* 000 pp , 50½ *;* 000 Euros�g (83)

f g KPI 0ð Þ ¼ f½ � 1*;* 000*;* 000 Euros , 200 ½ � *;* 000 Euros , 100 ½ *;* 000 pp�g, 50½ � *;* 000 Euros , PROD i*;* j 1 <sup>g</sup>

(84)

This expression means that the primary KPI indicator s closely related to the production core process quantified via [PROD (i, j1)]}. However, that KPI indicator does not consider the firm or company real possibilities related to its internal resources.

As a result of that adequate coefficient should be determined. They might be calculated based on data contained within appropriate technical and economic norms with the use of the following consideration.

#### *5.3.3 Determination of primary KPI indicators*

However our disposals are 170,000 Euros only and an appropriate coefficient might be calculated based on formula

$$\text{Coef} = \text{170}, \text{000}/\text{200} \\ \text{000} \\ \text{0} = \text{0}, \text{85} \tag{85}$$

Subsequently, we shall get s appropriate values related to {KPI (1)} and {KPI (2)} with the use of formula (8a) (8b). It means 1,000,000 x 0, 85, 200,000 x 0,85, 100,000 x 0,85 and 50,000 x0,85 and we get correct values for {KPI (1)} and {KPI (2)} indicators. Those indicators are denoted **as primary indicators** and they are closely related to core production process running at strategic management level and create bases for determination of the secondary KPI indicator values.

#### *5.3.4 Determination of secondary KPI indicators*

Let us consider the {KPI (2)} indicator values, which indicates that costs for production of [100,000 pp]} are [50,000 Euros]}. Now, we shall try decomposing the {KPI (2)} related to actual contracts and groups of business processes assigned to those contracts. However, before we start doing that, we have to manage several auxiliary actions. The first one is closely related to market required output products quantified via {[MROP (i, j)]}. We shall do it within following steps:

*Step 1* Determination of product number with respect to adequate Coef value.

½Mark\_res\_assets\_mat\_ires 0ð Þ�¼f½ � 100*;* 000 pp x 0, 85 ¼ 85*;* 000 pp (86)

$$\{ [\text{MROP} \ (\text{i}, \text{j})] \} = \mathbf{85}, \mathbf{000} \text{ pp} \tag{87}$$

Step 2 The {[MROP (i, j)]} content will be divided into subordinated product classes.

½ �¼ MROP ið Þ *;* 1 ½ � bowls ¼ 30*;* 000 pp (88)

$$[\text{MROP} \ (\text{i}, \text{2})] = [\text{bottle} = \text{30}, \text{000 pp}] \tag{89}$$

½ �¼ MROP ið Þ *;* 3 ½ � vases ¼ 25*;* 000 pp (90)

**5.3 Case study**

*5.3.1 Determination of production process KPI indicators*

*Operations Management - Emerging Trend in the Digital Era*

• Determination of initial KPI indicators

• Determination of primary KPI indicators

• Determination of secondary KPI indicators

• Determination of tertiary KPI indicators

*5.3.2 Determination of initial KPI indicators*

postulated within formulas (77–80)2, 3, 4, 5.

might be indicated as follows:

technological HR and operational costs

f g KPI 0ð Þ <sup>¼</sup> <sup>X</sup>Totfin

market

**178**

YTotmat

YTotfin

XTotfin

XTotmat

Costs ð Þ <sup>0</sup> *;* XTotmat

<sup>2</sup> Pp – number of products, which might be accepted in the market in pieces

<sup>5</sup> This value represents costs for recruitment of adequate material inputs

Assetst

Assetst

The case study aim is to show how the derived math formulas and relations should be applied in a practice, when calculating actual data. The algorithm proposed within previous sections is passing through the following main phases:

Furthermore, appropriate phases will be explained in more details.

while the data are categorized as the market research results and the firm or company internal resources. The market research results inform us about possibilities how to apply our production in market and give us information how many products is the market able to accept and in which structure and what about financial assets might be generated as a result of that acceptance. However, the information related to adequate costs plays a role of principle importance as well. It means, we are able to answer the question related to the linguistic set content

Before that phase is being activated a set of adequate data should be prepared,

With respect to those issues, the initial KPI indicator postulated via formula one

<sup>3</sup> Financial assets, which could be achieved based on acceptance of the product piece amount at the

<sup>4</sup> A need of total financial costs needed for production of products, while that number includes material,

Costs ð Þ <sup>0</sup> *;* YTotfin

 ¼ f g ½ � 100000 pp *;* ½ � 1000000 Euros *;* ½ � 200000 Euros *;* ½ � 50000 Euros

g ¼ ½ � 100000 pp , (77)

<sup>¼</sup> ½ � 1000000 Euros (78)

Costs ð Þ <sup>0</sup> <sup>¼</sup> ½ � 200000 Euros (79)

Costs ð Þ <sup>0</sup> <sup>¼</sup> ½ � 50000 Euros (80)

Assetst *;* YTotmat

Assetst

(81)

and appropriate customers {[Cust (1)]}, {[Cust (2)]} and {[Cust(3)]} will be determined Subsequently, we shall assign selected product groups to adequate customers and will be generated adequate orders.

$$\{ [\text{Cust}\ (1)] \} = \{ [\text{bowls} = \text{30}, \text{000 pp}], [\text{bottle} = \text{30}, \text{000 pp}] \} \tag{91}$$

$$\{ [\text{Cust } (2)] \} = \{ [\text{bowls} = 30,000 \text{ pp}], [\text{vases} = 25,000 \text{ pp}] \} \tag{92}$$

$$\{ [\text{Cust } (2)] \} = [\text{botters} = \text{30,000 pp}], [\text{passes} = \text{25,000 pp}] \tag{93}$$

In that step we shall extend the orders and add the data concerned with adequate financial costs (see also formulas 94–97).

$$\begin{aligned} \{ [\text{RROP}\_{\text{selfinst}} \ (\text{i}, \text{j})] \} &= [\text{X}^{\text{TOTmat}}\_{\text{Costs}} \ (\text{0})] \ \text{x Coef} = [\text{50, 000 Exros}] \ \text{x 0, 85} \\ &= [\text{42, 500 Exros}] \\ \{ [\text{Cust } (\text{i})] \} &= \{ [\text{bowls} = \text{30, 000 pp}], [\text{bottle} = \text{30, 000 pp}], [\text{14, 000 Exros}] \end{aligned} \tag{95}$$
 
$$\{ [\text{Cust } (\text{2})] \} = \{ [\text{bowls} = \text{30, 000 pp}], [\text{varses} = \text{25, 000 pp}], [\text{18, 000 Exros}] \} \tag{96}$$
 
$$\{ [\text{Cust } (\text{3})] \} = [\text{buttle} = \text{30, 000 pp}], [\text{vases} = \text{25, 000 pp}], [\text{10500}] \} \tag{97}$$

and we shall create the basic order (CONTRACTC).

$$\{ [\text{CONTRACTC}(i)] \} = \{ [\text{Cust }(1)], [\text{Cust }(2)], \{\text{Cust }(3)\} ] \tag{98}$$

However, a set of adequate business processes should be applied in order to manage production of products related to pre-defined orders or contracts as well, while formula (85) should be extended about linguistic sets, which quantify those groups of business processes – see also formula (50).

f g ½ � CONTRACTD ið Þ ¼ f½ � Cust 1ð Þ , BPG1 i*;* j <sup>61</sup> , Cust 2 ½ � ð Þ , BPG2 i*;* <sup>j</sup> <sup>62</sup> , Cust 3ð Þ�*;* BPG3 i*;* j 6 (99)

With respect to the above-mentioned issues the KPI (i, 2) content is defined via formula (88) and KPI (i, 2) content is defined via formula (89) and we have derived a set of the **secondary KPI indicators.**

$$\text{KPI}\left(\text{i}, \text{2}\right) = \{ \left[ \text{Cust}\left(\text{1}\right) \right], \left[ \text{Cust}\left(\text{2}\right) \right], \left[ \text{Cust}\left(\text{3}\right) \right] \}\tag{100}$$

above-mentioned formulas we shall get partial KPI indicators related the selected BP external and internal metrics in form of adequate linguistic sets (see also for-

BP (1,1) BP (1,1)

BP (1,2) BP (1,2)

BP (1,3) BP (1,3)

Description

Description

Description

f g ½ � KPIemb ið Þ *;* 3 ¼ f g ½ � BP 1ð Þ *;* 1 ½ � bowls ¼ 10*;* 000 pp *;* ½ � 1700 Euros (102) f g ½ � KPIimb ið Þ *;* 3 ¼ f½ � BP 1ð Þ *;* 1 , HRcosts ½ � ¼ 1100 Euros , DEVcosts ½ � ¼ 800 ,

A set of derived KPI indicators via formulas (91, 92, 93) is closely related so selected BP implemented and operated at operational management level and is

The case study previous sections deals with KPI indicator creation and decomposition steps, while those steps are closely related to three management levels: (a) strategic, (b) tactic, and (c) operational management level. In that section an overview summary with supplementary visual components will be done.

KPIter ¼ KPIemb ið Þ *;* 3 ⊗ KPIemb ið Þ *;* 3 (104)

(103)

½Toolcosts ¼ 300 Euros�g

mulas (91) and (92).

*Source: The Authors.*

**Table 3.**

**Product class value BPG**

[bowls = 30,000 pp] [BPG1

**Product class value BPG**

[bowls = 30,000 pp] [BPG1

*Source: The Authors.*

**Table 2.**

**number**

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

(i, 1)],

[BPG1 (i, 2)],

[BPG1 (i, 3)],

*Business processes as the BP group members (external metrics).*

**number**

(i, 1)],

[BPG1 (i, 2)],

[BPG1 (i, 3)],

*Business processes as the BP group members (internal metrics).*

**BP Number**

**BP Number**

BP (1,1) BP (1,1)

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

BP (1,2) BP (1,2)

BP (1,3) BP (1,3)

Description

Description

Description

**BP Description BP External metrics**

**BP Description BP Internal metrics**

**HR Costs Dev**

**costs**

1100Euros 800 300

1100Euros 800 300

1100Euros 800 300

**Tool cost**

**Output prod assets Input mat.**

[bowls = 10,000 pp] 1700 Euros

[bowls = 10,000 pp] 1700 Euros

[bowls = 10,000 pp] 1700 Euros

**Costs**

denoted as **tertiary indicator set.**

*5.3.6 Case study – summary*

**181**

$$\text{KPI}\begin{pmatrix}\text{i},\text{3}\end{pmatrix} = \{ [\text{Cust }(\text{1})], [\text{BPG1}\begin{pmatrix}\text{i},\text{j}\_{61}\end{pmatrix}], [\text{Cust }(\text{2})], [\text{BPG2}\begin{pmatrix}\text{i},\text{j}\_{62}\end{pmatrix}], \{\text{Cust }(\text{3})\}, [\text{BPG3}\begin{pmatrix}\text{i},\text{j}\_{6}\end{pmatrix}] \} \tag{101}$$

Each business process group consists of appropriate business process quantified via adequate linguistic set (see also **Tables 2** and **3**).

#### *5.3.5 Determination of tertiary KPI indicators*

Let us consider a group of business processes represented by **Tables 2** and **3** and let us select one of those business processes in order to derive the tertiary KPI indicators, which are closely related to BP external and internal metrics. Formulas (63 and 64) will be applied for those purposes. When installing adequate data in the *Business Process Linguistic Modeling: Theory and Practice Part I: BPLM Strategy Creator DOI: http://dx.doi.org/10.5772/intechopen.95096*


#### **Table 2.**

and appropriate customers {[Cust (1)]}, {[Cust (2)]} and {[Cust(3)]} will be determined Subsequently, we shall assign selected product groups to adequate

f g ½ � Cust 1ð Þ ¼ f g ½ � bowls ¼ 30*;* 000 pp *;* ½ � bottles ¼ 30*;* 000 pp (91) f g ½ � Cust 2ð Þ ¼ f g ½ � bowls ¼ 30*;* 000 pp *;* ½ � vases ¼ 25*;* 000 pp (92) f g ½ � Cust 2ð Þ ¼ ½ � bottles ¼ 30*;* 000 pp , vases ½ � ¼ 25*;* 000 pp (93)

In that step we shall extend the orders and add the data concerned with adequate

f g ½ � Cust 1ð Þ ¼ f½ � bowls ¼ 30*;* 000 pp , bottles ½ � ¼ 30*;* 000 pp , ½14*;* 000 Eurosg

f g ½ � Cust 2ð Þ ¼ f g ½ � bowls ¼ 30*;* 000 pp *;* ½ � vases ¼ 25*;* 000 pp *;* ½ � 18*;* 000 Euros

f g ½ � Cust 3ð Þ ¼ ½ � bottles ¼ 30*;* 000 pp , vases ½ � ¼ 25*;* 000 pp , 10500 ½ �g (97)

However, a set of adequate business processes should be applied in order to manage production of products related to pre-defined orders or contracts as well, while formula (85) should be extended about linguistic sets, which quantify those

Cust 3ð Þ�*;* BPG3 i*;* j

, Cust 2 ½ � ð Þ , BPG2 i*;* <sup>j</sup>

With respect to the above-mentioned issues the KPI (i, 2) content is defined via formula (88) and KPI (i, 2) content is defined via formula (89) and we have derived

Each business process group consists of appropriate business process quantified

Let us consider a group of business processes represented by **Tables 2** and **3** and

let us select one of those business processes in order to derive the tertiary KPI indicators, which are closely related to BP external and internal metrics. Formulas (63 and 64) will be applied for those purposes. When installing adequate data in the

f½ � CONTRACTC ið Þ g¼f½ � Cust 1ð Þ , Cust 2 ½ � ð Þ , Cust 3 f g ð Þ� (98)

61

6

KPI ið Þ¼f *;* 2 ½ � Cust 1ð Þ , Cust 2 ½ � ð Þ , Cust 3 f g ð Þ� (100)

62

, Cust 3ð Þ�*;* BPG3 i*;* <sup>j</sup>

, Cust 2 ½ � ð Þ , BPG2 i*;* <sup>j</sup>

and we shall create the basic order (CONTRACTC).

groups of business processes – see also formula (50).

f g ½ � CONTRACTD ið Þ ¼ f½ � Cust 1ð Þ , BPG1 i*;* j

via adequate linguistic set (see also **Tables 2** and **3**).

*5.3.5 Determination of tertiary KPI indicators*

61

a set of the **secondary KPI indicators.**

KPI ið Þ¼f *;* 3 ½ � Cust 1ð Þ , BPG1 i*;* j

**180**

Costs ð Þ <sup>0</sup> x Coef <sup>¼</sup> ½ � <sup>50</sup>*;* 000 Euros x 0, 85 <sup>¼</sup> ½ � <sup>42</sup>*;* 500 Euros (94)

(95)

(96)

62 ,

(99)

6

(101)

customers and will be generated adequate orders.

*Operations Management - Emerging Trend in the Digital Era*

financial costs (see also formulas 94–97).

MROPselfinass f g ½ � ð Þ <sup>i</sup>*;* <sup>j</sup> <sup>¼</sup> XTotmat

*Business processes as the BP group members (external metrics).*


#### **Table 3.**

*Business processes as the BP group members (internal metrics).*

above-mentioned formulas we shall get partial KPI indicators related the selected BP external and internal metrics in form of adequate linguistic sets (see also formulas (91) and (92).

$$\{ [\text{KPIemb } (\mathbf{i}, \mathbf{3})] \} = \{ [\text{BP } (\mathbf{1}, \mathbf{1})] \text{ [bowls} = \mathbf{10}, \mathbf{000} \text{ pp}], [\text{1700 Euros}] \} \tag{102}$$

$$\{ [\text{KPIimb } (\mathbf{i}, \mathbf{3})] \} = \{ [\text{BP } (\mathbf{1}, \mathbf{1})], [\text{HRcosts} = \mathbf{1100 Euros}], [\text{DEVcosts} = \mathbf{800}],$$

$$\{ \text{Toolcosts} = \mathbf{300 Euros} \}$$

(103)

$$\text{KPIter} = \text{KPIemb}\,\left(\text{i}, \mathfrak{Z}\right) \otimes \text{KPIemb}\,\left(\text{i}, \mathfrak{Z}\right) \tag{104}$$

A set of derived KPI indicators via formulas (91, 92, 93) is closely related so selected BP implemented and operated at operational management level and is denoted as **tertiary indicator set.**

#### *5.3.6 Case study – summary*

The case study previous sections deals with KPI indicator creation and decomposition steps, while those steps are closely related to three management levels: (a) strategic, (b) tactic, and (c) operational management level. In that section an overview summary with supplementary visual components will be done.
