Application of the Fuzzy-AHP method in the optimization of production of concrete blocks with addition of casting sand

Abstract

Currently, the concern with renewable resources has led the society to create several initiatives to approach the subject, proposing viable solutions. One of the biggest challenges is the conservation of the environment due to its unbridled degradation. Thus, companies must act in an ecologically responsible way so as not to threaten future survival, thus contributing to sustainable development. The present study applied the FAHP method to optimize the processes aiming to eliminate production bottlenecks in the manufacture of concrete blocks with the use of foundry sand from a metalworking industry located in the South of Brazil. Results demonstrated that the prioritized alternatives were transportation outsourcing (24.24%), while the analysis of toxicity and resistance within the norms obtained the same prioritization (22.38%), these alternatives contributed to suppress the bottleneck of production process. The industry hired a third party company with reference in the market, so there was no involvement with labor laws, in addition, the analysis of toxicity contributed with reduction costs and wasted time; consequently, reducing in 100% the chance of Contamination, due to the adoption of correct practices. Resistance within the norms helped in the reduction of the rework (98%) due to breaks and chipping. The improvements found through the FAHP method were achieved through the degree of importance of alternatives, in order to maximize the profit of the industry.

Keywords

Concrete blocks productive process decision making

1 Introduction

In recent years, among environmental impacts with greater volume, caused by economic activities there are solid waste. In this way, organizations are developing solutions for the recycling and reuse of waste, which is necessary to explore ways of transforming industrial waste into building materials [28, 34].

Therefore, the foundry industry seeks a flexible and agile management for the waste generated (foundry sand) [30], reducing the amount of sand deposited in landfills. Discarded sand casting (ADF) is used as casting molding material because it has high thermal conductivity. In the casting process, molding sands are recycled and reused several times; however, the recycled sand degrades to the point where it can no longer be reused in the casting process [11, 30].

The major problem in this case is ADF, which is produced in large volumes, and reuse of waste is directed to the construction area as tiles, bricks and blocks of cements: hollow blocks and solid blocks. The study demonstrated the process of production of this reuse in solid cement blocks. In this sense, it is necessary to guide, monitor and evaluate the decision-making processes, helping the sector decision-making. For Rosa [19], the development of new modeling techniques, algorithmic solutions and computer technologies have brought different possibilities in modeling a problem. In the present research, there are several multicriteria analysis techniques, for example, the Fuzzy-Analytic Hierarchy Process (FAHP) methodology is a technique that has been distinguished by the use of Fuzzy logic to deal with imprecision inherent in the decision process [12 , 33] (Sellitto, et al., 2012).

Given the current scenario where the world suffers, development of innovations, there are several options of methodologies and different modeling accompanied by methods of problem solving that can be used by companies to seek competitive advantage in the market. Therefore, the proposal of this research and the application of the FAHP method to optimize the processes aiming to eliminate production bottlenecks regarding the manufacture of concrete blocks with the use of sand casting of a metalworking industry located in the South of Brazil. Thus, the originality of the research implies in the dissemination of sand use, revealing descriptions about residue enriching the knowledge on the subject, which shows that the multicriteria FAHP analysis technique can be used to eliminate production bottlenecks.

In this context, the criteria to be considered are: quality, time, cost and resources involved in the production of concrete blocks. In addition, to elaborate such analyzes it is necessary to consider some alternatives to better elucidate the bottlenecks in the productive process. The alternatives highlighted were: toxicity analysis, transportation outsourcing, storage, resistance within the norms and necessary equipment.

2 Theoretical review

2.1 Operations and production management

Companies compete for resources and customers and must somehow evaluate the results of their decisions and actions (Bentes et al., 2011), which is fundamental to maximize their resources to improve their performance. Thus, the reuse of in natura sand, which after being used in casting process becomes the main component discarded. This sand is now referred as waste by changes in its physical and chemical characteristics. With the growing interest in preserving the environment, it is necessary to explore ways of transforming, recycling and reusing industrial waste into building materials [34]. Operations production process are controlled in time and space and are aided by suppliers and customers (Hald and Mouritsen, 2012).

Enterprise resource planning systems are considered as solutions to minimize the difficulties of process coordination [9], in this way, the productive process is responsible for the activities developed. Production professionals must plan and control these processes in order to produce quality products at a lower cost, so when controlled, they guarantee through the operations carried out, the efficiency of all the activities involved in the process. Planning covers costs, quality, in addition to reducing time and minimizing resource spending. Enterprise resource planning stabilizes practices, improves the ability of the organization and its processes to adapt to innovative change [9].

From the exposed content, it can be seen the importance of planning processes and the responsibility of managers regarding the analysis of the activities that involve the productive process. Based on this, the analysis of decision-making through multi-criteria methods contributes to the organization performance.

2.2 Analysis of multicriteria decision-making

The decision-making process is associated with multi-criteria methods. This search is the choice of the best alternative for the elimination of production bottlenecks and, consequently, optimization of processes. In this context, the use of multi-criteria methods for decision-making emerges as an important methodology for managers, minimizing time and cost, improving quality and maximizing resource utilization, and reducing risks arising from a wrong choice of an alternative. Thus, the decision process is associated with conflicting objectives in choosing the best option among all feasible alternatives [19]. Therefore, the multicriteria decision analysis method (MMAD) appears as an option to obtain a purpose as an appropriate methodology for decision making [1]. In addition, the basis for the construction of a multicriteria model of decision support is formed, which will encourage the effective participation of all actors involved in the production process. The multi-criteria method in the context of the decision-making process analyzes the decision and tests its robustness, recommends courses of action or selects the best action to be implemented [31].

The MMAD is considered a flexible method since it considers both qualitative and quantitative analysis. Productive environment has become increasingly complex and dynamic due to increased competitiveness and market practices, all requiring rapid and accurate responses from decision makers [31]. The method easily clarifies the knowledge of subsidies for the final decision, both for managers of companies and interested parties, from the available options, using the multicriteria decision. So, in this research the characteristics of the evaluated context were identified, organized, measured and integrated according to values and preferences. Structure allows professionals to understand the current situation more accurately in relation to each criterion [31].

The MMAD in Brazil is widely used for the analysis of sustainable production and health, as well as analyzing uncertainties and risks, always present in production processes. Thus, the most used methods in the literature will be briefly presented [7, 19]. Organization method of sorting preferences for enrichment evaluations (PROMETHEE) family of methods based on selecting a preference function for each criterion that forms a MMAD problem. Elimination et Choix Traduisant la Realité, (ELECTRE) group of techniques aimed to overcome a set of alternatives which determine their agreement and disagreement of indices. Analytic Hierarchy Process (AHP): structured technique to analyze problems and prioritize hierarchical criteria, subcriteria and alternatives. Complex proportional evaluation (COPRAS): the objective of this method was to classify a set of alternatives and their meaning and degree of utility. Analytic Network Process (ANP) generalization of the AHP method that allows the existence of interdependencies between the criteria. Data Envelopment Analysis (DEA) non-parametric system to measure the efficiency of a set of multiple decision-making units. Delphi is an iterative method designed to obtain the maximum reliable consensus from a group of experts on a series of questionnaires. FUZZY sets the traditional concept’s extension of sharp sets which states that an element belongs to a set and can vary within the range [0, 1]. FUZZY - Analytic Hierarchy Process (FAHP), a technique that allows a more precise description of the decision process and rationalizes uncertainty associated with precision. This Fuzzy-AHP method was used to explain the occurrence of bottlenecks in the production process.

2.3 Fuzzy-analytic hierarchy process (FAHP)

The hierarchical analysis method (AHP) is considered to be one of the most effective because it involves decision making and also when more objectivity is required in the responses in complex environments (Satelite et al., 2012). The purpose of the studies carried out by the AHP methodology is to rank the actions that are in the foreground and those of the background to choose the order of decision making.

To model this kind of uncertainty (of human preference), the fuzzy sets can be incorporated in the pair wise comparison of AHP. Therefore, the FAHP approach allows a more precise and robust description of the decision process [13, 29]. Zadeh [32] introduced the theory of fuzzy sets, to rationalize the uncertainty associated with imprecision, analogously to human thought. The AHP now has a fuzzy extension, being developed to solve problems of hierarchical inaccuracy [29] (Stephan, 2014). Matrices of preferences are constructed by means of cells j calculated by matched comparison between constructs and dimensions (ai) according to the importance scale of Saaty [20], presented in Table 1.

Table 1
Assessment scale of AHP and fuzzy-AHP

If ai with respect to aj is: Then cij is If ai with respect to aj is Then cij is

Equal importance 1 Equal importance 1

Moderate importance 3 Moderate importance 1/3

Strong importance 5 Strong importance 1/5

Very strong importance 7 Very strong importance 1/7

Extremely important 9 Extremely important 1/9

If ai with respect to aj is:	Then cij is	If ai with respect to aj is	Then cij is
Equal importance	1	Equal importance	1
Moderate importance	3	Moderate importance	1/3
Strong importance	5	Strong importance	1/5
Very strong importance	7	Very strong importance	1/7
Extremely important	9	Extremely important	1/9

Source: Saaty and Shih [22]

The AHP applies the hierarchical structure to simplify complex problems, as shown in Fig. 1. The first step is to define the main goal, which is followed by global and local criteria. In this case the number of levels was determined in the information obtained from the company that manufactures the cement blocks. For this, it was related to the differentiation of the criteria that the decomposition process can provide, where the matrices, in which the inputs point to the relative strength or dominance of one element over another.

Fig. 1

Hierarchical structure of the problem. Source: Dağedeviren; Yavuz; Kilinc [5].

Following the process, the consistency index (CI) is calculated using the λmax, obtained by: IC = (λmax - n)/(n - 1) and to finalize the calculation of the consistency ratio in: CR = IC/IR. Random index (IR) is obtained by simulation and synthesized in Table 2, and in general, an acceptable consistency for n > 4 is RC ≤ 0.10 [21].

Table 2

Random index

n	3	4	5	6	7	8	9	10
IR	0,58	0,9	1,12	1,24	1,32	1,41	1,45	1,49

Source: Saaty [21].

After, the pair wise comparison of the criteria and subcriteria by means of the values (crisp) of the original AHP method is determined a scale with triangular fuzzy numbers for conversion. For this research the fuzzy scale of Somsuk was used; Laosirihongthong (2013), as shown in Table 3.

Table 3

Fuzzy linguistic scale

Fuzzy triangular scale	Reciprocal reverse	Definition
(1, 1, 3)	(1/3, 1, 1)	Equal importance
(1, 3, 5)	(1/5, 1/3, 1)	Low importance
(3, 5, 7)	(1/7, 1/5, 1/3)	Sligth importance
(5, 7, 9)	(1/9, 1/7, 1/5)	Moderate importance
(7, 9, 9)	(1/9, 1/9, 1/7)	Strong importance

Source: Adapted from Somsuk; Laosirihongthong (2013).

Regarding the choice of scale, the extension method proposed by Chang [4] follows the 6 steps used in the development of the method, which will be highlighted in the methodology of this research. Therefore, the advantage of using the Fuzzy-AHP method is that it allows a more precise description of the decision-making process with the introduction of fuzzy set theory to rationalize the uncertainty associated with imprecision, comparable to human thinking.

3 Methodology

Aiming to provide a perceptibility of points resulting from this evaluation, the research includes the following steps: bibliographic research, diagnosis of the industry under study, comparisons between peers and local priorities, application of the alternative, verification plans, and finally conclusions. In the bibliographic research, the topics related to the foundry sand generation process, management of production operation focused on concrete blocks, multicriteria decision methods using Fuzzy-AHP were used. The purpose of this step was to understand the fundamental definitions of these approaches, including management, process analysis and systems modification to ensure greater efficiency and effectiveness in production.

Thus, the process of producing concrete blocks using the casting sand was meticulously analyzed in order to obtain the most accurate data possible. The diagnosis stage was carried out, with the observation of the production cycle of the concrete blocks, as well as interviews with the managers and operators, with the purpose of collecting the necessary information to justify the present study. It is evidenced that this stage lasted about 6 months, during which the research was being carried out in the company. The AHP modeling stage is the definition of the criteria and alternatives, evidenced during the investigation. Arguments presented by Saaty [23], concerning the judgment of the comparison with each other, were considered. The order of the definition of the criteria and alternatives is in agreement with the elaboration of the structure of the problem evidenced in Fig. 2.

Fig. 2

Hierarchical structure of the problem. Source: Research data (2017).

In order to model the uncertainties in the AHP method, the Fuzzy sets can be incorporated in the judgment comparison, thus generating the Fuzzy-AHP allowing a more precise definition in the decision process (Stefano, 2014). Results of the comparisons show the relative relevance of each criterion and alternative. For this work, a Saaty and Shih scale [22] adapted with the Fuzzy triangular numbers scale of Somsuk and Laosirihongthong (2013) was used, being the same evidenced in Table 4.

Table 4

AHP and fuzzy-AHP rating scale

AHP		Fuzzy AHP
Intensity of importance	Definition	Fuzzy rating	Fuzzy reverse
1	Equal importance	(1; 1; 3)	(1/3; 1; 1)
3	Moderate importance	(1; 3; 5)	(1/5; 1/3; 1)
5	Strong importance	(3; 5; 7)	(1/7; 1/5; 1/3)
7	Very strong importance	(5; 7; 9)	(1/9; 1/7; 1/5)
9	Extremely important	(7; 9; 9)	(1/9; 1/9; 1/7)

Source: Adapted from Saaty and Shih [22] and Somsuk; Laosirihongthong (2013).

Once the scale has been defined, the extension method based on Chang [4] follows the following steps:

Step 1. Transformation of the original (crisp) values of the original AHP model into triangular fuzzy numbers using the pair wise comparison of each criterion and alternative in a matrix. This operation can be viewed by the following mathematical expression: ${(M_{g 1}^{j})}_{n \times n} = [\begin{matrix} M_{g 1}^{1} & M_{g 1}^{2} & \dots & M_{g 1}^{m} \\ M_{g 2}^{1} & M_{g 2}^{2} & \dots & M_{g 2}^{m} \\ ⋮ & ⋮ & ⋮ & ⋮ \\ M_{gn}^{1} & M_{gn}^{2} & \dots & M_{gn}^{m} \end{matrix}]$ $[\begin{matrix} (1, 1, 1) & (a_{12}, b_{12}, c_{12}) & \dots & (a_{1 m}, b_{1 m}, c_{1 m}) \\ (a_{21}, b_{21}, c_{21}) & (1, 1, 1) & \dots & (a_{2 m}, b_{2 m,} c_{c m}) \\ ⋮ & ⋮ & ⋮ & ⋮ \\ (a_{n 2}, b_{n 1}, c_{n 1}) & (a_{n 2}, b_{n 2}, c_{n 2}) & \dots & (1, 1, 1) \end{matrix}]$

Step 2. The value of the synthetic Fuzzy measure in relation to the ith object is based on the following equations: $s_{i} = {\sum_{j = 1}^{m} m_{g^{i}}^{j} \otimes [\sum_{i = 1}^{n} \sum_{j = 1}^{m} M_{g^{i}}^{j}]}^{- 1}$ (1)

$\sum_{j = 1}^{n} M_{i j} = (\sum_{j = 1}^{n} l_{i j}, \sum_{j = 1}^{n} m_{i j}, \sum_{j = 1}^{n} u_{i j}), i = 1, 2, 3, \dots, n$ (2)

$\sum_{i = 1}^{m} \sum_{j = 1}^{n} M_{g^{i}}^{j} = (\sum_{i = 1}^{m} \sum_{j = 1}^{n} l_{i j}, \sum_{i = 1}^{m} \sum_{j = 1}^{n} m_{i j}, \sum_{i = 1}^{m} \sum_{j = 1}^{n} u_{i j})$ (3)

$\begin{matrix} {[\sum_{i = 1}^{m} \sum_{j = 1}^{n} M_{ij}]}^{- 1} \\ = (\frac{1}{\sum_{i = 1}^{m} \sum_{j = 1}^{n} u_{ij}}, \frac{1}{\sum_{i = 1}^{m} \sum_{j = 1}^{n} m_{ij}}, \frac{1}{\sum_{i = 1}^{m} \sum_{j = 1}^{n} l_{ij}}) \end{matrix}$ (4)

Step 3. The degree of possibility of M₂ = (l₂, m₂, u₂) ≥ M₁ = (l₁, m₁, u₁) is determined by Equation 5: $V (M_{2} \geq M_{1}) = sup_{y \geq x} [min (μ_{M_{2}} (x), μ_{M_{2}} (y))]$ (5)

E, may be equivalent to Equation 6: $\begin{matrix} V (M_{2} \geq M_{1}) = hgt (M_{1} \cap M_{2}) = μ_{M_{2}} (d) \\ = {\begin{matrix} 1, se m_{2} \geq m_{1} \\ 0, se l_{1} \geq l_{2} \\ \frac{l_{1} - u_{2}}{(m_{2} - u_{2}) - (m_{1} - l_{1})}, cc \end{matrix} \end{matrix}$ (6)

Where d is the ordinate Fig. 3 of highest point intersection D between μ_{M
₁} e μ_{M
₂}.

Fig. 3

Intersection between M₁ e M₂. Source: Stefano, et al. [26].

As previously discussed the formulation of this research was based on the original method of Chang [4]; therefore, the first and third condition of Equation 7 was used.

Step 4. The degree of possibility for a convex Fuzzy number to be greater than Fuzzy convex numbers M_i (i = 1, 2, 3, …, k) can be defined: $\begin{matrix} V (M \geq M_{1}, M_{2}, \dots, M_{k}) \\ = V [(M \geq M_{1})] e (M \geq M_{2}) e \dots e (M \geq M_{k}) \\ = min V (M \geq M_{i}), i = 1, 2, 3, \dots, k \end{matrix}$ (7)

Equation 6 takes the form of Equation (8) evaluating the minimum of possibilities: $d^{^{'} (A_{i})} = \min v (s_{j} \geq s_{i})$ (8)

Step 5. Through normalization, the weight vectors are obtained by Equation 9 where W is a non-Fuzzy number. $W_{i} = \frac{{w^{'}}_{i}}{\sum_{i = 1}^{n} {w^{'}}_{i}}$ (9)

Step 6. Calculate the global weights for the criteria and alternatives, these weights represented by w2 are obtained by multiplying the local weight, which belongs wi.w1, according to Table 6.

With all these results, the global ranking of the alternatives is calculated according to the following equation: $P (An) = \sum_{1}^{n} (pCrn) * (pAn)$

P (An)= Alternative weight of alternative n;

pCrn= Relative importance of criterion n;

pAn= Level of preference of alternative n in relation to criterion n.

The overall value of each alternative and its weightings result in the list of priorities, organized from the least important, in order to assist the manager in making decisions regarding the alternatives in the production process.

The elaboration of the action plan aiming to apply the alternatives was developed after the FAHP analysis. Thus, the industry applied three alternatives, this application was justified due to the prioritization attributed to the participants. This application sought to complement the objective of the study; consequently, reached the analysis and discussion of the effects and the elaboration of the results.

4 Result

4.1 Initial diagnosis

The organization under study is a family structure industry, with a corporate characteristic framed in the Federal Revenue as a Small Business Company (SBC), founded in 2007. It is managed by two partners and has four employees, acting directly in its manufacturing park. Products manufactured are: pre-lage, cement artifacts, concrete, roman tile, bricks of all kinds and commercialization of building materials in general. But the main product of the industry under study is the manufacture of concrete blocks for masonry and paving.

It presents a productive capacity of 90.000 pieces/month of concrete blocks and uses of waste from the foundry sand approximately 100 tons / month. Currently the industry manufactures 72.000 pieces / month of concrete blocks. For the manufacture of products and artifacts the company offers an area away from the city due to the sound emitted by the machinery. Area has a space for locating machines and equipment, warehouses, among others and its facilities are housed in a pavilion with about 800m2 with a total area of approximately 20.000m2. As for the basic equipment used to manufacture their products, they can be divided into two scales: less sophisticated (concrete mixers, block machines, various tools - wheelbarrows, buckets, shovels, etc.) and more sophisticated ones (automatic dosing machines, Helical conveyors, programmable logic controllers, control units, steam curing systems, thermal molds, clamps, cubers, palletizers, among others).

In the analysis of the process the production bottleneck was identified. It was noticed that in the manufacture of the blocks there is a delay in the process, through this fact a thorough evaluation was carried out throughout the production to detect the location of the bottleneck and propose solutions.

4.2 Analysis of the productive process of concrete blocks

The first step after receiving the casting sand, it is carried to the hoods by means of mats to be weighed separately. In the second stage the mixture of the residue inside a mixer takes place, where additives and cement are added together with the casting sand, generating the base raw material for the blocks. The third step is that of the vibratory press, where the base material is loaded by mats to such a press, so that there is the necessary modeling and final production of the blocks. Finally, the brushing and elimination of the chips are carried out, verifying if they are in accordance with the norms, where the structural part of the block (resistance to compression and water absorption), are meeting the specifications of ABNT NBR 6136:2010, NBR 12118:2012 and NBR 9781:2013. If they meet the specifications, the blocks are stored, however, due to the possibility of contamination the blocks can not be exposed to rain or contact with the ground, so the company improvise a storage, working with orders ready to be delivered soon after manufacture. Thus, the blocks are allocated in closed trucks, because as mentioned, they can not have contact with humidity, it is worth emphasizing in relation to the transportation, that at the moment of its movement, one must be very careful that the blocks do not suffer damage, so the transport should be done carefully and safely.

4.3 Definition of alternatives

The process of judgment allows us to choose the best alternative that comes to eliminate the bottleneck and to improve the production process. Thus, five different alternatives were developed: toxicity analysis (A1), transport outsourcing (A2), equipment required (A3), resistance within (A4), storage (A5). The toxicity analysis addresses the ability of a particular substance, product or set of substances to cause harmful effects to organisms in which it may contact [6]. Varying such effects between behavioral changes, alteration of growth or reproduction can even lead to organisms death. Therefore, the toxicity analysis aims to verify which and how many substances exist in the product that can be harmful to the environment and people. The toxicity analysis is only accepted if it is carried out by a laboratory accredited by the State Foundation of Protection to the environment FEPAM, in the case of the current work a favorable report was issued. Transportation outsourcing presents lower initial investment by contracting outsourced service; It is not necessary to get involved with the direct contracting labor lawsuits; Contract with company with reference in the logistics market; Reduction of costs for losses with breaks and chipping in the transport of the product, thus increasing productivity with agility in delivery. It is very important that the blocks meet the resistance described by the standards, so that their use is possible. After the tests, it can be concluded that the sample meets the resistance specifications for Class B blocks, as stated by the interested party (equal to or greater than 4.00Mpa, NBR 6136:2007), it is emphasized that all Traces are above 4.00 MPa, so all traces are suitable for use as structural materials in construction. For the manufacture of concrete blocks it is necessary, modern equipment that will improve the productive process, as well as to elaborate a product with quality. As for the way of storage can bring countless benefits reducing risk of accidents, reducing losses and uselessness and even the best use of space.

4.4 Definition of criteria

The study presented four criteria that contributed to the selection of the best alternative that were quality, time, cost and resources. Quality (CR1): The quality of cement blocks differs from one company to another due to the different methods used in the production processes and the properties of the components of the materials used. In this case, quality comes with new technologies and techniques for effective preventive control, which works economically and efficiently, characteristic of today’s companies. The adoption of a quality program, when well implemented, makes it more likely to increase competitiveness. Concomitantly, this offers products with quality certification, or even reduces production costs, this alternative is the most used for the survival of the industry. Therefore, quality control is an important tool that ensures that the product meets the needs of customers [17]. This criterion points out the best alternative that aims efficiency in relation to the quality of blocks produced. By means of the experimental tests, the alternatives that have positive impacts against the final result of the block are identified.

Time (CR2): the new productive model demands the exercise of productive flexibility, which refers to the ability to respond in a timely manner to the changes that demand imposes, either technologically or only on the appearance of the product. In this context, companies that provide products and services with shorter term; therefore, tend to raise their price and conquer larger share in the market [10]. This criterion involves the analysis of variables, which influence the time of the processes performed, which could be the delay of the suppliers. The lack of interest of the employees in the actions carried out and limitations related to the development of the product, such as: possible problems for the arrival of the foundry sand to the company that manufactures the blocks, thus generating a delay in the productive process and; consequently, deadlines.

Cost (CR3): The main goal of knowing and having control of costs is to increase the competitiveness of the company through a methodology that generates products costs, their profitability and viability before market [18]. Thus, this criterion analyzes the overall cost of operations (study cost, investment cost) related to the alternatives presented. The cost of operations involves all costs related to the process being spent on inspections and maintenance of equipment. It can be seen that costs play an important role in industries, where the market often demands high; although, they are limited in cost.

Based on this assumption, managers should seek alternatives that meet the needs of their clients, optimizing costs efficiently and efficiently, having sensitivity and acumen in making decisions to allocate resources in alternatives that will generate positive consequences for the client industry [18]. The study cost covers all expenses related to data collection and analysis of results. And, finally, the investment cost, this one considers the expenses directed to the infrastructure and materials related to each alternative. These expenses can be the qualification of the employees, quality control, acquisition of materials and equipment, among others.

Features (CR4): Dynamic production environments require a flexible process planning and control system in response to change availability of manufacturing resources, production uncertainty, and dynamic machining conditions. In this way, resources must be worked in such a way as to meet the processes needs [14]. This criterion is related to the analysis of the implementation of each alternative, observing through the research the materials that are necessary in the use of the productive process. The availability of resources to supply the production is of paramount importance, because in the manufacture of the blocks it is necessary besides the foundry sand, other materials where they will cause the generated product to be commercialized and used respecting the norms. Figure 4 shows the criteria and alternatives used in processes optimization, aiming to eliminate production bottlenecks in manufacture of concrete blocks with the use of casting sand.

Fig. 4

Criteria and alternatives used in the research.

Thus, the concrete block manufacturing company first determined the criteria of quality, time, cost and characteristics to evaluate the alternatives, with these being used to describe a decision problem.

4.5 Comparisons between peers and local priorities (PMLs)

For the joint judgment of the evaluation criteria and alternatives, the Saaty Scale Table 4 was adopted, in which managers and experts established value judgments, as shown in Table 5. The criteria weights were made according to the importance of the peers, always focusing on eliminating the bottleneck of the cement block production process. From these comparisons in pairs, there is an index that is called relative importance,where it can be noted that, according to Cr1 “quality” reached the highest degree of importance compared to the others, reaching 45.21%. It can be seen that this criterion is associated with strength and compression, showing the ability to withstand the loads coming from the transport and the settlement as structures. Followed by resource criteria, with 20.66%, overall costswith17.45%, and implementation time criterion with 16.68%. These results are shown in Table 5.

Table 5
Weights assigned for each criterion and final prioritization

Cr₁ Cr₂ Cr₃ Cr₄ PMLs

Cr₁ (1; 1; 3) (5; 7; 9) (1; 3; 5) (3; 5; 7) 0,4521

Cr₂ (1/9; 1/7; 1/5) (1; 1; 3) (1/7; 1/5; 1/3) (1/5; 1/3; 1) 0,1668

Cr₃ (1/5; 1/3; 1) (3; 5; 7) (1; 1; 3) (1; 3; 5) 0,1745

Cr₄ (1/7;1/5; 1/3) (1; 3; 5) (1/5; 1/3; 1) (1; 1; 3) 0,2066

	Cr₁	Cr₂	Cr₃	Cr₄	PMLs
Cr₁	(1; 1; 3)	(5; 7; 9)	(1; 3; 5)	(3; 5; 7)	0,4521
Cr₂	(1/9; 1/7; 1/5)	(1; 1; 3)	(1/7; 1/5; 1/3)	(1/5; 1/3; 1)	0,1668
Cr₃	(1/5; 1/3; 1)	(3; 5; 7)	(1; 1; 3)	(1; 3; 5)	0,1745
Cr₄	(1/7;1/5; 1/3)	(1; 3; 5)	(1/5; 1/3; 1)	(1; 1; 3)	0,2066

Following the procedure, the consistency index was calculated with 0.0374 and the consistency ratio of 0.0424 calculated from the criteria judgment. In order for the matrices to be adequate and satisfactory for research, according to Saaty, CR values were <0.10.

The procedure applied to the criteria determines the preference level of the alternatives chosen by managers and specialists. The purpose is to compare the alternatives to eliminate the bottleneck of the production process of blocks. The comparisons of alternatives were made considering each of the criteria, resulting in four matrices, as shown in Table 6, thus, at the end of the trials, the priority of the alternatives was evidenced. The overall classification of the alternatives was achieved by the weighted sum of the relative importance indices of the priority level of the mentioned criteria.

Table 6

Judgments of the alternatives related to the 4 criteria

Quality	A1	A2	A3	A4	A5
A1	(1; 1; 3)	(1; 1; 3)	(1; 3; 5)	(1; 1; 3)	(3; 5; 7)
A2	(1; 1; 3)	(1; 1; 3)	(1; 3; 5)	(1; 1; 3)	(3; 5; 7)
A3	(1/5; 1/3; 1)	(1/5; 1/3; 1)	(1; 1; 3)	(1/5; 1/3; 1)	(1; 3; 5)
A4	(1; 1; 3)	(1; 1; 3)	(1; 3; 5)	(1; 1; 3)	(3; 5; 7)
A5	(1/7; 1/5; 1/3)	(1/7; 1/5; 1/3)	(1/5; 1/3; 1)	(1/7; 1/5; 1/3)	(1; 1; 3)
Time	A1	A2	A3	A4	A5
A1	(1; 1; 3)	(1/5; 1/3; 1)	(1; 1; 3)	(1; 1; 3)	(1; 1; 3)
A2	(1; 3; 5)	(1; 1; 3)	(1; 3; 5)	(1; 3; 5)	(1; 3; 5)
A3	(1; 1; 3)	(1/5; 1/3; 1)	(1; 1; 3)	(1; 1; 3)	(1; 1; 3)
A4	(1; 1; 3)	(1/5; 1/3; 1)	(1; 1; 3)	(1; 1; 3)	(1; 1; 3)
A5	(1; 1; 3)	(1/5; 1/3; 1)	(1; 1; 3)	(1; 1; 3)	(1; 1; 3)
Cost	A1	A2	A3	A4	A5
A1	(1; 1; 3)	(1; 1; 3)	(1/5; 1/3; 1)	(1; 1; 3)	(1/5; 1/3; 1)
A2	(1; 1; 3)	(1; 1; 3)	(1/5; 1/3; 1)	(1; 1; 3)	(1/5; 1/3; 1)
A3	(1; 3; 5)	(1; 3; 5)	(1; 1; 3)	(1; 3; 5)	(1; 1; 3)
A4	(1; 1; 3)	(1; 1; 3)	(1/5; 1/3; 1)	(1; 1; 3)	(1/5; 1/3; 1)
A5	(1; 3; 5)	(1; 3; 5)	(1; 1; 3)	(1; 3; 5)	(1; 1; 3)
Resources	A1	A2	A3	A4	A5
A1	(1; 1; 3)	(1; 1; 3)	(1; 1; 3)	(1; 1; 3)	(1/5; 1/3; 1)
A2	(1; 1; 3)	(1; 1; 3)	(1; 1; 3)	(1; 1; 3)	(1/5; 1/3; 1)
A3	(1; 1; 3)	(1; 1; 3)	(1; 1; 3)	(1; 1; 3)	(1/5; 1/3; 1)
A4	(1; 1; 3)	(1; 1; 3)	(1; 1; 3)	(1; 1; 3)	(1/5; 1/3; 1)
A5	(1; 3; 5)	(1; 3; 5)	(1; 3; 5)	(1; 3; 5)	(1; 1; 3)

The overall classification of each alternative was obtained from the weighted sum of indices of relative importance and level of preference of each of criteria. Judgment of alternatives returns to the criterion quality that presented IC 0.0112 and RC 0.0101. In other alternatives, the trial presented CI = 0.0000 and RC = 0.0000. Thus, as a general rule, if the consistency index is less than 0.10, then there is consistency.

In Table 7, the weight of each alternative was analyzed against the mentioned criteria. Thus, it can be seen that Alternative A1 was the one that obtained the highest degree of importance in relation to these criteria, and the least prioritized A3. Result obtained by the application of the FAHP method presents the transport of the cement blocks as the most important. This alternative has a greater impact on productivity and, consequently, eliminates the bottleneck of the cement block production process using casting sand, as it reached (24.24%), preferably between alternatives. This alternative is associated with the movement of raw materials, products or changes in positions. Transport and handling of the blocks are factors that generate losses, due to breaks and chipping of the same, thus being discarded.

Table 7

Weight of each alternative against the mentioned criteria

	CR1	CR2	CR3	CR4
A1	0,1239	0,0344	0,0311	0,0344
A2	0,1239	0,0529	0,0311	0,0344
A3	0,04	0,0109	0,0336	0,0476
A4	0,1239	0,0344	0,0311	0,0344
A5	0,0403	0,0344	0,0475	0,0558

The other preference lies in two alternatives: toxicity and storage analysis both with (22.38%). The toxicity analysis meets the requirements of CONSEMA 129/06 resolution, as defined in Art. 9. As for the storage, it contributes to facilitate the product distribution. Regarding the equipment (17.45%), due to the company use high-tech equipment, benefits of this alternative, aims to offer superior products to final consumers. The resistance within the standards with (13.20%), the quality sector strictly controls the resistance of product as declared by the responsible manager (equal or superior to 4.00Mpa, NBR 6136:2007).

4.6 Application of the alternative and evolution of the results

The implementation phase was established according to the dates foreseen in the research schedule. Results obtained with the analysis of the process were described with the purpose of increasing the productivity of the block industry, thus the priority alternative was applied: outsourcing of transport (Fig. 6). Results achieved during 60 days demonstrated that the industry obtained gains such as: lower initial investment for contracting outsourced service; it was not necessary to get involved with the direct contracting labor lawsuits; contract with company with reference in the logistics market; reduction of costs by 25% for losses with breaks and chipping in transportation of product; increase productivity with agility in the delivery of products, thus eliminating the production bottleneck; Focus on the company’s main objective to increase the consumption of discarded sand casting (ADF), contributing to the sustainable development of the foundry sector.

Fig. 5

Criterion prioritized.

Fig. 6

The most relevant alternative.

As for the alternative, toxicity analysis, after the implementation phase, monthly tests are performed to verify if they are in accordance with the standards, so the objective was met, there was a reduction in the reworking and leveraged in productivity. Due to the existence of foundry residues as well as heavy metals which can harm the environment through contamination, it has been reported that the implementation of toxicity analysis has resulted in the industry greater confidence for consumers of concrete blocks, besides contributing to sustainability. Thus, it is perceived that the industry is concerned about the environment, it has managed to reduce the chance of contamination by 100%, adopting correct practices. The toxicity analysis test also benefited the event of any type of accident, and they will not be harmful to living organisms. When the level of toxicity is above the allowed, rework generates costs and wastes of time, with monthly monitoring of toxicity analyzes there is a guarantee that there will be no rework, avoiding cost and time wastage.

Regarding alternative of resistance within the norms, after the moment of implementation, it was observed that the products presented greater resistance, that is, they provided the lowest index of breaks and chipping, resulting in the minimization of costs and time. Resistance standards of the concrete blocks guarantee their conformity, taking place in the product quality. In the verification of resistance within the defined period it was verified that the productivity increased by 25% and the reduction of rework due to breaks and chipping reached 98%. In this way, the alternative demonstrated an economy of R $ 7,532.00 / month, reaching R $ 90,384.00 / year. The monthly tests avoided product failures if a lack of quality control attention occurred.

4.7 Sensitivity analysis

From the analyzes made using the Fuzzy AHP method, it was verified that the outsourcing transport (A2) was prioritized, showing relevant returns to the company during its application. However, in order to verify if constant changes in relative weights would provide relevant changes in the final ranking, a sensitivity analysis was performed. The analysis demonstrated scenarios that reflect future alternative developments or even different points of view regarding the importance of the relative weights of the criteria [3, 16]. For this purpose, the weights of the criteria are changed individually, making up a simulation environment between 0% and 100%. For Chang et al. [3], the sensitivity analysis is necessary since, changing the criteria weights, require different levels of management. In this way, Table 8 shows the simulations made, following in a constant way the increase of the weight of the quality criterion, being shown in Fig. 7, the behavior obtained.

Table 8
Simulations for sensitivity analysis of the quality criterion

Quality A1 A2 A3 A4 A5

0% 0,2993 0,3358 0,2043 0,2993 0,2953

10% 0,2818 0,3146 0,1878 0,2818 0,2698

20% 0,2642 0,2934 0,1714 0,2642 0,2443

30% 0,2467 0,2722 0,1550 0,2467 0,2188

40% 0,2291 0,2510 0,1386 0,2291 0,1933

50% 0,2116 0,2298 0,1221 0,2116 0,1678

60% 0,1941 0,2087 0,1057 0,1941 0,1423

70% 0,1765 0,1875 0,0893 0,1765 0,1168

80% 0,1590 0,1663 0,0729 0,1590 0,0913

90% 0,1414 0,1451 0,0564 0,1414 0,0658

100% 0,1239 0,1239 0,0400 0,1239 0,0403

Quality	A1	A2	A3	A4	A5
0%	0,2993	0,3358	0,2043	0,2993	0,2953
10%	0,2818	0,3146	0,1878	0,2818	0,2698
20%	0,2642	0,2934	0,1714	0,2642	0,2443
30%	0,2467	0,2722	0,1550	0,2467	0,2188
40%	0,2291	0,2510	0,1386	0,2291	0,1933
50%	0,2116	0,2298	0,1221	0,2116	0,1678
60%	0,1941	0,2087	0,1057	0,1941	0,1423
70%	0,1765	0,1875	0,0893	0,1765	0,1168
80%	0,1590	0,1663	0,0729	0,1590	0,0913
90%	0,1414	0,1451	0,0564	0,1414	0,0658
100%	0,1239	0,1239	0,0400	0,1239	0,0403

Fig. 7

Simulation of changing the weights of the Quality Criterion.

As mentioned, for each criterion (Quality, Time, Cost and Resources), simulations were performed with the purpose of verifying the behavior of the final ranking. In Fig. 7, it is possible to verify that in no moment, with the changes of the weights occurring in the criterion quality, there were change in the final ranking, denoting that in any circumstance Alternative 2 would be the one selected. Since the weights of Alternatives 1 and Alternative 4 are equal, the line in Alternative 1 is not shown in any of the figures.Following the same reasoning, Table 9 demonstrates the simulations made for the time criterion.

Table 9

Simulations for sensitivity analysis of the time criterion

Time	A1	A2	A3	A4	A5
0%	0,2572	0,2775	0,1538	0,2572	0,2091
10%	0,2349	0,2550	0,1395	0,2349	0,1917
20%	0,2126	0,2325	0,1253	0,2126	0,1742
30%	0,1903	0,2101	0,1110	0,1903	0,1567
40%	0,1681	0,1876	0,0967	0,1681	0,1392
50%	0,1458	0,1652	0,0824	0,1458	0,1218
60%	0,1235	0,1427	0,0681	0,1235	0,1043
70%	0,1012	0,1203	0,0538	0,1012	0,0868
80%	0,0790	0,0978	0,0395	0,0790	0,0693
90%	0,0567	0,0754	0,0252	0,0567	0,0519
100%	0,0344	0,0529	0,0109	0,0344	0,0344

Observing Fig. 8, it is possible to note that in all simulations, similar to the quality criterion, the modified weights for the time criterion did not change the final decision.

Fig. 8

Simulation of changing the weights of the criterion Time.

Regarding the criterion cost, Table 10, shows the changes in weights.

Table 10

Simulations for sensitivity analysis of the criterion Cost

Cost	A1	A2	A3	A4	A5
0%	0,2599	0,2842	0,1504	0,2599	0,2080
10%	0,2370	0,2589	0,1387	0,2370	0,1920
20%	0,2142	0,2335	0,1270	0,2142	0,1759
30%	0,1913	0,2082	0,1153	0,1913	0,1599
40%	0,1684	0,1829	0,1037	0,1684	0,1438
50%	0,1455	0,1576	0,0920	0,1455	0,1278
60%	0,1226	0,1323	0,0803	0,1226	0,1117
70%	0,0997	0,1070	0,0686	0,0997	0,0957
80%	0,0769	0,0817	0,0570	0,0769	0,0796
90%	0,0540	0,0564	0,0453	0,0540	0,0636
100%	0,0311	0,0311	0,0336	0,0311	0,0475

In Fig. 9 it is possible to observe that if the weight of the criterion were determined from 80% it would generate an inversion in the final ranking, causing alternative 5 (A5) to take first place.

Fig. 9

Simulation of changing the weights of the cost criteria.

Finally, we performed simulations for the resources criterion, being shown in Table 11, the variations of weights.

Table 11

Simulations for sensitivity analysis of the criterion Resources

Resources	A1	A2	A3	A4	A5
0%	0,2683	0,2935	0,1515	0,2683	0,2123
10%	0,2449	0,2676	0,1411	0,2449	0,1967
20%	0,2215	0,2417	0,1307	0,2215	0,1810
30%	0,1982	0,2158	0,1203	0,1982	0,1654
40%	0,1748	0,1899	0,1099	0,1748	0,1497
50%	0,1514	0,1640	0,0995	0,1514	0,1341
60%	0,1280	0,1381	0,0891	0,1280	0,1184
70%	0,1046	0,1121	0,0788	0,1046	0,1028
80%	0,0812	0,0862	0,0684	0,0812	0,0871
90%	0,0578	0,0603	0,0580	0,0578	0,0715
100%	0,0344	0,0344	0,0476	0,0344	0,0558

In Fig. 10, it is possible to observe the variations obtained with the simulations. It is observed that when the Resources criterion assumes 70% priority, it causes Alternative A5 to equal Alternatives 2 and 4, and as the percentage increases, the inversion of the final Ranking, with alternative A5 (Storage) as the most prioritized, being no longer the alternative A2. Such a change can be explained, since this alternative concerns the storage, being evident the importance of the resources within that alternative.

Fig. 10

Simulation of changing the weights of the criteria resources.

The results regarding sensitivity analysis indicated that the main change occurred when the weights of the cost and resources criteria increased to 90%. However, it was noted that there were no major changes in the final decision, showing that the decision is relatively insensitive to changing the weights of the criteria.

5 Conclusions

Proper disposal of the sands is a challenge for industries that are increasingly concerned about the need to preserve the environment in the pursuit of sustainable development. The production of the concrete blocks tends to present a lower cost, since the manufacturer must pay less for the raw material, this being a symbolic value, or even at no cost, since the foundry industry generates a great quantity of this residue. Today, reuse is an economically advantageous solution for the foundry industry, as companies are responsible for discarding this waste and pay a high price for this process.

The basis of this research was the use of the FAHP method, which contributed to the decision making, using the relevant criteria related to the highlighted alternatives. Thus, the objective of the research was to optimize the processes aiming to eliminate production bottlenecks with regard to the manufacture of concrete blocks using the casting sand of a metalworking industry. The alternative prioritized by the managers and specialists was the outsourced transportation, being advantageous for the industry due to the non-involvement with labor laws and the transport company presents references in the market, reducing costs in 25% directed to losses with breaks and chipping transport of the product; increase of productivity with the agility in the delivery of goods, thus collaborating to eliminate the bottleneck of production.

The improvements presented by the alternatives: analysis of toxicity and resistance within the norms, also helped industrial productivity. The toxicity analysis contributed to the reduction of costs and wastes of time; consequently, avoiding rework, reducing in 100% the chance of contamination, due to the adoption of correct practices. The resistance within the standards ensured product conformity, achieving a 25% increase in productivity, which resulted in the use of the industry’s maximum capacity. The improvements reported through the FAHP method were achieved through the degree of importance of alternatives, in order to maximize the industry profit.

Regarding the economical part of manufacturing, the reduction in the general costs of the components used when using the ADF is proven. Levels of reduction of costs reach 4% and 8%, when the substitution of fresh sand by the ADF occurred with 35% or 70% respectively. These data are definitely decisive for the economic viability of the research project. The feasibility will only be confirmed if the actions mentioned above are developed, namely the liberation by the liberating agency, the production of other products developed by the industry, as well as the possibility of substitution in the percentages of 70%, already proven in tests developed in the university’s laboratories. The final amounts of approximately R$ 60.00 (US $ 16.00) spent by the industry for each tonne deposited in landfills are required to comply with current legislation for environmentally responsible disposal. However, it is known that these costs have a tendency to rise over the years, precisely so that the responsible sector finds solutions to its waste, motivated also by the growth of movements in defense of the environment, which are constantly advancing in the achievements of their ideals. For the extension of this research, the ANP fuzzy method can be applied to consider interrelations between the criteria and the alternatives, but there are other multicriteria decision analysis methods that can be used in similar case studies. In addition, this organization is relatively recent in the use of casting sand for the manufacture of cement blocks, so there is limited data on performance. To evaluate your success and compare it to another similar organization, future research is needed for more information on its performance.

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