*5.4.1 Definition of the problem*

*PMt* ¼ *μtf Xt* ð Þ¼ ; *β g St* ð Þ ; *γ f Xt* ð Þ ; *β* (18)

� � *f Xit*; *β*^*<sup>i</sup>*

*<sup>s</sup>* ð Þ *<sup>i</sup>* <sup>¼</sup> 1, … ,*r and t* <sup>¼</sup> 1, … , *<sup>s</sup>* (20)

ð Þ *i* ¼ 1, … ,*r and t* ¼ 1, … , *s* (21)

*<sup>s</sup>* ð Þ *<sup>i</sup>* <sup>¼</sup> 1, … ,*r and t* <sup>¼</sup> 1, … , *<sup>s</sup>* (22)

� � (19)

*it* )

To estimate the parameter γ and β, both parameters further designated to be ^*γ*

In this case, PVit is the performance values of the processing unit or the firm. If

Both the Eqs. (19) and (20) result in the currency value, however, that is further common, it would be superior if presented in the form of an index ratio. Consequently, PVit should be divided by the real output (yit), instead of a "devisor" (*y*<sup>Δ</sup>

The average value (APR) of Eq. (21) is calculated using the subsequent formula:

Using this method, it is plausible to consider the amount of value between the IT capital presence and the absence of it within a capital expenditure of the firm. In other words, the IT value model using the PAV guides the study to comprehend the

In essence, the applied method in this chapter is identical to the abovementioned method, namely starting from the structure of the conceptual model of IT value consisting of two types of models: three and two-factor models up until valuation of performance measures. However, the difference is simply on the goal, namely the earlier method aims to examine the PAV theory using the real facts to make sure that the IT inclusion in the business organization is material and valuable, while, this subchapter is to validate the resulted experiment data in several IT-based firms to certify that the PAV theory encounters the criteria of system measurements from a statistical point of views [8] to identify the level of the IT value of each firm. The

Here, the exploited data have been covering the period, for example, from 2004 to 2014, collected from the audited financial statements and the published annual reports. To compare between the presence (with It) and absence (without It) of the IT capital in the PAV approach [20], the estimation involves both Xt = (Kt, Lt, It), and Xt = (Kt, Lt) where t = 1..., 11 at the time of confirmed data from 2004 to 2014

as suggested by [19] to be an index of performance ratio (PR). Therefore, the equation seems as the Eq. (21), and if averaged, the equation becomes the Eq. (22), which it can measure to what extent value the role of IT spending in the business

� � <sup>¼</sup> *g Si t*ð Þ; ^*γ<sup>i</sup>*

<sup>d</sup>*it* <sup>¼</sup> *<sup>μ</sup>*^*i t*ð Þ *f Xit*; *<sup>β</sup>*^*<sup>i</sup>*

*PVit*

and *β*^, thus the Eq. (18) converts to:

averaged, the Eq. (19) results in:

*PVit* ¼ *PM*

*Computational Optimization Techniques and Applications*

*APVi* <sup>¼</sup> <sup>X</sup>

organization, compared with no the investment.

*APRi* <sup>¼</sup> <sup>X</sup>

validation is through model data examinations.

for both static and dynamic speed of adjustment.

**5.3 The PAV approach validation**

value of IT.

**202**

*t*

*PRit*

*PRit* <sup>¼</sup> *PVit yit*

*t*

As mentioned, the primary problem of this chapter is how to carry out the need of worthy performance of the IT-based business organization to sustain competitive advantages by optimal costs, especially IT costs. Since this problem involves a variety of factors such as functional subsystems of RBV point of views, financial systems, competitive forces, business performance, risk management, resource management, and so forth. Accordingly, to solve this problem needs a systems engineering approach integrating various components into a unity solving the needed values.

## *5.4.2 Invention, evaluation, and selection of alternative solutions*

In order to solve the problem, various alternative solutions could be a means to undo. Examples of the alternatives are with increasing the firm performance while the IT capital is constant, improving the IT competency and capability of the organization, and cost optimization by encouraging innovation, restructuring, IT cost-saving/ efficiency, and effective IT procurement. Indeed, each alternative has advantages and disadvantages, therefore, the preferred solution is all alternatives combinations to compile in a systems engineering process.

In the meantime, the preferred solution selected based on the five criteria that Kosky et al. (2013) initiated, namely "minimize information content, maintain the independence of functional requirements, ease of manufacture, robustness, and design for adjustability" [10].

#### *5.4.3 Detail of design*

According to [56], the systems engineering life cycle phases and the systems engineering method merges, which denotes that for each engineering phase of a horizontal nature, is vertically explored using these engineering models. This step is for concept development and engineering development phases, including each block of the phases. Meanwhile, the post-development phase is beyond this study. Consequently, the analytical results separated into two tables.

#### *5.4.4 Development and validation of the model*

Furthermore, the information technology value engineering model exists to develop three types of models: parallel, serial, and hybrid ITVE. Likewise, their validation takes place to certify that the model is reasonable philosophically and technically.

## *5.4.4.1 Parallel approach model*

The parallel model is in **Figure 3** [25, 26]. This figure explicates that the principal subsystems of the model consist of firm performance (FP), firm core competence (FCC), firm capability (FC), and IT resource (ITR), which each subsystem links one to another in a parallel fashion. In a mathematical relationship, the parallel connection manifests an add operation (see **Figure 3**). It implies that the input (yt \*) is proportionally divided into four sub-inputs, i.e. y\*1t, y\*2t, y\*3t, and y\*4t or

yt \* = y\*1t + y\*2t + y\*3t + y\*4t. Each subsystem has each speed of adjustment (μit, i = 1,2,3,4 and t = period), i.e. FP has μ1t, FCC has μ2t, FC has μ3t, and ITR has μ4t, whether static (constant) or dynamic [20]. Likewise, the output consists of four sub outputs, i.e. y1t, y2t, y3t, and y4t, which can appear as yt = y1t + y2t + y3t + y4t.

Using the partial adjustment valuation approach [see the Eq. (3)], each subsystem could be mathematically revealed as follows [25, 26], see **Figure 3**:

Firm Performance (FP):

$$
\mu\_{\mathbf{1}\_{\ell}} - \boldsymbol{\mathcal{y}}\_{\mathbf{1}\_{\ell-1}} = \mu\_1 \left( \boldsymbol{\mathcal{y}}\_{\mathbf{1}\_{\ell}}^{\*} - \boldsymbol{\mathcal{y}}\_{\mathbf{1}\_{\ell-1}} \right) \tag{23}
$$

Where yt = the real output of period t, y1t = the real output of FP at period t, y\*1t = the desired output (input) of FP, y1t-1 = the real output of the previous period (t-1), and μ<sup>1</sup> = the constant speed of adjustment of FP. Similarly, y2t = the real output of FCC at period t, y\*2t = the desired output (input) of FCC at period t, y2t-1 = the real output of the previous period (t-1), and μ<sup>2</sup> = the constant speed of adjustment of FCC. Afterwards, y3t = the real output of FC at period t, y\*3t = the desired output (input) of FC at period t, y3t-1 = the real output of the previous period (t-1), and μ<sup>3</sup> = the constant speed of adjustment of FC. Finally, y4t = the real output of ITR at period t, y\*4t = the desired output (input) of ITR period t, y4t-1 = the real output of the previous period (t-1), and μ<sup>4</sup> = the constant speed of adjustment

Instead of the parallel fashion, the serial ITVEM appears, in which to do so, suppose the Eq. (24), the Eq. (26), the Eq. (28), and the Eq. (30) exhibit in a serial relationship (see **Figure 4**), with an assumption that each output of a subsystem fully becomes an input of the subsequent ones, the end result is as Eq. (32) [25, 26].

*<sup>t</sup>* <sup>þ</sup> *<sup>μ</sup>*3*μ*<sup>2</sup> <sup>1</sup> � *<sup>μ</sup>*<sup>1</sup> ð Þ*y*<sup>1</sup>*t*�<sup>1</sup> <sup>þ</sup> *<sup>μ</sup>*<sup>3</sup> <sup>1</sup> � *<sup>μ</sup>*<sup>2</sup> ð Þ*y*<sup>2</sup>*t*�<sup>1</sup> <sup>þ</sup> <sup>1</sup> � *<sup>μ</sup>*<sup>3</sup> ð Þ *<sup>y</sup>*<sup>3</sup>*t*�<sup>1</sup> h i

As for the explanation of the symbols is equal to the parallel ITVE.

*<sup>t</sup>* <sup>þ</sup> *<sup>μ</sup>*<sup>2</sup> <sup>1</sup> � *<sup>μ</sup>*<sup>1</sup> ð Þ*y*<sup>1</sup>*t*�<sup>1</sup> <sup>þ</sup> <sup>1</sup> � *<sup>μ</sup>*<sup>2</sup> ð Þ*y*<sup>2</sup>*t*�<sup>1</sup> h i

h i

The hybrid configuration [27] is an option for structuring each subsystem in the chapter. **Figure 5** explicates that the principal subsystems of the model consist of ITR, FC, FCC, and FP. It appears that the resources are the ITR consisting of the regular capital (Kt), the regular labor expense (Lt), and the technology spending, in this chapter related to IT spending (It). Furthermore, the resources become inputs of the FC subsystem as Kcap, Lcap, and Icap to be processed in resulting the FC output, viz. wmt (m = 1,2,3) or w1t, w2t, and w3t, see **Figure 5**. Likewise, the resources also become inputs of the FCC subsystem as Kcom, Lcom, and Icom to be processed in resulting the FC output, viz. vjt (j = 1,2,3) or v1t, v2t, and v3t, see

*<sup>t</sup>* <sup>þ</sup> *<sup>μ</sup>*4*μ*3*μ*<sup>2</sup> <sup>1</sup> � *<sup>μ</sup>*<sup>1</sup> ð Þ*y*<sup>1</sup>*t*�<sup>1</sup> <sup>þ</sup> *<sup>μ</sup>*4*μ*<sup>3</sup> <sup>1</sup> � *<sup>μ</sup>*<sup>2</sup> ð Þ*y*<sup>2</sup>*t*�<sup>1</sup> <sup>þ</sup> *<sup>μ</sup>*<sup>4</sup> <sup>1</sup> � *<sup>μ</sup>*<sup>3</sup> ð Þ *<sup>y</sup>*<sup>3</sup>*t*�<sup>1</sup> <sup>þ</sup> <sup>1</sup> � *<sup>μ</sup>*<sup>4</sup> ð Þ*yt*�<sup>1</sup>

(32)

of ITR.

*yt* <sup>¼</sup> *<sup>μ</sup>*1*<sup>y</sup>* <sup>∗</sup>

**Figure 4.**

**205**

*IT value engineering model in a serial relationship [25].*

<sup>þ</sup> *<sup>μ</sup>*<sup>3</sup> *<sup>μ</sup>*<sup>2</sup> *<sup>μ</sup>*1*<sup>y</sup>* <sup>∗</sup>

<sup>þ</sup> *<sup>μ</sup>*<sup>4</sup> *<sup>μ</sup>*<sup>3</sup> *<sup>μ</sup>*<sup>2</sup> *<sup>μ</sup>*1*<sup>y</sup>* <sup>∗</sup>

*5.4.4.2 Serial approach model*

*Information Technology Value Engineering (ITVE) DOI: http://dx.doi.org/10.5772/intechopen.95855*

> *<sup>t</sup>* <sup>þ</sup> <sup>1</sup> � *<sup>μ</sup>*<sup>1</sup> ð Þ*y*<sup>1</sup>*t*�<sup>1</sup> h i <sup>þ</sup> *<sup>μ</sup>*2*μ*1*<sup>y</sup>* <sup>∗</sup>

*5.4.4.3 Hybrid approach model*

$$
\boldsymbol{\nu}\_{\mathbf{1}\_{\ell}} = \mu\_{\mathbf{1}} \boldsymbol{\nu}\_{\mathbf{1}\_{\ell}}^{\*} + (\mathbf{1} - \mu\_{\mathbf{1}\_{\ell}}) \boldsymbol{\nu}\_{\mathbf{1}\_{\ell-1}} \tag{24}
$$

Firm Core Competence (FCC):

$$
\mu\_{2\_{\epsilon}} - \mu\_{2\_{\epsilon - 1}} = \mu\_2 \left( \mathcal{y}\_{2\_{\epsilon}}^{\*} - \mathcal{y}\_{2\_{\epsilon - 1}} \right) \tag{25}
$$

$$y\_{2\_t} = \mu\_2 y\_{2\_t}^\* + (1 - \mu\_2) y\_{2\_{t-1}} \tag{26}$$

Firm Capability (FC):

$$
\boldsymbol{\nu}\_{\mathfrak{Z}\_{\mathsf{k}}} - \boldsymbol{\nu}\_{\mathfrak{Z}\_{\mathsf{k}-1}} = \mu\_3 \left( \boldsymbol{\nu}\_{\mathfrak{Z}}^\* - \boldsymbol{\nu}\_{\mathfrak{Z}\_{\mathsf{k}-1}} \right) \tag{27}
$$

$$y\_{3\_t} = \mu\_3 y\_{3\_t}^\* + (1 - \mu\_3) y\_{3\_{t-1}} \tag{28}$$

Information Technology Resource (ITR):

$$
\mathcal{Y}\_{\mathfrak{A}\_t} - \mathcal{Y}\_{\mathfrak{A}\_{t-1}} = \mu\_4 \left( \mathcal{Y}\_{\mathfrak{A}\_t}^\* - \mathcal{Y}\_{\mathfrak{A}\_{t-1}} \right) \tag{29}
$$

$$\boldsymbol{\mathcal{Y}\_{\mathfrak{A}\_{t}}} = \mu\_{4}\boldsymbol{\mathcal{Y}\_{\mathfrak{A}\_{t}}^{\*}} + (\mathbf{1} - \mu\_{4})\boldsymbol{\mathcal{Y}\_{\mathfrak{A}\_{t-1}}} \tag{30}$$

If Eq. (24), Eq. (26), Eq. (28), and Eq. (30) are together added would result in Eq. (31) [25, 26]:

$$\begin{aligned} y\_t &= \mu\_1 y\_{1\_t}^\* + (\mathbf{1} - \mu\_1) y\_{1\_{t-1}} + \mu\_2 y\_{2\_t}^\* + (\mathbf{1} - \mu\_2) y\_{2\_{t-1}} + \\ &\quad \mu\_3 y\_{3\_t}^\* + (\mathbf{1} - \mu\_3) y\_{3\_{t-1}} + \mu\_4 y\_{4\_t}^\* + (\mathbf{1} - \mu\_4) y\_{4\_{t-1}} \end{aligned} \tag{31}$$

**Figure 3.** *IT value engineering model in a parallel relationship [25].*

*Information Technology Value Engineering (ITVE) DOI: http://dx.doi.org/10.5772/intechopen.95855*

Where yt = the real output of period t, y1t = the real output of FP at period t, y\*1t = the desired output (input) of FP, y1t-1 = the real output of the previous period (t-1), and μ<sup>1</sup> = the constant speed of adjustment of FP. Similarly, y2t = the real output of FCC at period t, y\*2t = the desired output (input) of FCC at period t, y2t-1 = the real output of the previous period (t-1), and μ<sup>2</sup> = the constant speed of adjustment of FCC. Afterwards, y3t = the real output of FC at period t, y\*3t = the desired output (input) of FC at period t, y3t-1 = the real output of the previous period (t-1), and μ<sup>3</sup> = the constant speed of adjustment of FC. Finally, y4t = the real output of ITR at period t, y\*4t = the desired output (input) of ITR period t, y4t-1 = the real output of the previous period (t-1), and μ<sup>4</sup> = the constant speed of adjustment of ITR.

#### *5.4.4.2 Serial approach model*

yt

Firm Performance (FP):

Firm Capability (FC):

Eq. (31) [25, 26]:

**Figure 3.**

**204**

Firm Core Competence (FCC):

\* = y\*1t + y\*2t + y\*3t + y\*4t. Each subsystem has each speed of adjustment

*Computational Optimization Techniques and Applications*

*<sup>y</sup>*1*<sup>t</sup>* � *<sup>y</sup>*1*t*�<sup>1</sup> <sup>¼</sup> *<sup>μ</sup>*<sup>1</sup> *<sup>y</sup>* <sup>∗</sup>

*<sup>y</sup>*<sup>2</sup>*<sup>t</sup>* � *<sup>y</sup>*<sup>2</sup>*t*�<sup>1</sup> <sup>¼</sup> *<sup>μ</sup>*<sup>2</sup> *<sup>y</sup>* <sup>∗</sup>

*<sup>y</sup>*<sup>3</sup>*<sup>t</sup>* � *<sup>y</sup>*<sup>3</sup>*t*�<sup>1</sup> <sup>¼</sup> *<sup>μ</sup>*<sup>3</sup> *<sup>y</sup>* <sup>∗</sup>

*<sup>y</sup>*<sup>4</sup>*<sup>t</sup>* � *<sup>y</sup>*<sup>4</sup>*t*�<sup>1</sup> <sup>¼</sup> *<sup>μ</sup>*<sup>4</sup> *<sup>y</sup>* <sup>∗</sup>

<sup>1</sup>*<sup>t</sup>* <sup>þ</sup> <sup>1</sup> � *<sup>μ</sup>*<sup>1</sup> ð Þ*y*<sup>1</sup>*t*�<sup>1</sup> <sup>þ</sup> *<sup>μ</sup>*<sup>2</sup> *<sup>y</sup>* <sup>∗</sup>

<sup>3</sup>*<sup>t</sup>* <sup>þ</sup> <sup>1</sup> � *<sup>μ</sup>*<sup>3</sup> ð Þ*y*<sup>3</sup>*t*�<sup>1</sup> <sup>þ</sup> *<sup>μ</sup>*<sup>4</sup> *<sup>y</sup>* <sup>∗</sup>

If Eq. (24), Eq. (26), Eq. (28), and Eq. (30) are together added would result in

*<sup>y</sup>*1*<sup>t</sup>* <sup>¼</sup> *<sup>μ</sup>*<sup>1</sup> *<sup>y</sup>* <sup>∗</sup>

*<sup>y</sup>*<sup>2</sup>*<sup>t</sup>* <sup>¼</sup> *<sup>μ</sup>*<sup>2</sup> *<sup>y</sup>* <sup>∗</sup>

*<sup>y</sup>*<sup>3</sup>*<sup>t</sup>* <sup>¼</sup> *<sup>μ</sup>*<sup>3</sup> *<sup>y</sup>* <sup>∗</sup>

*<sup>y</sup>*<sup>4</sup>*<sup>t</sup>* <sup>¼</sup> *<sup>μ</sup>*<sup>4</sup> *<sup>y</sup>* <sup>∗</sup>

Information Technology Resource (ITR):

*yt* <sup>¼</sup> *<sup>μ</sup>*<sup>1</sup> *<sup>y</sup>* <sup>∗</sup>

*IT value engineering model in a parallel relationship [25].*

*μ*<sup>3</sup> *y* <sup>∗</sup>

<sup>1</sup>*<sup>t</sup>* � *<sup>y</sup>*1*t*�<sup>1</sup> 

<sup>2</sup>*<sup>t</sup>* � *<sup>y</sup>*<sup>2</sup>*t*�<sup>1</sup> 

<sup>3</sup>*<sup>t</sup>* � *<sup>y</sup>*<sup>3</sup>*t*�<sup>1</sup> 

<sup>4</sup>*<sup>t</sup>* � *<sup>y</sup>*<sup>4</sup>*t*�<sup>1</sup> 

*<sup>y</sup>*1*t*�<sup>1</sup> (24)

<sup>2</sup>*<sup>t</sup>* <sup>þ</sup> <sup>1</sup> � *<sup>μ</sup>*<sup>2</sup> ð Þ*y*<sup>2</sup>*t*�<sup>1</sup> (26)

<sup>3</sup>*<sup>t</sup>* <sup>þ</sup> <sup>1</sup> � *<sup>μ</sup>*<sup>3</sup> ð Þ*y*<sup>3</sup>*t*�<sup>1</sup> (28)

<sup>4</sup>*<sup>t</sup>* <sup>þ</sup> <sup>1</sup> � *<sup>μ</sup>*<sup>4</sup> ð Þ*y*<sup>4</sup>*t*�<sup>1</sup> (30)

þ

<sup>2</sup>*<sup>t</sup>* <sup>þ</sup> <sup>1</sup> � *<sup>μ</sup>*<sup>2</sup> ð Þ*y*<sup>2</sup>*t*�<sup>1</sup>

<sup>4</sup>*<sup>t</sup>* <sup>þ</sup> <sup>1</sup> � *<sup>μ</sup>*<sup>4</sup> ð Þ*y*<sup>4</sup>*t*�<sup>1</sup>

<sup>1</sup>*<sup>t</sup>* þ 1 � *μ*1*<sup>t</sup>*

(23)

(25)

(27)

(29)

(31)

(μit, i = 1,2,3,4 and t = period), i.e. FP has μ1t, FCC has μ2t, FC has μ3t, and ITR has μ4t, whether static (constant) or dynamic [20]. Likewise, the output consists of four sub outputs, i.e. y1t, y2t, y3t, and y4t, which can appear as yt = y1t + y2t + y3t + y4t. Using the partial adjustment valuation approach [see the Eq. (3)], each subsystem could be mathematically revealed as follows [25, 26], see **Figure 3**:

> Instead of the parallel fashion, the serial ITVEM appears, in which to do so, suppose the Eq. (24), the Eq. (26), the Eq. (28), and the Eq. (30) exhibit in a serial relationship (see **Figure 4**), with an assumption that each output of a subsystem fully becomes an input of the subsequent ones, the end result is as Eq. (32) [25, 26].

$$\begin{aligned} y\_t &= \left[ \mu\_3 \mathbf{y}\_t^\* + (1 - \mu\_1) \mathbf{y}\_{1\_{t-1}} \right] + \left[ \mu\_2 \mu\_3 \mathbf{y}\_t^\* + \mu\_2 (\mathbf{1} - \mu\_1) \mathbf{y}\_{1\_{t-1}} + (1 - \mu\_2) \mathbf{y}\_{2\_{t-1}} \right] \\ &+ \left[ \mu\_3 \mu\_2 \mu\_3 \mathbf{y}\_t^\* + \mu\_3 \mu\_2 (\mathbf{1} - \mu\_1) \mathbf{y}\_{1\_{t-1}} + \mu\_3 (\mathbf{1} - \mu\_2) \mathbf{y}\_{2\_{t-1}} + (1 - \mu\_3) \mathbf{y}\_{3\_{t-1}} \right] \\ &+ \left[ \mu\_4 \mu\_3 \mu\_2 \mu\_3 \mathbf{y}\_t^\* + \mu\_4 \mu\_3 \mu\_2 (\mathbf{1} - \mu\_1) \mathbf{y}\_{1\_{t-1}} + \mu\_4 \mu\_3 (\mathbf{1} - \mu\_2) \mathbf{y}\_{2\_{t-1}} + \mu\_4 (\mathbf{1} - \mu\_3) \mathbf{y}\_{3\_{t-1}} + (\mathbf{1} - \mu\_4) \mathbf{y}\_{t-1} \right] \end{aligned} \tag{32}$$

As for the explanation of the symbols is equal to the parallel ITVE.

#### *5.4.4.3 Hybrid approach model*

The hybrid configuration [27] is an option for structuring each subsystem in the chapter. **Figure 5** explicates that the principal subsystems of the model consist of ITR, FC, FCC, and FP. It appears that the resources are the ITR consisting of the regular capital (Kt), the regular labor expense (Lt), and the technology spending, in this chapter related to IT spending (It). Furthermore, the resources become inputs of the FC subsystem as Kcap, Lcap, and Icap to be processed in resulting the FC output, viz. wmt (m = 1,2,3) or w1t, w2t, and w3t, see **Figure 5**. Likewise, the resources also become inputs of the FCC subsystem as Kcom, Lcom, and Icom to be processed in resulting the FC output, viz. vjt (j = 1,2,3) or v1t, v2t, and v3t, see

**Figure 4.** *IT value engineering model in a serial relationship [25].*

**Figure 5**. Moreover, the output of both FC and FCC turn into the input of the FP. In other words, (w1t, w2t, w3t) and (v1t,v2t, v3t) appear as inputs of the FP.

Therefore, the PAV model of the hybrid configuration (see **Figure 5**) is as follows [27]:

Firm Capabilities "cap" (FC):

$$\begin{aligned} \left(w\_{m\_t} - w\_{m\_{t-1}} = \mu\_m \left(a\_m K^{\beta\_{\text{1m}}}\_{\text{cap } m} L^{\beta\_{\text{2m}}}\_{\text{cap } m} I^{\beta\_{\text{3m}}}\_{\text{cap } m} - w\_{m\_{t-1}}\right) \\ \left(m = 1, 2, 3; t = 1, \dots, 11\right) \end{aligned} \tag{33}$$

Where vjt = the real output of FCC at period t, λ<sup>j</sup> = the constant speed of adjustment of FCC, λ<sup>j</sup> = a constant of Cobb–Douglas function; σ1,σ2, and σ<sup>3</sup> are input elasticity of production factors regarding the regular capital (K), the labor expense (L), and the IT capital (I), and vjt-1 = the real output of the previous period (t-1). Hence, if the FCC consists of three variables (j = 1, 2, and 3), viz. IT knowledge, IT operations, and IT objects [35], thus each variable has output as follows [27].

*<sup>σ</sup>*<sup>31</sup> *com* <sup>1</sup> <sup>þ</sup> ð Þ <sup>1</sup> � *<sup>δ</sup>*<sup>1</sup> *<sup>v</sup>*1*t*�<sup>1</sup> (40)

*<sup>σ</sup>*<sup>32</sup> *com* <sup>2</sup> <sup>þ</sup> ð Þ <sup>1</sup> � *<sup>δ</sup>*<sup>2</sup> *<sup>v</sup>*2*t*�<sup>1</sup> (41)

*<sup>σ</sup>*<sup>33</sup> *com* <sup>3</sup> <sup>þ</sup> ð Þ <sup>1</sup> � *<sup>δ</sup>*<sup>3</sup> *<sup>v</sup>*<sup>3</sup>*t*�<sup>1</sup> (42)

�*znt*�<sup>1</sup> �

*per n* þ 1 � *η<sup>n</sup>* ð Þ *znt*�<sup>1</sup> (44)

*per* <sup>1</sup> þ 1 � *η*<sup>1</sup> ð Þ*z*<sup>1</sup>*t*�<sup>1</sup> (45)

*per* <sup>2</sup> þ 1 � *η*<sup>2</sup> ð Þ*z*<sup>2</sup>*t*�<sup>1</sup> (46)

*per* <sup>3</sup> þ 1 � *η*<sup>3</sup> ð Þ*z*<sup>3</sup>*t*�<sup>1</sup> (47)

(43)

*per n <sup>v</sup>*<sup>1</sup>*<sup>t</sup>* , *<sup>v</sup>*<sup>2</sup>*<sup>t</sup>* , *<sup>v</sup>*<sup>3</sup>*<sup>t</sup>* ð Þ*<sup>φ</sup>*2*<sup>n</sup>*

*per n* <sup>h</sup>

*per n <sup>v</sup>*<sup>1</sup>*<sup>t</sup>* , *<sup>v</sup>*<sup>2</sup>*<sup>t</sup>* , *<sup>v</sup>*<sup>3</sup>*<sup>t</sup>* ð Þ*<sup>φ</sup>*2*<sup>n</sup>*

Where znt = the real output of FP at period t, η<sup>n</sup> = the constant speed of adjustment of FC, γ<sup>n</sup> = a constant of Cobb–Douglas function; ϕ<sup>1</sup> and ϕ<sup>2</sup> are input elasticity of production factors regarding the FC output (w1t,w2t,w3t) and the FCC output (v1t,v2t,v3t), and znt-1 = the real output of the previous period (t-1). Hence, if the FP consists of three variables (n = 1, 2, and 3), viz. ROE, ROA, and Revenue

*per* <sup>1</sup> *v*<sup>1</sup>*<sup>t</sup>* , *v*<sup>2</sup>*<sup>t</sup>*

*per* <sup>2</sup> *v*<sup>1</sup>*<sup>t</sup>*

*per* <sup>3</sup> *v*<sup>1</sup>*<sup>t</sup>*

, *<sup>v</sup>*<sup>3</sup>*<sup>t</sup>* ð Þ*<sup>φ</sup>*<sup>21</sup>

, *<sup>v</sup>*<sup>2</sup>*<sup>t</sup>* , *<sup>v</sup>*<sup>3</sup>*<sup>t</sup>* ð Þ*<sup>φ</sup>*<sup>22</sup>

, *v*<sup>2</sup>*<sup>t</sup>* , *<sup>v</sup>*<sup>3</sup>*<sup>t</sup>* ð Þ*<sup>φ</sup>*<sup>23</sup>

The ITVE optimization involves the cost minimization in accordance with the major problem of this research to raise the firm performance at optimal cost [26]. To do so, it needs several assumptions [57] along with the optimization process. For example, the Cobb–Douglas production function [20] replaces each the desired output (the starred y\*it, i = 1, 2, 3, 4 and t = 1, ..., 11, for example) of subsystems. The

*<sup>v</sup>*1*<sup>t</sup>* <sup>¼</sup> *<sup>δ</sup>*<sup>1</sup> *<sup>λ</sup>*1*K<sup>σ</sup>*<sup>11</sup> *com* <sup>1</sup> *<sup>L</sup><sup>σ</sup>*<sup>21</sup> *com* <sup>1</sup> *<sup>I</sup>*

*<sup>v</sup>*2*<sup>t</sup>* <sup>¼</sup> *<sup>δ</sup>*<sup>2</sup> *<sup>λ</sup>*<sup>2</sup> *<sup>K</sup><sup>σ</sup>*<sup>12</sup> *com* <sup>2</sup> *<sup>L</sup><sup>σ</sup>*<sup>22</sup> *com* <sup>2</sup> *<sup>I</sup>*

*<sup>v</sup>*<sup>3</sup>*<sup>t</sup>* <sup>¼</sup> *<sup>δ</sup>*<sup>3</sup> *<sup>λ</sup>*<sup>3</sup> *<sup>K</sup>σ*<sup>13</sup> *com* <sup>3</sup> *<sup>L</sup>σ*<sup>23</sup> *com* <sup>3</sup> *<sup>I</sup>*

IT knowledge (v1t):

Collaboration (v3t):

or

ROE (z1t):

ROA (z2t):

Revenue (z3t):

**207**

*z*<sup>1</sup>*<sup>t</sup>* ¼ *η*<sup>1</sup> *γ*<sup>1</sup> *w*<sup>1</sup>*<sup>t</sup>*

*z*<sup>2</sup>*<sup>t</sup>* ¼ *η*<sup>2</sup> *γ*<sup>2</sup> *w*<sup>1</sup>*<sup>t</sup>* , *w*<sup>2</sup>*<sup>t</sup>*

*z*<sup>3</sup>*<sup>t</sup>* ¼ *η*<sup>3</sup> *γ*<sup>3</sup> *w*<sup>1</sup>*<sup>t</sup>*

Cobb-Douglass function is as follows:

**6. System optimization**

IT managerial skills (v2t):

*Information Technology Value Engineering (ITVE) DOI: http://dx.doi.org/10.5772/intechopen.95855*

Firm Performance "per" (FP):

ð Þ *n* ¼ 1, 2, 3; *t* ¼ 1, … , 11

*znt* <sup>¼</sup> *<sup>η</sup><sup>n</sup> <sup>γ</sup><sup>n</sup> <sup>w</sup>*<sup>1</sup>*<sup>t</sup>* , *<sup>w</sup>*<sup>2</sup>*<sup>t</sup>* , *<sup>w</sup>*<sup>3</sup>*<sup>t</sup>* ð Þ*<sup>φ</sup>*1*<sup>n</sup>*

*znt* � *znt*�<sup>1</sup> <sup>¼</sup> *<sup>η</sup><sup>n</sup> <sup>γ</sup><sup>n</sup> <sup>w</sup>*<sup>1</sup>*<sup>t</sup>* , *<sup>w</sup>*<sup>2</sup>*<sup>t</sup>* , *<sup>w</sup>*<sup>3</sup>*<sup>t</sup>* ð Þ*<sup>φ</sup>*1*<sup>n</sup>*

[16], thus each variable has output as follows [27].

, *<sup>w</sup>*<sup>2</sup>*<sup>t</sup>* , *<sup>w</sup>*<sup>3</sup>*<sup>t</sup>* ð Þ*<sup>φ</sup>*<sup>11</sup>

, *<sup>w</sup>*<sup>3</sup>*<sup>t</sup>* ð Þ*<sup>φ</sup>*<sup>21</sup>

, *<sup>w</sup>*<sup>2</sup>*<sup>t</sup>* , *<sup>w</sup>*<sup>3</sup>*<sup>t</sup>* ð Þ*<sup>φ</sup>*<sup>31</sup>

or

$$
\mu\_{m\_t} = \mu\_m a\_m K^{\beta\_{1m}}\_{\,\,cap\,m} L^{\beta\_{2m}}\_{\,\,cap\,m} I^{\beta\_{3m}}\_{\,\,cap\,m} + (1 - \mu\_m) w\_{m\_{t-1}} \tag{34}
$$

Where wmt = the real output of FC at period t, μ<sup>m</sup> = the constant speed of adjustment of FC, α<sup>m</sup> = a constant of Cobb–Douglas function; β1, β2, and β<sup>3</sup> are input elasticity of production factors regarding the regular capital (K), the labor expense (L), and the IT capital (I), and wmt-1 = the real output of the previous period (t-1). Hence, if the FC consists of three variables (m = 1, 2, and 3), viz. IT infrastructures, IT managerial skills, and Collaboration [54], thus each variable has output as follows [27].

IT infrastructures (w1t):

$$
\omega\_{\mathbf{1}\_t} = \mu\_\mathbf{1} a\_\mathbf{1} K^{\beta\_{\mathbf{1}\mathbf{1}}} {}\_{cap\ 1} L^{\beta\_{\mathbf{1}\mathbf{1}}} {}\_{cap\ 1} I^{\beta\_{\mathbf{1}\mathbf{1}}} {}\_{cap\ 1} + (\mathbf{1} - \mu\_\mathbf{1}) \omega\_{\mathbf{1}\_{t-1}} \tag{35}
$$

IT managerial skills (w2t):

$$
\omega\_{2\epsilon} = \mu\_2 a\_2 K^{\beta\_{12}}\_{\,\,\alpha p \, 2} L^{\beta\_{22}}\_{\,\,\alpha p \, 2} I^{\beta\_{32}}\_{\,\,\alpha p \, 2} + (1 - \mu\_2) w\_{2\epsilon \, \, 1} \tag{36}
$$

Collaboration (w3t):

$$
\mu\_{\eth\_1} = \mu\_3 a\_3 K^{\beta\_{13}}\_{\!\!\!axp \;3} L^{\beta\_{23}}\_{\!\!\!axp \;3} I^{\beta\_{33}}\_{\!\!\!axp \;3} + (\mathbf{1} - \boldsymbol{\mu\_3}) w\_{\eth\_{\natural -1}} \tag{37}
$$

Firm Core Competence "com" (FCC):

$$\begin{aligned} \boldsymbol{v}\_{\boldsymbol{\dot{\boldsymbol{\gamma}}}} - \boldsymbol{v}\_{\boldsymbol{\dot{\boldsymbol{\gamma}}}-1} &= \boldsymbol{\delta}\_{\boldsymbol{\dot{\boldsymbol{\beta}}}} \left( \lambda\_{\boldsymbol{\dot{\boldsymbol{\beta}}}} K^{\sigma \boldsymbol{\dot{\boldsymbol{\gamma}}}} {}\_{\boldsymbol{\alpha} \boldsymbol{m} \boldsymbol{j}} I^{\sigma \boldsymbol{\dot{\boldsymbol{\gamma}}}} {}\_{\boldsymbol{\alpha} \boldsymbol{m} \boldsymbol{j}} I^{\sigma \boldsymbol{\dot{\boldsymbol{\gamma}}}} - \boldsymbol{v}\_{\boldsymbol{\dot{\boldsymbol{\gamma}}}-1} \right) \\ \boldsymbol{\dot{\boldsymbol{\gamma}}} (\boldsymbol{j} = \mathbf{1}, \mathbf{2}, \mathbf{3}; t = \mathbf{1}, \dots, \mathbf{11}) \end{aligned} \tag{38}$$

or

$$\boldsymbol{\upsilon}\_{\dot{\boldsymbol{\eta}}\_{t}} = \boldsymbol{\delta}\_{\dot{\boldsymbol{\beta}}} \boldsymbol{\lambda}\_{\dot{\boldsymbol{\beta}}} \boldsymbol{K}^{\sigma \dot{\boldsymbol{\eta}}\_{\boldsymbol{\alpha}}} \boldsymbol{L}^{\sigma \dot{\boldsymbol{\eta}}\_{\boldsymbol{\alpha}}} \boldsymbol{c}\_{comj} \boldsymbol{I}^{\sigma \dot{\boldsymbol{\eta}}\_{\boldsymbol{\alpha}}} \boldsymbol{c}\_{comj} + (\mathbf{1} - \boldsymbol{\delta}\_{\dot{\boldsymbol{\beta}}}) \boldsymbol{\upsilon}\_{\dot{\boldsymbol{\beta}}\_{t-1}} \tag{39}$$

**Figure 5.** *IT value in the hybrid configuration [27].*

*Information Technology Value Engineering (ITVE) DOI: http://dx.doi.org/10.5772/intechopen.95855*

Where vjt = the real output of FCC at period t, λ<sup>j</sup> = the constant speed of adjustment of FCC, λ<sup>j</sup> = a constant of Cobb–Douglas function; σ1,σ2, and σ<sup>3</sup> are input elasticity of production factors regarding the regular capital (K), the labor expense (L), and the IT capital (I), and vjt-1 = the real output of the previous period (t-1). Hence, if the FCC consists of three variables (j = 1, 2, and 3), viz. IT knowledge, IT operations, and IT objects [35], thus each variable has output as follows [27].

IT knowledge (v1t):

**Figure 5**. Moreover, the output of both FC and FCC turn into the input of the FP. In

*<sup>β</sup>*3*<sup>m</sup> cap m* � *wmt*�<sup>1</sup>

*<sup>β</sup>*3*<sup>m</sup> cap m* <sup>þ</sup> ð Þ <sup>1</sup> � *<sup>μ</sup><sup>m</sup> wmt*�<sup>1</sup> (34)

*<sup>β</sup>*<sup>31</sup> *cap* <sup>1</sup> <sup>þ</sup> <sup>1</sup> � *<sup>μ</sup>*<sup>1</sup> ð Þ*w*<sup>1</sup>*t*�<sup>1</sup> (35)

*<sup>β</sup>*<sup>32</sup> *cap* <sup>2</sup> <sup>þ</sup> <sup>1</sup> � *<sup>μ</sup>*<sup>2</sup> ð Þ*w*<sup>2</sup>*t*�<sup>1</sup> (36)

*<sup>β</sup>*<sup>33</sup> *cap* <sup>3</sup> <sup>þ</sup> <sup>1</sup> � *<sup>μ</sup>*<sup>3</sup> ð Þ*w*<sup>3</sup>*t*�<sup>1</sup> (37)

*t*�1

*<sup>t</sup>*�<sup>1</sup> (39)

 ð Þ *<sup>m</sup>* <sup>¼</sup> 1, 2, 3; *<sup>t</sup>* <sup>¼</sup> 1, … , 11 (33)

Therefore, the PAV model of the hybrid configuration (see **Figure 5**) is as

Where wmt = the real output of FC at period t, μ<sup>m</sup> = the constant speed of adjustment of FC, α<sup>m</sup> = a constant of Cobb–Douglas function; β1, β2, and β<sup>3</sup> are input elasticity of production factors regarding the regular capital (K), the labor expense (L), and the IT capital (I), and wmt-1 = the real output of the previous period (t-1). Hence, if the FC consists of three variables (m = 1, 2, and 3), viz. IT infrastructures, IT managerial skills, and Collaboration [54], thus each variable has output as fol-

other words, (w1t, w2t, w3t) and (v1t,v2t, v3t) appear as inputs of the FP.

*wmt* � *wmt*�<sup>1</sup> <sup>¼</sup> *<sup>μ</sup><sup>m</sup> <sup>α</sup><sup>m</sup> <sup>K</sup><sup>β</sup>*1*<sup>m</sup> cap m <sup>L</sup><sup>β</sup>*2*<sup>m</sup> cap m <sup>I</sup>*

*wmt* <sup>¼</sup> *<sup>μ</sup><sup>m</sup> <sup>α</sup><sup>m</sup> <sup>K</sup><sup>β</sup>*1*<sup>m</sup> cap m <sup>L</sup><sup>β</sup>*2*<sup>m</sup> cap m <sup>I</sup>*

*<sup>w</sup>*<sup>1</sup>*<sup>t</sup>* <sup>¼</sup> *<sup>μ</sup>*<sup>1</sup> *<sup>α</sup>*1*Kβ*<sup>11</sup> *cap* <sup>1</sup> *<sup>L</sup>β*<sup>21</sup> *cap* <sup>1</sup> *<sup>I</sup>*

*<sup>w</sup>*<sup>2</sup>*<sup>t</sup>* <sup>¼</sup> *<sup>μ</sup>*<sup>2</sup> *<sup>α</sup>*<sup>2</sup> *<sup>K</sup>β*<sup>12</sup> *cap* <sup>2</sup> *<sup>L</sup>β*<sup>22</sup> *cap* <sup>2</sup> *<sup>I</sup>*

*<sup>w</sup>*<sup>3</sup>*<sup>t</sup>* <sup>¼</sup> *<sup>μ</sup>*<sup>3</sup> *<sup>α</sup>*<sup>3</sup> *<sup>K</sup>β*<sup>13</sup> *cap* <sup>3</sup> *<sup>L</sup>β*<sup>23</sup> *cap* <sup>3</sup> *<sup>I</sup>*

*<sup>t</sup>*�<sup>1</sup> <sup>¼</sup> *<sup>δ</sup> <sup>j</sup> <sup>λ</sup> <sup>j</sup> <sup>K</sup>σ*1*<sup>j</sup>*

*com j L<sup>σ</sup>*2*<sup>j</sup>*

*com j Lσ*2*<sup>j</sup>*

*com jI σ*3*j* *com jI σ*3*j*

*com j* þ 1 � *δ <sup>j</sup> vj*

 ð Þ *<sup>j</sup>* <sup>¼</sup> 1, 2, 3; *<sup>t</sup>* <sup>¼</sup> 1, … , 11 (38)

*com j* � *vj*

Firm Core Competence "com" (FCC):

*vj <sup>t</sup>* � *vj*

*vj*

*IT value in the hybrid configuration [27].*

*<sup>t</sup>* <sup>¼</sup> *<sup>δ</sup> <sup>j</sup><sup>λ</sup> jK<sup>σ</sup>*1*<sup>j</sup>*

follows [27]:

or

lows [27].

or

**Figure 5.**

**206**

IT infrastructures (w1t):

IT managerial skills (w2t):

Collaboration (w3t):

Firm Capabilities "cap" (FC):

*Computational Optimization Techniques and Applications*

$$
\boldsymbol{\nu}\_{\mathbf{1}\_t} = \delta\_1 \lambda\_1 K^{\sigma\_{\mathbf{1}1}} {}\_{com \, 1} L^{\sigma\_{\mathbf{1}1}} {}\_{com \, 1} I^{\sigma\_{\mathbf{1}1}} {}\_{com \, 1} + (\mathbf{1} - \delta\_1) \boldsymbol{\nu}\_{\mathbf{1}\_{t-1}} \tag{40}
$$

IT managerial skills (v2t):

$$
\upsilon\_{2\_{\mathfrak{t}}} = \delta\_2 \lambda\_2 K^{\sigma\_{12}} {}\_{com \, 2} L^{\sigma\_{22}} {}\_{com \, 2} I^{\sigma\_{32}} {}\_{com \, 2} + (1 - \delta\_2) \upsilon\_{2\_{\mathfrak{t}-1}} \tag{41}
$$

Collaboration (v3t):

$$\boldsymbol{\nu}\_{\mathfrak{Z}\_{\mathfrak{t}}} = \,\,\delta\_{\mathfrak{Z}}\lambda\_{\mathfrak{Z}}K^{\sigma\_{\mathfrak{Y}}}{}\_{com \mathfrak{Z}}L^{\sigma\_{\mathfrak{Z}}}{}\_{com \mathfrak{Z}}I^{\sigma\_{\mathfrak{Y}}}{}\_{com \mathfrak{Z}} + (\mathbf{1} - \delta\_{\mathfrak{Z}})\boldsymbol{\nu}\_{\mathfrak{Z}\_{\mathfrak{t}-1}} \tag{42}$$

Firm Performance "per" (FP):

$$\begin{aligned} \mathbf{z}\_{n\_t} - \mathbf{z}\_{n\_{t-1}} &= \eta\_n \left[ \chi\_n(\boldsymbol{w}\_{1\_t}, \boldsymbol{w}\_{2\_t}, \boldsymbol{w}\_{3\_t})^{\rho\_{1u}}\_{\
perp}(\boldsymbol{v}\_{1\_t}, \boldsymbol{v}\_{2\_t}, \boldsymbol{v}\_{3\_t})^{\rho\_{2u}}\_{\
perp} - \mathbf{z}\_{n\_{t-1}} \right] \\ \mathbf{z}\_{\{n = 1, 2, 3; t = 1, \dots, 11\}} & \end{aligned} \tag{43}$$

or

$$z\_{n\_l} = \eta\_n \chi\_n(w\_{1\iota}, w\_{2\iota}, w\_{3\iota})^{\rho\_{1\iota}}\_{\
perp}(v\_{1\iota}, v\_{2\iota}, v\_{3\iota})^{\rho\_{2\iota}}\_{\
perp} + (1 - \eta\_n) z\_{n\_{l-1}} \tag{44}$$

Where znt = the real output of FP at period t, η<sup>n</sup> = the constant speed of adjustment of FC, γ<sup>n</sup> = a constant of Cobb–Douglas function; ϕ<sup>1</sup> and ϕ<sup>2</sup> are input elasticity of production factors regarding the FC output (w1t,w2t,w3t) and the FCC output (v1t,v2t,v3t), and znt-1 = the real output of the previous period (t-1). Hence, if the FP consists of three variables (n = 1, 2, and 3), viz. ROE, ROA, and Revenue [16], thus each variable has output as follows [27].

ROE (z1t):

$$\mathbf{z}\_{\mathsf{i}} = \eta\_1 \boldsymbol{\chi}\_1(\boldsymbol{w}\_{\mathsf{i}}, \boldsymbol{w}\_{\mathsf{i}}, \boldsymbol{w}\_{\mathsf{i}})^{\operatorname{\boldsymbol{\rho}}\_{\mathsf{i}1}}\_{\operatorname{per1}}(\boldsymbol{v}\_{\mathsf{i}}, \boldsymbol{v}\_{\mathsf{i}}, \boldsymbol{v}\_{\mathsf{i}})^{\operatorname{\boldsymbol{\rho}}\_{\mathsf{i}1}}\_{\operatorname{per1}} + (\mathbbm{1} - \boldsymbol{\eta}\_1) \mathbf{z}\_{\mathsf{i}-1} \tag{45}$$

ROA (z2t):

$$\mathbf{z}\_{2} = \eta\_{2}\boldsymbol{\gamma}\_{2}(\boldsymbol{w}\_{1\_{\mathrm{i}}}, \boldsymbol{w}\_{2\_{\mathrm{i}}}, \boldsymbol{w}\_{3\_{\mathrm{i}}})^{\varrho\_{21}}\_{\mathrm{per}2}(\boldsymbol{v}\_{1\_{\mathrm{i}}}, \boldsymbol{v}\_{2\_{\mathrm{i}}}, \boldsymbol{v}\_{3\_{\mathrm{i}}})^{\varrho\_{22}}\_{\mathrm{per}2} + (\mathbf{1} - \eta\_{2})\mathbf{z}\_{2\_{\mathrm{i}-1}} \tag{46}$$

Revenue (z3t):

$$\mathbf{z}\_{3\_{\shortparallel}} = \eta\_{\3} \boldsymbol{\chi}\_{\3}(\boldsymbol{w}\_{1\_{\shortparallel}}, \boldsymbol{w}\_{2\_{\shortparallel}}, \boldsymbol{w}\_{3\_{\shortparallel}})^{\boldsymbol{\wp}\_{\mathfrak{N}}}{}\_{\operatorname{per}\mathfrak{I}}(\boldsymbol{v}\_{1\_{\shortparallel}}, \boldsymbol{v}\_{2\_{\shortparallel}}, \boldsymbol{v}\_{3\_{\shortparallel}})^{\boldsymbol{\wp}\_{\mathfrak{N}}}{}\_{\operatorname{per}\mathfrak{I}} + (\mathbb{1} - \eta\_{\mathfrak{I}}) \mathbf{z}\_{3\_{\shortparallel}} \tag{47}$$

#### **6. System optimization**

The ITVE optimization involves the cost minimization in accordance with the major problem of this research to raise the firm performance at optimal cost [26]. To do so, it needs several assumptions [57] along with the optimization process. For example, the Cobb–Douglas production function [20] replaces each the desired output (the starred y\*it, i = 1, 2, 3, 4 and t = 1, ..., 11, for example) of subsystems. The Cobb-Douglass function is as follows:

$$\mathbf{y}\_{\text{it}}^{\*} = a \mathbf{K}\_{\text{it}}^{\beta\_1} \mathbf{L}\_{\text{it}}^{\beta\_2} \mathbf{I}\_{\text{it}}^{\beta\_3} \quad (i = 1, \dots, 4 \text{ and } \ t = 1, 2, \dots, 11) \tag{48}$$

Using the equivalent way, the variable L and I can become as follows:

�*β*1 *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> <sup>1</sup> *β*

<sup>3</sup> *yt* � <sup>1</sup> � *<sup>μ</sup><sup>t</sup>* ð Þ*yt*�<sup>1</sup>

<sup>3</sup> *yt* � <sup>1</sup> � *<sup>μ</sup><sup>t</sup>* ð Þ*yt*�<sup>1</sup>

If K, L, and I are multiplying p1, p2, and p3 as unit prices respectively, then it

*β*2þ*β*3 *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> <sup>1</sup> *β*

<sup>3</sup> *yt* � <sup>1</sup> � *<sup>μ</sup><sup>t</sup>* ð Þ*yt*�<sup>1</sup>

�*β*1 *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> <sup>1</sup> *β*

<sup>3</sup> *yt* � <sup>1</sup> � *<sup>μ</sup><sup>t</sup>* ð Þ*yt*�<sup>1</sup>

<sup>3</sup> *yt* � <sup>1</sup> � *<sup>μ</sup><sup>t</sup>* ð Þ*yt*�<sup>1</sup>

*β*3 *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup>

*β*1 *β*2 � � *<sup>β</sup>*<sup>2</sup>

"

�*β*1 *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> <sup>1</sup> *β*

�*β*1 *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> <sup>1</sup> *β*

*β*1þ*β*3 *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> <sup>2</sup> *β*

� � <sup>1</sup>

� � <sup>1</sup>

�*β*2 *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> <sup>2</sup> *β*

*β*1þ*β*3 *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> <sup>2</sup> *β*

�*β*2 *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> <sup>2</sup> *β*

<sup>3</sup> *yt* � <sup>1</sup> � *<sup>μ</sup><sup>t</sup>* ð Þ*yt*�<sup>1</sup>

*β*3 � � *<sup>β</sup>*<sup>3</sup> *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup>

� � <sup>1</sup>

*<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> *β*<sup>3</sup>

� � <sup>1</sup>

� � <sup>1</sup>

� � <sup>1</sup>

Moreover, the Eqs. (61), (62), and (63) substituted into Eq. (64), the total cost of yielding y units in the low-cost technique manifest as the Eq. (64) and (65).

*<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> *β*<sup>1</sup>

<sup>þ</sup> *<sup>β</sup>*<sup>3</sup> *β*1 � � *<sup>β</sup>*<sup>1</sup>

Whereas p1, p2, and p3 is unit prices of the regular capital (Kt), the labor expense (Lt), and the IT capital (It) respectively, yt is the real output of period t, yt-1 is the

The significant problem surrounding this study is to sustain superior firm performance as desired at optimal costs due to the IT presence, which has inevitably

become a need for running the business world. Numerous studies on the

�*β*2 *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> <sup>2</sup> *β*

�*β*3 *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> <sup>3</sup> *p*

*<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup>

*β*1þ*β*2 *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> <sup>3</sup> *p*

*<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup>

�*β*3 *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> <sup>3</sup> *p*

*<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup>

�*β*3 *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> <sup>3</sup> *p*

*<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup>

*β*1þ*β*2 *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> <sup>3</sup> *p*

*<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup>

*β*1 *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> 1

*β*1 *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> 1

*β*1 *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> 1

*β*1 *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> 1

*β*1 *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> 1

*<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup>

þ

*β*2 � � *<sup>β</sup>*<sup>2</sup> *<sup>β</sup>*1þ*β*2þ*<sup>β</sup>* ð Þ<sup>3</sup> (59)

(60)

(61)

(62)

(63)

(64)
