*3.4.1 The fuzzy logic and internal logistics*

Assessing the Internal Logistic Index of a Company is a very complex task due in some case to the lack of information and in other cases to the excess of information for decision-making. This leads to difficulty in defining, measuring and monitoring of objectives and targets to set rates compliance associated with measuring the performance of the Internal Logistics [93]. In response to these challenges of business management there have been emerged theories, approaches and methodologies (flexibility, resilience, etc.) using tools such as fuzzy logic for reliable solutions that adapt easily to changing parameters of imprecision [94].

In addition to the treatment of imprecise environments, another emerging challenge is to achieve that the measurement of organizational performance transcends the traditional financial approach and to be conducted throughout with suitable means to new generations of applications in the management of internal logistics.

#### *3.4.2 Method of fuzzy inference*

A fuzzy inference method allows deriving conclusions (a fuzzy value) from a set of if-then rules and a set of input values to the system, by applying composition ratios. The two inference methods commonly used are the Mamdani introduced by Mamdani and Assilian [95] and the TSK (Takagi-Sugeno-Kang) proposed by Takagi and Sugeno [96].

The main difference between these methods is the consequent type of the fuzzy rule. The systems Mamdani type use fuzzy sets as consistent rule and TSK used linear functions of the input variables with discrete data outputs. In this research the type Mamdani inference system (**Figure 3**) with outputs continuous values is used.

To facilitate the modeling of the problem in fuzzy logic, it was used the Fuzzy Logic Toolbox ™ of MATLAB software. The steps for formulating the model of fuzzy inference of Mamdani type were [97, 98]:

#### *3.4.3 Selection of indicators*

Performance measurement of the internal logistics can be based on the selection and definition of indicators used to evaluate the efficiency and effectiveness of its operations. Indicators should have a holistic approach and facilitate the implementation of initiatives for improvement. Indicators selected for the proposed fuzzy model to measure the performance of the Internal Logistics of the company studied are described in **Table 5**. The components were grouped into larger groups as shown therein. A letter from A to B. defines each group.

**Figure 3.** *Fuzzy system for asses the internal logistics. Source: Authors (2020).*

The Excel Tab developed to calculate the Internal Logistic Index was based on

**Component part Assigned weight by each company**

**Company 1 Company 2 Company 3 Arithmetic**

2 4 3 3.00 5.1%

2 5 5 4.00 8.5%

2 5 5 4.00 8.5%

2 5 5 4.00 8.5%

1 5 5 3.67 8.5%

3 5 4 4.00 6.8%

35 61 59 51.67 100%

Receipt 3 5 4 4.00 6.8%

Picking/packing 4 4 4 4.00 6.8% Storage 1 5 5 3.67 8.5%

Supplying 5 5 5 5.00 8.5%

Order processing 4 4 5 4.33 8.5% Internal transports 1 4 4 3.00 6.8% Customer support 5 5 5 5.00 8.5%

**mean**

**Company 3 Weight**

*Zi* 100 � �

*P <sup>j</sup>:Lj* 50 � �

where *P <sup>j</sup>* = Each of the parameters that assess the *Zi* property (always it going to assume the value 1 in the above expression); *Lj* = Value assigned to the parameter

*:Wi* � �

*:*100 (2)

(1)

*ILI* <sup>¼</sup> <sup>X</sup> 13

*Answers from the companies on the degree of importance of the elements of internal logistics.*

5 and divided by the maximum possible value to reach in% i.e.:

*Zi* <sup>¼</sup> <sup>X</sup> 10

*j*¼1

*i*¼1

where ILI = General index of the performance of the Internal Logistics; *Wi* = Weight attributed to each component part *i*; *i* = each of the properties analyzed; *Zi* = value reached in % for the property i based on the sum of all values given to each parameter of the corresponding property of the Likert scale from 1 to

the following equations:

*Source: Authors.*

**Table 4.**

**134**

Component parts of the Internal Logistics

Handling and movement

*Operations Management - Emerging Trend in the Digital Era*

Stocks management

PMC- planning and material control

PPC - planning and production control

WIP- working in process

I. T. information technology

Internal Logistic Index

*P <sup>j</sup>* at the Likert scale from 1 a 5.


*3.4.4 Development of fuzzy rules*

*DOI: http://dx.doi.org/10.5772/intechopen.94718*

in **Table 6**.

*Source: Authors.*

*companies evaluated.*

**Table 7.**

**137**

The model has 24 rules, which were created from the experience of official logistics industry specialists and numerical data from surveys and they are offered

*Conceptualization, Definition and Assessment of Internal Logistics through Different…*

problem were used criteria of 20 specialists in the field of Internal logistics.

**3.5 Assessment of internal logistics using neural networks**

The model has four inputs that are the four groups described in **Table 5** and an output that is the Internal Logistics Index. The parameters of pertinence functions associated with each variable were also specified. There were adjusted all inference functions and the defuzzification method used. The rules of an inference engine of a fuzzy system has to be made by experts, or learned by the system, in this case using neural networks to strengthen future decision-making. For making the rules in this

One problem with the method applied in the previous section is that the user of Excel tab has to assign a weight to each component part of the internal logistics based on in his own experience, which naturally influences the overall index of internal logistics of a company. Attempting to avoid subjectivity in determining this rate, it was looked to the technique of artificial neural networks. To analyze the Internal Logistics of an industrial company was used the Internal Logistics Index (ILI), evaluated between 0 and 100%. This index is calculated based on the values assigned to each of the internal logistics properties between 0 and 50 according to the 10 parameters of evaluation of each property in the Likert scale of 1 to 5.

There were selected the same 10 companies of the Industrial Pole of Manaus for

**Property Company number and value of the performance of each**

Receipt 30 35 36 50 42 47 32 18 50 22 Handling and movement 20 44 23 50 35 45 34 15 39 19 Picking/packing 50 22 32 48 26 34 45 21 40 23 Storage 40 33 41 43 12 50 23 32 35 34 Stocks management 30 11 25 21 18 16 15 18 18 35 Supplying 24 44 18 50 22 24 18 43 25 23 PMC- planning and material control 33 50 15 39 19 35 22 32 35 41 PP - planning and production control 28 33 21 40 23 32 18 19 28 19 WIP- working in process 16 22 32 35 34 18 34 42 47 32 Order processing 41 11 18 18 35 33 45 35 45 34 Internal transports 33 33 43 25 23 22 35 26 34 45 Customer support 23 45 32 35 41 43 25 12 50 23 I. T. information technology 33 44 19 28 19 21 18 18 16 15

*Different properties that compose the Internal Logistic Index of a company and their values for the 10*

**property E1 E2 E3 E4 E5 E6 E7 E8 E9 E10**

their study and analysis, all of them belonging to the productive sector.

#### **Table 5.**

*Component parts of internal logistics.*


*Source: Authors (2020). M = medium, G = good, B = bad.*

#### **Table 6.**

*Fuzzy rules.*

Each component part of the previous group is evaluated using 10 pertinent questions that reflect the behavior of the respective part.

*Conceptualization, Definition and Assessment of Internal Logistics through Different… DOI: http://dx.doi.org/10.5772/intechopen.94718*

### *3.4.4 Development of fuzzy rules*

The model has 24 rules, which were created from the experience of official logistics industry specialists and numerical data from surveys and they are offered in **Table 6**.

The model has four inputs that are the four groups described in **Table 5** and an output that is the Internal Logistics Index. The parameters of pertinence functions associated with each variable were also specified. There were adjusted all inference functions and the defuzzification method used. The rules of an inference engine of a fuzzy system has to be made by experts, or learned by the system, in this case using neural networks to strengthen future decision-making. For making the rules in this problem were used criteria of 20 specialists in the field of Internal logistics.

#### **3.5 Assessment of internal logistics using neural networks**

One problem with the method applied in the previous section is that the user of Excel tab has to assign a weight to each component part of the internal logistics based on in his own experience, which naturally influences the overall index of internal logistics of a company. Attempting to avoid subjectivity in determining this rate, it was looked to the technique of artificial neural networks. To analyze the Internal Logistics of an industrial company was used the Internal Logistics Index (ILI), evaluated between 0 and 100%. This index is calculated based on the values assigned to each of the internal logistics properties between 0 and 50 according to the 10 parameters of evaluation of each property in the Likert scale of 1 to 5.

There were selected the same 10 companies of the Industrial Pole of Manaus for their study and analysis, all of them belonging to the productive sector.


#### **Table 7.**

*Different properties that compose the Internal Logistic Index of a company and their values for the 10 companies evaluated.*

Each component part of the previous group is evaluated using 10 pertinent

**A B CD** Receipt WIP- working in process PPC - planning and

**Component parts/groups A B C D LI** 1 MBMB B 2 MGG BM 3 GBMB B 4 GGGBM 5 BGGB B 6 GBGGM 7 BGBMB 8 MG BMM 9 B MMMM 10 M B M M M 11 G M M M M 12 M B G B M 13 G G M G G 14 M B G G M 15 G M B M M 16 B B M B B 17 M M G G G 18 G M B M M 19 B B M G M 20 M G B G M 21 G M B G M 22 B M B G M 23 B G B M B 24 B M G R M

Storage Handling and movement PMC- planning and

*Operations Management - Emerging Trend in the Digital Era*

Stocks management Supplying Customer support I. T. information technology Internal transports Order processing

*Source: Authors.*

*Component parts of internal logistics.*

**Table 5.**

production control

material control

Picking/packing

questions that reflect the behavior of the respective part.

*Source: Authors (2020). M = medium, G = good, B = bad.*

**Table 6.** *Fuzzy rules.*

**136**


#### **Table 8.**

*Possible internal logistics indexes (ILI) for each company (*targets) *for training the ANN.*

#### **Figure 4.**

It was proposed to the ANN to determine the Internal Logistic Index of 10 companies in the industrial pole of Manaus. The values of the properties of the component parts of the 10 companies are given in **Table 7**.

The desired Internal Logistics Indexes for the aforementioned companies (supervised training), in order to train the ANN are given in **Table 8**.

In **Figure 4** it is showed the Architecture of the ANN implemented in MATLAB. In order to achieve reliable results, the network was trained five times. In **Figures 5** and **6** the training process is displayed.

> It was found that depending on the company and its respective sector, the priorities and the degree of importance may be subject to changes and therefore affect the performance index of internal logistics. The maximum score that each company can get is 65 points, which is the result of the multiplication of the 13 items by the maximum value of each item according to the Likert scale. It is noted for example that the company 1 attributed a very low note for the items: Storage, WIP and internal transport, while companies 2 and 3 attributed notes 5, 5 and 4 respectively for these same items, therefore, it follows which depending on the

*Conceptualization, Definition and Assessment of Internal Logistics through Different…*

*DOI: http://dx.doi.org/10.5772/intechopen.94718*

*Neural network training state. Source: Authors (from MATLAB).*

**Figure 5.**

**139**

## **4. Result analysis**

It was chosen randomly the company three to answer questionnaires regarding the 13 elements or components parts of internal logistics. This company filled the Excel tab, reaching a score in% of each property that was multiplied by the weights assigned in Table to each property. This company reached a general index of 79.17% for Internal Logistics as it is shown in **Table 9**.

*Artificial neural network implemented in MATLAB. Source: Authors (from MATLAB).*

*Conceptualization, Definition and Assessment of Internal Logistics through Different… DOI: http://dx.doi.org/10.5772/intechopen.94718*


#### **Figure 5.**

It was proposed to the ANN to determine the Internal Logistic Index of 10 companies in the industrial pole of Manaus. The values of the properties of the

**Company number and Internal Logistic Index possible according to the performance value of each property E1 E2 E3 E4 E5 E6 E7 E8 E9 E10**

ILI 65 75 70 67 78 60 70 65 78 65

*Possible internal logistics indexes (ILI) for each company (*targets) *for training the ANN.*

*Operations Management - Emerging Trend in the Digital Era*

The desired Internal Logistics Indexes for the aforementioned companies

It was chosen randomly the company three to answer questionnaires regarding the 13 elements or components parts of internal logistics. This company filled the Excel tab, reaching a score in% of each property that was multiplied by the weights assigned in Table to each property. This company reached a general index of 79.17%

(supervised training), in order to train the ANN are given in **Table 8**. In **Figure 4** it is showed the Architecture of the ANN implemented in MATLAB. In order to achieve reliable results, the network was trained five times. In

*Artificial neural network implemented in MATLAB. Source: Authors (from MATLAB).*

component parts of the 10 companies are given in **Table 7**.

**Figures 5** and **6** the training process is displayed.

for Internal Logistics as it is shown in **Table 9**.

**4. Result analysis**

**138**

**Figure 4.**

*Source: Authors.*

**Table 8.**

*Neural network training state. Source: Authors (from MATLAB).*

It was found that depending on the company and its respective sector, the priorities and the degree of importance may be subject to changes and therefore affect the performance index of internal logistics. The maximum score that each company can get is 65 points, which is the result of the multiplication of the 13 items by the maximum value of each item according to the Likert scale. It is noted for example that the company 1 attributed a very low note for the items: Storage, WIP and internal transport, while companies 2 and 3 attributed notes 5, 5 and 4 respectively for these same items, therefore, it follows which depending on the
