CELL FORMATION IN SHEET METAL PROCESSING INDUSTRY USING GENETIC ALGORITHM

CHAPTER 4

CELL FORMATION IN SHEET METAL PROCESSING INDUSTRY USING GENETIC ALGORITHM

4.1 OBJECTIVE

Modern competitive environment induces every organization to be on top of its competitors with better quality products at lower prices. To meet the demands of globalization, various products with different design is essential for a stable market. Group technology (GT) can be used as an option to meet the demands of the market. GT is a manufacturing philosophy based on the principle that similar things should be done similarly. The Cellular Manufacturing System (CMS) is one of the most critical applications of GT in production. CMS is used to divide the manufacturing facility into small cells in which the similar parts and its associated machines are grouped to form a manufacturing cell. The identification of part family and its associated machine cells are called Cell Formation (CF). Many metaheuristic techniques are used to develop cellular manufacturing systems. In this work, cell formation is done using genetic algorithm (GA) as a metaheuristic technique. Initially, GA is prepared for the concurrent formation of part families and machine cells for CMS. GA is designed to handle the objective of minimization of exceptional elements in the sheet metal industry, where exceptional elements are the machines and parts that are excluded from the suggested two or three cells. In this study, the machine parts incidence matrix is given as input for GA to minimize the total number of exceptional elements in order to evaluate the effectiveness of the CF.  The proposed GA is coded in C++ language on a personal computer with core Duo, the 2GHZ processor.

3.2 INTRODUCTION

In the present millennium, the industry venture into a new phase where it needs to sustain the long term economic vitality and at the same time has to discover new opportunities and possibilities. Indeed, recent years have seen an increasingly dynamic environment due to intensive international competitions. This intensified rivalry places persistent pressure on manufacturing systems to be enhanced both in efficiency and effectiveness. This is manifested in the rising tendency of more exceptional varieties of products with shrunk product life cycles. The traditional manufacturing systems are not able to satisfy these requirements. The manufacturing industries are under intense pressure from the increasingly competitive market. Proper scheduling of jobs is indispensable for the successful operation of a shop. Group technology has become an increasingly popular concept in manufacturing, which is designed to take advantage of mass production layout and techniques in the smaller batch production system.

Traditional layouts namely, the process layout and the product layout, are the two most standard means to locate machinery on the production floors. It shows the physical configuration of a process layout, where all the similar workstations are placed close to one another. The significant advantages of a process layout are its high flexibility in product routing and high machine utilization. Nevertheless, a process layout also creates many problems such as unmanageable material flow, significant work in process inventory. These shortcomings limit the extent of using a process layout in today’s competitive environment. A product layout has a different physical configuration of workstations in which workstations are located according to the sequence of the operations in manufacturing the parts. This layout provides an effortless material flow and reduces work-in-process inventory and production cycle time. However, the product layout works well only in mass production. When the product mix is consistent, it lacks the flexibility to adapt readily to changes in the manufacturing environment and becomes costly when it is applied to production in a wide diversity.

In this present scenario, Cellular Manufacturing Systems (CMS) have emerged as one of the most critical applications of Group Technology (GT) in production. It describes Cellular Manufacturing System (CMS) allows decomposing a manufacturing system into subsystems. Grouping the machines and parts in a cellular manufacturing system, based on similarities is known as cell formation problem (CFP). In CMS, the elements that undergo similar manufacturing operations are grouped as a part family, and the workstations that produce those parts are arranged to form a machine cell so that the parts can be provided within the cell. Since each cell contains only a few workstations, it can be easily located according to the operation sequences of the majority of the parts, and thus, simplifies the material flow within the manufacturing cells. Owing to the similarities of parts and the proximity of workstations, a cellular layout enjoys the advantages in managing material flow as a product layout.

4.2.1 CELLULAR MANUFACTURING SYSTEMS

The cellular manufacturing can be considered as the process of production that is a subsection of the just in time of construction as well as lean manufacturing encompassing the group based technology. When cellular manufacturing has the main aim to move them as quickly as possible, they make a wide variety of similar products. That they produce less waste as possible. Cellular manufacturing involves the purpose of many cells in the assembly lines based fashion. In each of the cell can be composed by the one as well as many various kinds of machines that can be accomplished a curtained tasks. The product that can be moved from one cell to another, in each station can be completing the part of the process based on the manufacturing. Often the cells can be arranged in a U shape the design because they allow for the overseer to move little and they have an ability for more readily to watch over the whole process. The more merits in cellular manufacturing can have the amount in the flexible. Hence most of the machine can be automatic; there are simple changes that can be made very rapidly. They can allow the various scaling for the product. The minor changes for the overall design they can have extreme cases, the complete changes in the entire plan. This type of changing, although the tedious that has to be accomplished in the exceptionally quickly. When the cell can be created the consolidating the process that can be required for they generate a specific output, in such apart as well as the set the instruction. Then the cells can be attained due to minimize the extraneous stage occur in the process for they create the specific output they can facilitate the quick identification of the issues they can arise them fast. The identification of the problems as well as they encourage the communication of the employees with the cell. To resolve the problem, they can arise them fast. They can implement the cellular-based manufacture that can be said to more reliable to create the massive depend on the gain that can be produced when the quality that can be simultaneously for they minimized the number of inventory. Space and the lead-based duration that they require to create a product. The problems solve occur in the cellular manufacture system are shown in figure 4.1.

Figure 4.1 problem-solving steps in cellular manufacture.

4.2.1.1 CELL FORMATION PROBLEM

They solving cell-based formation problems can be considered as the first step for the implementation of the cellular manufacturing system. The main objective for the cell formation problem that can be grouped the part at the similar at the design characteristics as well processing requirement for the part families and them corresponding machine into

one based cells. Then they process based on grouping that can reduce the latency manner.

4.2.1.2 MACHINE LAYOUT PROBLEM

The machine solving layout based problem can be considered as the second step toward the implementation of the cellular manufacturing system. They also consider the m as the machine and the p can be considered as the parts. When the single ————-machine can process the different parts that may be utilized due to the manufacture the +-*98/different and the several of the product. When the various part that may have the various functional based sequence as well as the various demands. The main aim of the machine layout problem that can be reduce for the total travelling the distance of the whole p part for they determine the optimal layout based scheme of the whole m based machine for they subject them to overlap as well as there is no duplication of the machine based constraints.

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4.2.1.3 CELL LAYYOUT PROBLLEM

The cell layout problem solving can be considered as the third step towards the implementation of the cellular manufacturing based system. The main aim is to found an optimal layout that can be scheme based cell within the factory as well as shop floor in way that can be reduce the inter cell based movement of the different parts.

4.2.2 SOLVING SEQUENCE

Cell formation problem, machine layout problem and cell layout problem should be sequentially, efficiently and optimally solved in order to optimize the performance of industrial manufacturing processes, to reduce total manufacturing cost, time and area and to improve profit, productivity and production quality.

Cell formation problem has been solved by most of the researchers, many researchers have solved only machine layout problem without first solving cell formation problem while only few researches have solved cell layout problem & these three problems completely. Cell formation problem, machine layout problem and cell layout problem should be sequentially solved in order to generate complete cellular manufacturing system design. Cell formation problem, machine layout problem and cell layout problem have been concurrently solved by some researchers by developing single approach. Concurrently solving two or more problems may waste computational time, may not find out optimum design of cellular manufacturing system and thus solving two or more problems concurrently is not advisable.

4.2.3 SOLVING METHOD

The heuristics, metaheuristic, hybrid based method as well as exact solution of the method may be used for the purpose of solve the cell formation based problem and the cell layout based problem. The genetic based algorithm depends on the approaches that the main famous as well as more researchers can be helps to solve the cellular manufacture based system problems.

The performance based on the genetic algorithm can still that improve the choose the proper requirements as well as suitable range of the parameter that can be implement the genetic algorithm. In the exact solution based method can be determine the optimized solution based on the cellular manufacture based system issues but they can be consumed the more much duration they can be determine the solution based on the cellular manufacture based system issues when compare to the heuristics, metaheuristic as well as hybrid method.

The exact solution based method can be recommended for they solving the small based sized as well as medium sized based cellular manufacture system based problem. When the exact solution based method can be find out the solution of the large sized cellular manufacture system based problem for the limitation in the hardware. When the heuristic, metaheuristic as well as hybrid based method is helps to solve the large sized the cellular that can be manufacture the system based problem they can be efficiently in the such situation they can be exact the solution based method they can be obtained the solution for the cellular based manufacture system in a practical length of the duration but the heuristic, metaheuristic as well as hybrid based method can determine the optimum for the solution based cellular manufacture based system problem. They can be recommended for they solve the large sized in the cellular manufacture based system problem.

4.2.4 BENEBITS OF THE CELLULAR MANUFACTURING

Many firms utilizing cellular manufacturing have reported near immediate improvements in performance, with only relatively minor adverse effects. Cited improvements which seem to have occurred fairly quickly include reductions in work-in-process, finished goods, lead time, late orders, scrap, direct labor, and workspace.

In particular, production and quality control is enhanced. By breaking the factory into small, homogeneous and cohesive productive units, production and quality control is made easier. Cells that are not performing according to volume and quality targets can be easily isolated, since the parts/products affected can be traced to a single cell. Also, because the productive units are small, the search for the root of problems is made easier.

Quality parameters and control procedures can be dovetailed to the particular requirements of the parts or workpieces specific to a certain cell. By focusing quality control activity on a particular production unit or part type, the cell can quickly master the necessary quality requirements. Control is always enhanced when productive units are kept at a minimum operating scale, which is what cellular manufacturing provides.

When production is structured using cellular manufacturing logic, flow systematization is possible. Grouping of parts or products into sets or families reveals which ones are more or less amenable to continuous, coupled flow. Parts that are standardized and common to many products will have very low changeover times, and thus, are quickly convertible to continuous, line-flow production. Products that are low-volume, high-variety and require longer set-up times can be managed so that they evolve toward a line flow.

Cells can be designed to exploit the characteristics peculiar to each part family so as to optimize the flow for each cell and for groups of cells as a whole. Flow systematization can be done one cell at a time so as to avoid large disruptions in operations. Then the cells that were easy to systemize can provide experience that can be exploited when the more difficult systematization projects occur later. Cells that have been changed to a line flow will invariably show superior performance in the areas of quality, throughput time, and cost, which can lead to eventual wide benefit.

Work flow that is adapted to the unique requirements of each product or part allows the plant to produce high-volume and high-variety products simultaneously. Since the cell structure integrates both worker and product versatility into a single unit, it has the potential to attain maximum system flexibility while maintaining factory focus. Cells can be designed around single products, product groups, unique parts, part families, or whatever unique market requirements are identified. For the same part, there may be one high-volume, standardized design and one low-volume customized design. Cells can be built specifically for any of these with a focus on the individual marketing or production requirement called for by the individual product or part.

Systematic job rotation and training in multiple skills also make possible quick, flexible work assignments that can be used to alleviate bottlenecks occurring within the cell. Since normal cell operation requires the workers to master all the skills internal to the cell, little or no additional training should be needed when workers have to be redeployed in response to volume or sales mix changes. When it is routine for workers to learn new skills, they can be easily transferred to another job within the cell or possibly even to an entirely different production unit. Without this worker flexibility and versatility, there can be no real production system flexibility.

4.2.5 LIMITATION

The implementation of the cellular manufacture can be lead for they reduce in the manufacturing flexibility. They can be felt that the conversion of the cell they may causes the some loss occur in the routing based flexibility. This can be having more impact occur in the viability of the cell use. They obtained the balance between the cells that has more difficult when compare to the flow as well as job shop. The flow shop that may have the reliability of the fixed capacity as well as the job shop can be draw from the pool of the skilled based labor so they balance cannot have much of the problem. For the contrast with the cell they can be demand the diminished greatly they may have necessary for they break up that they cell and redistribution of the equipment of the reforms of the families.

Some researcher has warmed that the uses of the cellular manufacture can be deteriorating over the various duration due to the ongoing changes based on the environment based production. Finally they must be note that the conversion of the cellular based manufacture that can be involve for the expenditure realign of the equipment. When the burden can be lies on the manger that can be helps to determine the expensive of the switching from a process based layout of the cellular one outweigh of the expensive efficiency and the flexibility of the conventional layout.

4.3 PROBLEM STATEMENT

In this work cell formation problem in the cellular manufacture can be presented. That can be done by using genetic algorithm GA as a metaheuristic technique. In the genetic algorithm can be developed in the concurrent based formation based on the part families as well as machine based cells for the cellular manufacture system. The genetic algorithm has to be design as well as it also handling the main aim of the manufacturing. Thus they reduction based on exceptional depend up on the elements can be consider as the machines as well as parts. They can be excluded from the investigation two or more than two cells. When the parts based on machine incidence matrix can be represented as input for the genetic algorithm with the main aim for the reduction based on total amount of element based on exceptional that can be evaluate the cell formation in effective manner. The proposed genetic algorithm can be coded with the help of C++ language with ore Duo, at the frequency range of about 2GHz based processor.

4.4 FLOW ANALYSIS

Production flow analysis attempts to identify and group parts according to their manufacturing processes. The application of production flow analysis involves three sequential steps.

• First, route cards are used to record the relationship between parts and the associated machines. Based on this information, parts which require identical manufacturing operations can be sorted out.
• Second, a machine – part incidence matrix is created by analyzing the manufacturing sequence and work load for producing the parts. Some researchers also refer to it as a “machine part incidence matrix.” A machine part matrix is a 0-1 binary matrix used to summarize the relationship between the machines and parts. The rows and columns of the matrix are used to indicate the machines and parts respectively. The entry of the i^th row and j^th column, a_ij would be equal to one, if machine I is involved in the production of part j; and, it would be equal to zero, if not. In some cases, the processing sequence and workload are also included in the matrix. In this case, the entries of the matrix will no longer be limited to zero or one, and the matrix is given another name, called “production flow analysis (PFA) chart.”
• Third, part families and machine cells are formed by re-arranging the rows and columns of the production flow analysis chart until diagonal blocks are generated. Since the re-arrangement usually involves grouping the parts and machines as a number of clusters, this approach is also known as “cluster analysis.”

They suggested the problem of cell-formation in cellular manufacturing systems with the objective of maximizing the grouping efficacy. He introduced the concept of PFA. The aim of the technique as stated by Burbidge is to find the families of components and associated groups of machines for group layout by a progressive analysis of the information in roads. It is based on the idea that parts with similar reputes can be put in the same group. It can concurrently form machine groups as well as part families. Later, this concept was used by other CF approaches.

The main disadvantage with implementation of PFA is the manual work involved in grouping parts and machines. Burbidge did not give any other way for grouping, but, tried all the possibilities and combinations manually. It is practically impossible to form cells in a factory which has many parts and machines. Burbidge suggested that a part can have more than one routing and a process can be done on more than one type of machine. This was a major and very important suggestion which helped to explore various economic and technical possibilities in forming cells.

The design of CMS starts with identifying part families and machine cells such that each part family is processed with in a cell with minimum interaction with other machine cells. This is commonly referred to as CF.

A large number of methods, heuristic and non heuristic have been developed for solving the CF problem. These approaches utilize either a sequential or simultaneous procedure to form machine cells and part families. The sequential procedure creates part families first, followed by machine assignment. The simultaneous procedure determines the part families and machine cells concurrently.

The operation requirements of parts on machines can be obtained from the routing cards. This information is commonly represented in a matrix called machine parts incidence matrix (MPIM).

Table 4.1.Example MPIM

In an incidence matrix, 1s in a column indicate that the particular part requires the corresponding row machine for an operation and 0 empty indicates otherwise. The sequence of operations ignored by this matrix and if a part requires more than one operation on a machine, this within the group to which the part is assigned has sufficient capacity to process the parts completely. The solution of the block diagonal matrix is shown in Table 4.1. In the solution, two diagonal blocks Cells are indentified which correspond to two part families and machines groups. Parts 1, 3, 5 and machines 2, 3, 5 are in one cell, while parts 2, 4, 6, 7 and machines 1, 4 are in the other cell.

Table 4.2.The Block diagonal matrix

From The Block diagonal matrix observed, the parts 6, 7 visit both cells to complete all the operations. It is indentified by the 1s outside the diagonal blocks. These are referred to as “exceptional” parts and or machines. In addition, it is observed that part 6 does not require machine 4, although it is provided in the cell. This is indicated by a 0 or empty inside the diagonal matrix.

To solve a problem and optimization technique is required. Optimization problems pertaining to the search for the optima of functions of distinct variables are called combinatorial optimization problems. Many of the combinatorial optimization problems, established NP-hard, can be solved by using Meta-heuristics algorithms. Meta-heuristics algorithms have been used to solve the cell formation and producing the best results with minimum time.  In this problem we considered GA for optimum cell formation with minimum exceptional elements.

CM, an important application of group technology, is an approach that can be used to enhance both flexibility and efficiency in today’s small to-medium lot production environment. In essence, a manufacturing system is decomposed into several manageable subsystems, named manufacturing cells. The design of a CMS includes

• CELL FORMATION (CF)

Grouping parts with similar design features or processing requirements into part families and associated machines into machine cells,

• GROUP LAYOUT

Laying out machines within each cell (intra-cell layout) and cells with respect to one another (inter-cell layout)

• GROUP SCHEDULING

They scheduling parts and part families for production and

• RESOURCE ALLOCATION

They assigning tools and human and materials resources.

Ideally, all of these decisions should be addressed simultaneously in order to obtain the best results. However, due to the complexity and NP-complete nature of each decision and the limitations of traditional approaches, most researchers have only addressed these decisions sequentially or independently. Genetic algorithms (GAs), developed. They have been used extensively as an alternative method for solving numerical optimization problems in a wide variety of application domains including engineering, biology, economics, agriculture, business, telecommunications, and manufacturing. As a general-purpose search method.

A GA combines elements of directed and stochastic search for exploring and exploiting the search space to obtain good solutions. In contrast to other stochastic searches. GAs has the following unique features: implicit parallelism, population based search, independence of gradient information, and flexibility to hybridize with domain-dependent heuristics. These features often make them a preferable choice over traditional heuristics. The GAs seems to perform well for some problems, but not so well for others, especially when multiple objectives and constraints are considered. Determining the contributing behavior of premature and slow convergence and examining the factors (operators and parameters) that have significant impacts on GA performance is important. Various explorations have been made to study the convergence behavior and/or process of GAs from different viewpoints. Notable developments include dynamic parameter encoding, migration and artificial selection, and cloning operations. Since most real-world problems involve multiple objectives and constraints, researchers have devoted their efforts to exploring methods that can solve such problems.

Typically, methods for handling multiple constraints include encoding, modifying genetic operator. They repairing, and penalizing or rejecting. Approaches to dealing with multi-objective problems include weighted sums, and Epsilon-constrained and sub-population approaches. Very limited research has been performed on solving concurrent decisions with multiple constraints and highly correlated multi objectives. Past researchers have studied the impact of various factors, including problem encoding, crossover, mutation, population size, crossover and mutation rates, and halting criteria, on different domains. Some of these factors will be examined in this study since they are closely interrelated and their impacts may be problem dependent. GAs has been effectively used to solve CF problems of CM or facility layout problems. But attempts to concurrently make these two decisions are limited. In this study, a hierarchical genetic algorithm (HGA) is developed to simultaneously form manufacturing cells and determine the group layout of a CMS. In order to manage the complicated and correlated decisions, a hierarchical chromosome structure, a dynamic selection strategy, and a group mutation operator are developed. The major objectives for the current study are:

(1) To develop a GA approach to solving the integrated CF and group layout problem in CM

(2) To determine the impacts of various parameters, specifically the impact of crossover rate, mutation rate, population size, and the maximum number of generations, on the GA’s performance.

3.3 PROPOSED METHODOLOGY

The following are the data collected from sheet metal manufacturing industry through route sheet which includes the machine and the processing parts details. The industry uses process type layout and has 26 machines for manufacturing the 24 parts. Here the Boctor’s formula (1991) was taken as reference for GA coding. The input for Visual basic C++ coding system was MPIM to form the cells and to find the exceptional elements.

A genetic algorithm is a search heuristic that is inspired by Charles Darwin’s theory of natural evolution. This algorithm reflects the process of natural selection where the fittest individuals are selected for reproduction in order to produce offspring of the next generation.

Figure 4.2 Genetic algorithm

The process of natural selection starts with the selection of fittest individuals from a population. They produce offspring which inherit the characteristics of the parents and will be added to the next generation. If parents have better fitness, their offspring will be better than parents and have a better chance at surviving. This process keeps on iterating and at the end, a generation with the fittest individuals will be found.

This notion can be applied for a search problem. We consider a set of solutions for a problem and select the set of best ones out of them.

Five phases are considered in a genetic algorithm.

1. Initial population
2. Fitness function
3. Selection
4. Crossover
5. Mutation

INITIAL POPULATION

The process begins with a set of individuals which is called a Population. Each individual is a solution to the problem you want to solve. An individual is characterized by a set of parameters (variables) known as Genes. Genes are joined into a string to form a Chromosome (solution).In a genetic algorithm, the set of genes of an individual is represented using a string, in terms of an alphabet. Usually, binary values are used (string of 1s and 0s). We say that we encode the genes in chromosomes.

FITNESS FUNCTION

The fitness function determines how fit an individual is (the ability of an individual to compete with other individuals). It gives a fitness score to each individual. The probability that an individual will be selected for reproduction is based on its fitness score.

SELECTION

The idea of selection phase is to select the fittest individuals and let them pass their genes to the next generation. Two pairs of individuals  are selected based on their fitness scores. Individuals with high fitness have more chance to be selected for reproduction.

CROSSOVER

Crossover is the most significant phase in a genetic algorithm. For each pair of parents to be mated, a crossover point is chosen at random from within the genes.

OFFSPRING

Offspring are created by exchanging the genes of parents among themselves until the crossover point is reached.

MUTATION

In certain new offspring formed, some of their genes can be subjected to a mutation with a low random probability. This implies that some of the bits in the bit string can be flipped.

3.3.1. GENETIC ALGORITHM

The methodology for cell formation was the output of the GA. The step by step procedure is given below.

Step 1. Initialization.

The initial parameters were selected and an initial diversified population was created.

(a) The value for PPSZ, XGEN, PCRS, PMUT1, PMUT2 and C was set.

(b) The part – machine matrix was read.

(c) An initial population of size PPSZ was created and called as OLDPOP.

(d) The objective value (weighted sum of voids and exceptional elements, w=0.7) and fitness value for each chromosome was computed.

(e) The strings were sorted in increasing order of objective value.

(f) GEN = 1 (i.e. current generation = 1) was set.

Step 2. Reproduction.

Strings were reproduced using stochastic sampling without replacement.

(a) The expected count e for each string in OLDPOP was calculated.

(b) Samples were allocated to a TEMPPOP according to the integer part of ei and the fractional part was treated as success probability.

Step 3. Recombination.

Recombination operator was applied to TEMPPOP to form a selection pool of population.

(a) Strings to be crossed were selected randomly.

(b) The crossover operator was used sequentially with a probability PCRS. Two chromosomes were chosen randomly to form two new chromosomes.

(c) Mutation was applied with a probability of PMUT1.

(d) The objective value and fitness value for each chromosome was calculated.

(e) The selection pool in increasing order of objective value was sorted out.

Step 4. Replacement.

The chromosomes of sorted OLDPOP and selection pool were compared for their fitness value and NEWPOP was created using the replacement policy.

(a) If all the off springs outperformed every existing chromosome in OLDPOP, then all off springs replaced the existing chromosomes in the new population.

(b) If some of them are better, then an equal number of existing chromosomes, i.e. those that are lowest order of performance in OLDPOP was replaced.

(c) For other off springs, a random selection was made with probability = 0.005.

Step 5. Diversification.

Mutation was applied to diversify the population.

(a) The diversity parameter H for the current population was calculated.

(b) The diversity with the given acceptable level was compared and mutation process was executed repeatedly with probability PMUT2 until the diversity of the population is equal to the acceptable level.

(c) If mutation was performed, the objective value of chromosome was calculated.

(d) The pool of chromosomes in increasing order of objective value was sorted out.

Step 6. New generation.

The current generation number was evaluating to determine the next step.

• If GEN < XGEN, then the current population becomes OLDPOP and the process was repeated from step 2.
• (b) If GEN > XGEN, then the process was stopped. The chromosome in the current population with the lowest objective value represented the best solution.

3.2 EXCEPTIONAL ELEMENTS

Exceptional elements (EEs) in cellular manufacturing are bottleneck machines and exceptional parts that span two or more manufacturing cells. This paper develops a mathematical programming model that retains the original cell formation, which is assumed to be optimal in the long term, and minimizes total costs of a cellular manufacturing system with exceptional elements through them.

(1) Intercellular transfer

(2) Machine duplication, and

(3) Subcontracting while taking machine capacities into account to avoid capacity violations.

4.5 RESULTS

The visual basic C++ 6.0 was used and the following results were obtained by giving input from MPIM. The Exceptional Elements (EE) was identified from the results.

Table 4.1. Two Cells with Exceptional Elements.

Table 4.2 Three Cells with Exceptional Elements.

4.6 SUMMARY

This work uses real time data from an industry making sheet metal components. The analyzed data were converted into Machine Parts Incidence Matrix (MPIM). The input to the Genetic Algorithm was the MPIM which gives number of Exceptional Elements with two or three cells. Hence the optimal value of Exceptional Elements with two or three cells is recommended to the industry.