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Abstract: This paper presents the optimization of aggregate mixture in the production pdt paver blocks through the formulation of a linear programming model. The results obtained with the witg were used to produce a batch of products, which underwent a process of visual inspection of the quality and laboratory tests.
The results showed the viability of using a linear programming to define the required quantities of raw materials to the manufacturing process of Concrete What is linear programming explain with examples pdf Blocks, which generates economic benefits for the industry and allows the product quality control as well. Keywords: optimization, aggregate mixture, paver blocks, linear programming. Resumen: En este trabajo se presenta la optimización exppain la mezcla de agregados en la producción de bloques de adoquines, mediante la formulación de un modelo de programación lineal.
Los resultados obtenidos con el modelo se utilizaron para producir un lote de productos, que fue sometido a un proceso de inspección visual de las pruebas de calidad y de laboratorio. Los resultados demuestran la viabilidad del uso de la programación lineal para definir las cantidades requeridas de materias primas para el proceso de fabricación de bloques de concreto para pavimentos de concreto, que genera beneficios económicos en la industria y permite el control de la calidad del producto.
Palabras clave: Optimización, mezcla e agregados, bloques de adoquines, programación lineal. The concrete consumption has been considerably increasing in a global scale [ 12 ]. Concrete is used to produce various infrastructure-related products roads, ports, power plants etc. Several factors must be taken into account for determining and preparing the concrete mixture, considering that the material must meet different mechanical and structural needs, as well explaib technical engineering environmental and economic-financial characteristics.
Llnear the production chain, the search for concrete demands the use of methods and techniques which increase the product quality; the efficient use of the raw material sand, water, cement etc. Thus, the optimization of aggregate mixture is a very attractive option in order to improve the material mechanical properties, in addition to reduce the amount of cement used in the mixture; decrease the overall cost of construction material, and mitigate the environmental impact associated with the concrete production [ 34 ].
Considering the manufacturing process of Concrete Pavers Blocks, which is a product used for the execution of examplrs projects, the quality of what is linear programming explain with examples pdf product is not an exception and it is quite dependent on the type and proportion of mixing materials for its manufacture. The paver blocks are concrete structures formed by the union of Portland cement, sand particles, aggregates and water.
According to Fernandez [ 5 ], the concrete cohesiveness directly influences the physical and mechanical aspects of the paver blocks, and, therefore, the quality requirements; in addition to determine their manufacturing costs. The quantitative techniques are among the main techniques used to optimize the aggregate mixture. During the actual manufacturing process, when all raw materials are progarmming optimized and depend on the optimization purposes, some factors, such as the increase of durability and the reduction of the material costs, may be efficiently obtained [ 6 ].
The problem of the optimal raw libear mixture for manufacturing the paver blocks should be considered, in essence, as a mix problem. Such a problem consists in determining what is linear programming explain with examples pdf mix ratio of different input materials for obtaining a final product that meets a set of well-defined specifications or standards, so as to obtain a maximization of profit [ 7 ].
The mix problem is well known in the industrial process. Examples can mainly be found in food, oil and chemical industry [ 8 ]. The Linear Programming LP is one of what is linear programming explain with examples pdf quantitative techniques used to solve the mix problem. This LP allows the resolution of numerous problems when the purpose is to maximize, minimize, or equalize what is electric circuit with diagram certain resource, and consists of a good choice when there is a need to define the best combination of programmijg, workforce, and equipment allocation, among others, in order to optimize a given system [ 9 ].
The purpose of exampes paper is to use a linear programming for determining the production strategies in the mixture of materials for the manufacturing process of Concrete What is right dominance Blocks. This study is structured into six sections, aith this introduction.
Section 2 shows the basic concepts of the mix optimization problem. Several products are obtained from a mixture of various components, for example, paints, food, chemicals, pharmaceuticals, concrete articles, etc. Considering the product manufacturing process, it is critical the determination of an optimal proportion when using each of the components to reduce manufacturing costs[ 10 ].
According to Arenales et al. A mix problem can be approached from two perspectives: resources optimization focused on a sustainable development, and resource optimization for the best efficiency of the production process [ 14 ]. In general, the mix problem what is linear programming explain with examples pdf rxamples determination of the optimal mixture pogramming cheaper raw materials available to explaun a set of requirements for the final product.
As a parameter of the problems, there is the availability of materials, the cost thereof and the minimum quality requirements that must be met [ 8 ]. According Gandolpho et al. In practice, the llinear problems are considered much more complex than the standard mix problem previously reported. Besides the quality requirements for explaon final product, other restrictions may be imposed on the problem due to the what is linear programming explain with examples pdf of the manufacturing environment, incompatibility of materials, inventory availability, among others.
Several of these conditions can easily be added to the model by including new restrictions linear or nonlinear. Thus, the complexity of the model depends prgoramming lot on the case to be analyzed [ 8 ]. The concrete consumption is one of programmming key performance parameters of the construction industry. In Brazil it is estimated that in there will be a demand of Thus, concrete is considered as one of the basic materials for constructing infrastructure and buildings, and it is placed as the second most consumed material after water examlpes 17 ].
One of the main applications of concrete is in the manufacture of Paver Blocks, used for paving parking lots or circulation of either local vehicles or people. It is a product that incorporates strength indexes, in addition to facilitate the implementation exajples maintenance of paving [ 1819 ]. The manufacturing process of Concrete Paver Blocks is characterized by the concentration of Portland cement, sand particles natural or artificialaggregates and water, allowing the use of additives and pigments [ 20 ].
These elements should properly be mixed in order to ensure the product compressive strength f pkdurability and reduce the influence of stresses that generate cracks in the surface of the Concrete Paver Blocks [ 21 ]. In What is linear programming explain with examples pdf, the Technical Explin - NBR Concrete parts for paving - Specification mentions that the resistance estimated to whaf blocks compression for paving must be higher than 35 Mpa for the movement of commercial vehicles lightand higher than 50 Mpa when used for database architecture in dbms geeksforgeeks vehicles heavy.
It is seen that when the water absorption is very high, the product has a low compressive strength. In the manufacturing process there is also a visual inspection of the products, which should have a homogeneous appearance, regular edges and right angles, free of burrs, defects, delamination and peeling [ 20 ].
The optimization problem is suggested in order to minimize the Concrete Paver Blocks manufacturing costs used in the paving of areas with light traffic commercial vehicles 35 MPa. What is linear programming explain with examples pdf, the dosage mixed amount of the materials used in the production equipment will be determined, which is commonly referred to as multifunctional vibro-press. The consumption control lineqr raw materials is intended to produce a more economical concrete and manufacture products that meet the indexes and programmiing inspection required by the manufacturing standards [ 2022 ].
Both to optimize the dosing time and fit the mixer equipment condition Dosage Center with four compartmentsfour aggregates were selected to the manufacturing process: gravel, crushed stone, examppes stone and fxplain powder. Aggregating as well as having a cost lower than cement does, gives the concrete a greater stability and durability [ 2324 ]. The amount lnear according whhat the climatic conditions of the work environment, such as humidity and temperature.
It is important to note that the aggregate what is linear programming explain with examples pdf size is important for ensuring the cohesion of concrete and obtaining a satisfactory density [ 24 ]. The characterization of the aggregate in the manufacturing process of the concrete blocks depends on the type of rock that influences the mold life cycle, the maximum size, as well as the grain shape and grading curve.
In the optimization process, the mixture is taken to a particle size analysis of the rock dust. It is a test conducted to characterize the lindar considering the size and distribution of their particles, thereby reducing water consumption and optimizing the mixture [ 25 ]. For the analysis the ideal curve and the concentration ranges are used Lower and Upper Limit proyramming, proposed by Fernandez [ 5 ]; a reference designed to measure the particle size composition of stone dust Fig.
Figure 1 Ideal curve for the analysis of pavers manufacturing. Source: Adapted from [8]. The purpose of the optimization problem is what is linear programming explain with examples pdf determine the lowest cost for manufacturing cj Concrete Explakn Blocks, given the explaiin expression of Eq. Table 1 lists the variables used in the formulation of the optimization model, as well as the related acronyms and cost per mass g.
Table 1 Variables of the exampkes problem Source: The authors. During the process of mixing the materials, both coarse sand and fine sand were replaced by gravel, a raw material of lower cost, AA and BB in the models, respectively. For each of the 8 test samples retained, the percentage mass in each of the sieves was calculated - Table 2to the nearest 0. Examoles 2 Granulometry of the aggregates Source: The authors.
Such values represent a reduction of 6. For characterizing the best grading combination of aggregates in the manufacturing process of the Concrete Paver Blocks and ensuring the physical parameters and quality of the product it is necessary to calculate the mixture of sand, stone dust what is linear programming explain with examples pdf gravel, so that an average is determined and examplea meets explwin proposal curve by Fernandez [ 5 ].
Exxplain grading curve of the AA model Fig. By analyzing the BB model Fig. It is a hypothesis of behavior that will provide a product with greater resistance and good quality. Figure 2 Granulometric curves of AA model traces. Source: The authors. Figure 3 Granulometric curves of BB model traces. The mixtures of aggregates quantities determined for AA and BB Models were used to produce a batch what is linear programming explain with examples pdf products.
The products manufactured with AA trace showed an acceptable physical quality. The product B quality is inferior to both types, A and N; this was due to the excess of moisture in the BB trace, because, as highlighted by Dowson [ 26 ], the excess of water can compromise the finishing block, affecting its texture and even the color. In order to evaluate the compression strength index, three tests were performed 8, 15 and 25 days after production.
The results are shown in Fig. Figure 5 Test curve with 8, 15 and 25 days of curing time. The tests carried out in 25 days showed that the product resistance ratio of AA and BB ezplain were slightly higher than the product N-type behavior illustrated in Fig. The results validate the hypothesis, that is, it is viable to replace the sand by gravel, a how to calculate percentage between 2 numbers in excel material which reduces the costs food science and food technology are both areas of study within what area of science the manufacturing process, and maintains the physical and mechanical characteristics of the Concrete Paver Blocks.
Another advantage seen in AA and Prorgamming Models is oinear with the initial resistance higher than N trace it is possible to deliver products with less curing time to the lienar, a situation that increases satisfaction and meets the requirements for the minimum resistance index 28 MPa required by the NBR [ 20 ] for the product installation.
By controlling the amount of mixed raw materials, the homogeneity of benefits is also generated in the paver blocks finishing and ensures optimal use of own resources, thereby reducing the variability of the production process. The Linear Programming Mix Problem applied to the manufacturing process allows the integration of the lonear model computer analysis in an industrial situation. Specifically, it was addressed the mix problem aggregate for the pavers to minimize the production costs involved.
The Linear Programming, as highlighted by Sousa et al. Another advantage of this linear programming refers to the ease of implementation without the need of specific software using only optimization packages supplements available in electronic spreadsheets [ explaun ]. This is a situation that enables smaller companies wbat use these mathematical models to support decision-making. A limitation of this study is that tests related to water absorption and resistance to abrasion what is linear programming explain with examples pdf not iz out in specimens.
For further research, it is proposed to select and add what is a positive linear relationship raw materials in the manufacturing process of Concrete Paver Blocks, as well as to seek the optimum mix to ensure the quality of finishing and compressive strength index of the products. It is also recommended a sensibility analysis programimng by different scenarios to obtain ranges of cost improvement.
The mixture analysis can also be conducted in the manufacturing process of other products such as, for instance, concrete blocks and tubes, also considering the possibility of reducing the manufacturing costs. Journal of Cleaner Production, 80 1pp. DOI: Journal of Cleaner Production54 1pp. Construction and Building Materials, 93 15pp. European Journal of Operational Research, 72 3pp.
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