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In recent years some major changes, such as variable customer demand, short period life cycle, and increasing worldwide competition, have taken place in the manufacturing industry. To meet these changes a company must be able to offer superior quality products at lower cost than competitors and still remain flexible if it wants ti survive in the business world. To achieve this goal, new manufacturing systems have emerged. All these trends lead to the recognization of the need of an integrated manufacturing. Integrated manufacturing means the integration at different manufacturing activities like processes, operations, product designs and their management which were treated separately in the traditional methods, into one system for complete control of the manufacturing facility and there by achieving the goal to find the optimum method of producing high quality, low costs products efficiently. All these have led to the innovations of a number of manufacturing strategies [18]. The major advances in integrating all aspects of manufacturing have led to computer integrated manufacturing which includes flexible manufacturing systems, JIT systems, agile manufacturing system, and the cellular manufacturing systems.

A flexible Manufacturing System (FMS) integrates all major elements of manufacturing that have been described so far. It consists of a number of manufacturing cells. It consists of a number of manufacturing cells each having an individual robot and serving several CNC machines and an automated material handling system interfaced with the computer. This system is highly automated and is capable of optimizing each step of the total manufacturing operation. It can handle a variety of part configurations and produce them in any order. The quick response to product and market demand variation is a major attribute of FMS.

The Just-In-Time production concept was developed in Japan to eliminate waste of materials, machines, capital, and inventory throughout the manufacturing systems. It has the goals like purchase supplies just in time to be used, produce parts just in time to be made into subassemblies, produce subassemblies just in time to be assembled into finished products and produce and delivery finished products just in time to be sold. It is a pull system meaning that parts are produced to order and production is matched with demand for final assembly of products. The advantages of JIT are low inventory carrying costs, reduced inspection and rework of parts etc[18].

It is the science of business system that integrates the management, technology and workforce and makes the system flexible enough for a manufacturer to switch over from production of one component to other component in a cost effective manner. It includes the entire business starting from planning, finance, processes, design, layout, materials and inventory, marketing, sales, series, technical supports etc. It has become an absolute necessity in view of the demands on customer-oriented products to produce components of international standards in terms of quality and costs. Integration of information technology is the core of Agile Manufacturing System

Batch manufacturing is a dominant activity in the world, generating much industrial output. The major characteristics of batch manufacturing are a level of product variety and small manufacturing lot sizes. The product variations present design engineers with the problem of a design stage that significantly affects manufacturing cost, quality and delivery times. The impacts of these product variations in manufacturing are high investment in equipment, high tooling costs, complex scheduling and loading, lengthy set-up times and costs, excessive scrap and high quality control costs. However, to compete in a global market, it is essential to improve the productivity in small batch manufacturing industries [3]. For this purpose, some innovative methods are needed to reduce product costs, reduce lead time and enhance product quality to help increase market share and profitability. Group technology concepts allows for small batch production to gain economic advantages similar to mass production while retaining the flexibility of job shops methods.

This project study relates to algorithms to forms cells and the specific scope can be identified as to study the concepts of Cellular manufacturing,have an overview of the various traditional cell formation algorithms, study and analyze various innovations in cell formation algorithms, especially the recent applications in cellular manufacturing systems develop a few algorithms and carryout detailed comparative studies, using simulation

This chapter discusses about manufacturing systems, its advances and types of manufacturing system in CIM environment

Chapter2 gives a brief review of perspectives of Group technology- historical development of CMS, issues related to CMS, its advantages and disadvantages along with its applications

Chapter 3 discusses about different cell formation techniques with their advantages and disadvantages.

Chapter 4 focuses on the traditional algorithms developed so far.

Chapter 5 discusses about the modern techniques of cell formations. It gives a brief idea of how the concept of fuzzy logic, neural network, Genetic algorithm, Simulated annealing are applied to CMS

Chapter 6 summarizes the whole report and present the problem on hand and the plan for future work

Group technology (GT) is one of the most important technological improvements applied to the batch processing industries. Group Technology is the management philosophy that believes similar activities should be grouped and performed with similar methods. The activities include product design, process planning, fabrication, assembly and production control. Apart from this, Group Technology can be applied to administrative functions as well. Burbidge (1971, 1975) [8]and Mitrofanov (1966) originally proposed this approach. This philosophy with his broad applicability potentially is affecting all areas of a manufacturing organization (De Vries et al, 1976 Hyes 1984). [42] One such application of Group Technology is Cellular Manufacturing.

Cellular manufacturing is a hybrid system linking the advantages of both the job shop and the product layout of the continuos flow line. It focuses on the creation of manufacturing cells within which a number of part families are manufactured. A cell consists of a set of functionally dissimilar machines, which are placed in close proximity to one another and dedicated to the manufacture of a set of part families. A part family is a set of parts that are similar in terms of processing requirements. A fundamental issue of cellular manufacturing is the determination of part families and machine cells. This issue is known as cell formation problem

Research into the application of group technology for manufacturing first began during the late 1950’s. Around this time, researchers began to recognize that some parts share common manufacturing approaches. They soon concluded that parts with common manufacturing attributes could be grouped together and processed in a manner similar to mass production. Using this theory, they would create groups of similar parts and then dedicate groups of machines and tools specific to the production of these parts to reduce setup times. The first researcher to gain renown for this theory was S.P. Mitrofanov of the U.S.S.R. Though Mitrofanov began his work in the early 1950’s, but the genesis of group technology can be traced backed to the work carried out in the erstwhile U.S.S.R (Lpkplovsky, 1938) and Germany (Brady 1933), to extend formal standardization as reported by Gallagher et al. [17].

In subsequent years, several classifications and coding systems for forming part family were proposed. Companies first started to reorganize manufacturing facilities along GT lines in the early 1960’s and the concept of GT was strongly accepted round the globe. The approach of Production flow analysis (PFA) introduced by Burbidge considers wider aspects of production such as factory flow system, plant layout etc. Even though GT concepts can be applied for a variety of business problems in this area, the largest application has been in the manufacturing area and since then, always used in conjunction with Cellular manufacturing systems. During the 1970’s cellular manufacturing systems gained much more importance and later on this concept of manufacturing cells was extended to flexible manufacturing cells to cope with dynamic market situations. Today most of the developed countries have set Group technology in its proper context as a mainstream contributor to improved productivity and have applied this concept in all directions of manufacturing like JIT, CIM systems.

Issues involved in designing of cellular manufacturing systems are identification of part families, the identification of cell equipment and allocation of families to equipment (or vice versa). Besides identifying similar parts and machines, several objectives and constraints are of importance when cell systems are created.[33]

The traditional type of organization for manufacturing is process organization, in which organizational units each specializes in a particular process. This is gradually being replaced by GT, in which the organizational units (groups) complete all the parts they make at their particular processing stage, and are equipped with all the machines and other facilities they need to do so. GT addresses a lot of benefits like [9];

Table 2.1 Reasons for establishing manufacturing cells [42]

The major limitations of the GT are that it depends on the assumptions made and is too idealistic. GT has limitations on two issues,

The formation of proper cells cannot be separated from the success of a GT system. There are certain critical problems associated with such design.

Many GT assumptions are impractical and hence invalidate many of the advantages addressed.

Implementing cellular manufacturing is not as easy as it looks. It involves a series of vital steps so that parts or products are actually produced by the system. The scale of the cellular manufacturing implementation varies from manufacture to manufacture depending on the scale of the business and on the objectives of the firm.

The following 5 steps are necessary for manufactures to successfully implement cellular manufacturing[42].

Step 5: The final step is relocating the machine to begin production in the cells. Although the amount of time and cost it takes depends on the scale of rearrangement it requires, the rearrangement should avoid conflicts with any other production lines.

Figure 2.2 Factors considered of great importance to cell operation and implementation [42 ]

This grouping philosophy has been widely used in Flexible Manufacturing System (FMS) (Kumar et al 1986,Kusiak 1985) and in JIT production. Schonberger 1982, Stecke 1983 [40] has identified five sub problems to be solved before production in the FMS begins which are - part type selection problem, machine grouping problem, part mix ratio problem, resource allocation problem and machine loading problem.

Ingersoll-Rand Company’s Engineered Pump Division manufactures centrifugal and hydraulic pumps for the mining, military, flood control, and municipal water supply industries. In 1984, a management evaluation concluded that the operation was antiquated and too large to maintain its competitive position.

Their machining, assembly, and test departments were scattered throughout four buildings up to half a mile apart. Also, machines were grouped together by type, resulting in inefficient material flow. Existing equipment included a low quantity of NC/CNC machines. Specifically, the evaluation indicated that lead times were high due to

Table 2.3 Factors affecting cell design [5]

manufacturing methods, planning, and part flow, that inventory levels were high, and systems were outdated. In short, the facility was a low-tech shop trying to produce a highly engineered product with consistent quality and tight tolerances.

This evaluation led to a corporate commitment to improve the operations by creating a "factory of the future." Initially, a thorough analysis of the existing business was conducted, including future markets, old and new products, and sales levels. Next came an in-depth analysis of parts and their manufacturing strategies, and existing equipment, and the development of part families to support planning for cellular manufacturing. A team-oriented structure was used through the planning and implementation process. Employee groups, including direct labor worker, supervisors, and engineering support, worked to define the needs, secure capital equipment, implement the physical and philosophical changes.

The result of these preliminary-planning steps was a division wide objective-to consolidate and modernize the Phillipsburg operation, to reduce: product cost, manufacturing lead times, space requirements and overhead costs, and inventory levels (while improving inventory turns). While the primary emphasis was on implementation of cell technology and conversion to Just in Time manufacturing, several other subprojects were also completed, facility upgrades (new floors, shipping and receiving areas, and manufacturing offices), acquisition and installation of new manufacturing equipment, implementation of DNC (direct numerical control) technology, relocation and modernization of: support functions such as hydro test, shipping, receiving, and inspection), storerooms, and test stands/loops.

The overall program was planned as a five-year effort. An extension portion of this time (four years) was to be devoted to planning and detail engineering. Final implementation was to take place during the fifth year. (Part of the "planning" phase was actual implementation of a pilot cell to debug the approach, identify critical roadblocks-either people or technology-to ultimate success, and give everyone firm successes before undertaking the full-scale implementation.)

The team members going through this process encountered a number of psychological barriers, including a "resistance to change" attitude within the division. Some of the diverse disciplines now interacting together had years of isolation to overcome with regard to participating in any division improvement activities. In some cases, no one had ever asked these people what they thought before.

A part family analysis indicated that 12 manufacturing cells would be required in the manufacturing operation. Parts were first grouped by geometry (complexity), size, and annual production quantity. The resulting cells were first analyzed on paper, and then detailed in a scaled 3-D model. This model gave the team the ability to rearrange the individual machines within the cell and all the cells to optimize both the internal cell flow and overall factory flow. The model was also a display tool for the various vendors and contractors, and a teaching tool for internal personnel. Since it was decided that production would not be slowed during the rearrangement, a detailed proximity and sequence of machine tool/area moves was developed. The 12 cells that were developed and implemented were: four ring cells, grind cells, shaft cells, impeller cell, one small VTL (vertical turret lathe) cell, one large VTL cell, prismatic cell, material prep cell, and a general machining cell. In excess of $10 million was invested to purchase CNC tools, build shipping and receiving facilities and new test loops, and rebuild selected equipment. Additional expenditures were for small equipment and tools, and DNC implementation.

Nearly five years after the project began, the results of the cells are evident: reduced lead times, part manufacturing cycle times, and work-in-process and finished inventory levels. The four ring cells, the first to be installed, resulted in specific productivity improvements:

The facility space reduction project, also part of the factory-of-the-future effort, resulted in a revised facility with wider buildings, more height under crane hooks, increased crane capacity, and improved access. The new layout of the five shops (Shops 7 through 11) enabled work to move from shop to shop without exposure to the elements. Initially, the production process required 381,000 square feet; after consolidation, only 250,000 square feet were required—a 34% reduction. The picture below shows the consolidated shop layout, where overall part flow is less than 10% of the original. Machine tools are grouped according to the family of parts being manufactured in each cell.

According to managers at Ingersoll-Rand Company’s Engineered Pump Division, this effort provided many lessons, among them:

Another important conclusion was that consultants should be part of the process to introduce new concepts, establish goals, and prepare and execute plans. At a certain point however, they should be phased out so the internal employee team can finish developing and implementing the plans, fostering ownership, reliance on textbook solutions should be avoided. A blend of textbook concepts and real-life experience will produce a plan that is realistic, achievable, and livable.

The implementation of this factory of the future was a major undertaking for the division compared to the size and scope of previous projects. New manufacturing strategies were introduced—cells, JIT receipt of materials, production per customer order (not made for stock), DNC—and involved a division wide team effort with full corporate support. The successes at the Engineered Pump Division prompted other Ingersoll-Rand sites to plan to implement similar strategies.

Cellular manufacturing is gaining increasingly popularity as a way to quickly improve productivity and competitiveness. As a result, it becomes necessary to address the issues related to CMS. An attempt has been made to describe the issues related to CMS, advantages and disadvantages of GT and the factors to be considered for implementing GT. Apart from this, development of GT and it applications are also been discussed in this chapter. Finally a case study of Ingersoll-Rand Company has been presented. In the next chapter, we will discuss about the cell formation techniques

The problem of cell design is a very complex exercise with wide ranging implications for any organizations. Normally, cell design is understood as the problem of identifying a set of part types that are suitable for manufacture on a group of machines.

Various algorithms have been developed to tackle with the problem, each of them have their own advantages and drawbacks. In this chapter, a concise review of the cell formation methods is considered.

A logical way of classifying these methods is on the basis of the elements into cells- components, machines or both. The three methods of cell formation are:

Here we form the part families and then, group Machines into cells. This method is of restricted value now a days, but it is still useful in single machining centers. Existing techniques for part family grouping based on routing sheet information are:

A classification and coding scheme sorts parts into different classes based on certain part characteristics, (such as routings) and assigns a code (usually alphanumeric) such that parts having similar codes can be easily identified as part families. A code is required as a drawing identification number, for the analysis and retrieval of salient features of the component and for administrative and information purposes. By control and variety reduction thus attained, significant money saving and degree of standardization is achieved. Typically a code includes the following three parts:

Examining the fundamental concepts of component classification lead to the recognition of two basis approaches; viz. The Design Oriented Approach and the Product Oriented Approach.

This method was first suggested by the originator of GT, [9] Mitrafanov in 1959. The procedure used here is to look at the component as a whole and on basis of the similarity in design/physical features like size, shape, presence of certain surfaces etc/ group the parts into families. It just requires study of the component drawings. This method is a universal method as it’s code can be applied to a general set of parts. Mitrafonav [9] has suggested a composite component approach in which a master component incorporating the features of all the components in the group is selected and artificially designed and a setup for processing this component on the appropriate machines is provided, which will take care of all other components as well. Rajagopalan and Batra [31] further used a graph theoretic approach as well as fuzzy set clustering to make the method applicable to real life.

This approach has generally been preferred to the design oriented procedure, even though the latter is faster easier, and cheaper to implement. This is because the universal framework of that method often gives unnecessary information about the parts in great detail, while missing out information really relevant to the factory. The product oriented approach, in addition to various advantages of data retrieval mentioned in design oriented method, makes the production planning simple and hence is the more popular one.

The classification and coding system are the legacy of the early days of GT. They are just the modification of design retrieval techniques. The advantages of the methods have been dealt with in the respective sub classifications. They do make things standardized and systematic, but the trend now is to avoid going into them and opting for simpler procedures. Recent computer aided techniques by Wemmerlov and Hyer, Zelenovic et. al., Zhu and Zhang – an expert system, and the Reklenik and Grum [9] have done much to reduce the complexity of the problem, but still the basic flaws remain.

Classification is fast becoming obsolete as they involve a lot of time and effort as well as stand-alone techniques for part family formation. This is due to the fact that all the codes do not refer to the machine capabilities and hence the machines cells cannot be easily determined because of the difference in quality of the process required in the members of it’s part family.

Carrie [30] used cluster analysis in 1973 for grouping parts with common characteristics (resulting in a high mutual similarity coefficient) together in a group. Shunk and Reed in 1975 [12] also devised a method using similar principles.

This method is free from the biggest flaw of the classification systems in the sense that it does not need much time or effort to be implemented. It just needs the data available in the route cards, which is easily available in all factories. The concept of similarity is easy to understand and implement and cluster analysis is one of the most reliable methods available. The parts that are grouped together are by definition the most similar. Still this procedure is hampered by the basic faults of part family grouping. The similarity is defined based on the operation and still no consideration is given to the machine capabilities and so the machine cell formation is difficult. The problem of machine duplication and exceptional components is not considered and hence this requires a separate procedure for machine cell formation.

Some researchers have attacked the problem of group formation as a two-stage process. In this first stage of their analysis, they group machines and form cells based on the information contained in the part routings. The next stage usually consists of allocating parts to cells and re-evaluating the cells on the other factors such as machine utilization. Such machine grouping may be further broken into two sub classes, namely:

These are based on the visual examination of matrices constructed from the routing sheet information. These follow a subject methodology and are not really useful for large sized practical problems. Hence it’s practical implications are limited.

De Beer et. al. in 1976[28] introduced a procedure which considers divisibility of machines of the same type when forming machine cells. This same method was extended in the production flow synthesis approach (De Beer and De Witte) In 1978 to consider the divisibility of operation rather than of machines. A digraph showing the number of transitions between any pairs of operations is used to analyze inter-cell and intra –cell work flows. Their contribution lies in their presentation of important production issues such as divisibility of machines/operations, balancing work ,load of cells, etc.)

These methods have a well defined methodology and can be represented and run easily on the computer based on the techniques used these may be further classified as cluster Analysis and Graph Theoretical Method.)

Here similarity coefficients (a correlation-like measure to characterize some desired relationship between a pair of objects – machines here) are calculated between the various pairs of machines, which are then grouped together in clusters (with machines having a mutually large similarity coefficient in the same cluster). The idea was borrowed from the field of Numerical Taxonomy when McAuley [22] used single linkage Cluster Analysis (SLCA) for clustering machines into groups. A detailed analysis of his method will be dealt with in the next chapter. The basic process of all the clustering techniques is the same as what is true for SLCA.

De Witte [22] was a strong criticizer of McAuley’s method especially of the inappropriateness of the Jaccard coefficient to group the machines. His method hence described three different types of similarity coefficients and divided the machines into three different classes: Primary, secondary, and tertiary depending on the extent of their use. The clustering technique is different for each class. The linkages between the machines, which have a similarity coefficient above a minimum threshold level, is plotted on a graph and the machine are grouped. This method has several advantages; being the first method to take cognizance of the component flow volume, using a reliable similarity coefficient, differentiating between machines according to their degree of use and allowing for the inclusion of the same type of machine in greater than one cell, giving a proper procedure for machine loading, etc. But the machine-classification into three classes is ambiguous and creates more problems than it solves, the drawing o graphs is time consuming and not suited for large problems. Further, many drawbacks of SLCA such as an arbitrary threshold level, still remain.

Another method is MACE – Machine component CELL formation given by Waghodekar and Sahu [21] . There are three stages. The first stage involves assigning the pair of machines with the highest similarity coefficient to a cell and coupling all other machines close to this pair into the cell. The procedure is repeated till all the machines are assigned to cells. Then in the second stage, the intercell moves are calculated and similarity between cells are , calculated on basis of this, Merging of cells into clusters is then done in a way similar to that of machine clustering in the first stage. The components are placed as per the sequence of machines computed in the second stage in the third stage. The advantages claimed for MACE include possible control over cell size and number , reduced number of exceptional components by the very nature of clustering, crosschecks by two offering two other types of similarity coefficient, etc. But the drawbacks remain that the three similarity coefficients given here suffer from the same disadvantages that De Witte [21] pointed out in his paper, the procedure of machine duplication is not defined, and from the paper, the details of the overall methodology is not clear.

Other methods in this approach include a method by Ballakur and steudel [14], in which they seek to optimize the machine utilization and form clusters of machines from clusters of machines from this point of view. Another method is by Seifodinni and Wolfe [28] which does not contribute much in methodology, but merely adds a facility of machine duplication to the already existent method of Average Linkage Cluster Linkage (to be described in chapter 4). Lemoine and Mutel [28] in 1983 present a dynamic clustering technique for machine grouping. Their non – hierarchical cluster analysis procedure is based on the minimization of statistical distances with loads and capacities of machines as statistical weights.

The cluster analysis techniques make use of the fact that irrespective of any sequence or numbering of machines and components. The interrelationship (in terms of similarity coefficients) between any two machines remains unchanged. [31] Hence, They are most reliable and give very consistent results in bringing out the natural clusters in the system. But a number of drawbacks exist in these methods which include a disregard of the machine duplication problem, no direct attempt to minimize the exceptional components, a unrealistic picture of the similarity portrayed by most coefficients, arbitrary selection of the threshold etc. The graph theoretic approach scores over this method as it has a systematic procedure for determining the threshold value.)

This method utilizes Graph Theory to form the machine component cells. It was introduced by Rajgopalan and Batra [32] as a three phase procedure in 1975. The first phase consists of deriving the machine graph and formation of clusters. The machine graph has each vertex corresponding to a machine and edges are drawn between those machines whose similarity coefficient (of the jaccard type) exceeds a certain threshold value. The threshold value is calculated by a systematic trial-and –error procedure which involves the plotting of a graph of number of edges vs. the value of T (threshold coefficient) and selecting an appropriate coefficient which gives a stable number of edges. The cliques (which are defined as "maximal complete sub graphs" – a subset of the vertices of the graph such that there is an edge connecting every pair in the subset while no clique is connected in a larger clique) are now identified.

The second stage uses graph partitioning to merge cliques into a smaller number of cells such that the relationship within a cell is strong while inter-cell relationships are weak. The components are now allotted to various cells according to certain rules and their inter cell moves are calculated and stored in a move matrix from which a move graph is drawn. This is then partitioned such that the total weight or the cost of the edges (which are assigned according to the inter-cell move in question) that connect any pair of partitions is a minimum. Each partition is then a set of cells, thus yielding cells with minimum intercell moves. Allocation of components to cells is done in phase three of the procedure according to some allocation rules. The machine load is calculated to find the number of each machines required in each cell.

The advantages of the method used here is that it uses a systematic procedure for finding the threshold value. Considers the duplication of machines, tries to reduce the number of exceptional components (by the move graph procedure), gives control to some extent over the number and size of the cells. However, the drawbacks of the jacard coefficient remain and as the number of cliques varies exponentially with the number of vertices, the clique approach is acceptable for a few machines, but the complicated and time-consuming nature of the allocation procedure means that application to large problems would be difficult. Interest has awakened anew in this method in recent years. A noteworthy article was one by Chakravarty and shtun [29] in which they discussed and integrated approach taking into consideration the in-process inventory costs and they have also discussed the layout aspects. However due to restriction in size of the problem, the application is limited.)

When one attempts to groups parts into part families and machines into cells simultaneously, then such a procedure would be defined as machine-part grouping, The three main subclassfications are:

These methods are more comprehensive in their scope than algorithms for forming part families and machine groups. These are subjective in nature and require familiarity and knowledge of the system characteristics. They are also interactive and can be tailor-made to the factory’s requirements. There are three main techniques used.

These three steps, factory flow analysis, group analysis and line analysis, are progressive sub techniques of production flow analysis, and each should be completed before the next can start. Apart from these three stages, company flow analysis, tooling analysis are also considered in production flow analysis. The next step after production flow analysis is grouping of machines. This analysis is carried out by clustering technique.

This method was suggested by EI Essawy and Tirrance [2] in an attempt to modify PFA and overcome it’s defects. However, there has been lot of debate as to how different from PFA it actually is. The basic method of CFA proceeds in a way opposite to PFA – it starts at the component level and proceeds to the form cells using three stages ir the whole process. The first phase involves analysis of the component mix, the second –groupings of the machines-component cells, and the third stage does a detailed analysis of the loading and flow pattern and adjusts the cell compositions. CFA, while being applied, was found superior to PFA in various companies [2] This is because it is more sensitive to the machine – component cell formation by virtue of it’s very technique, and hence we get better cells. It suffers from many of the other drawbacks of PFA, though and in addition has problems of load balancing, as its procedure doesn’t take care of that aspect.

Connoly et. al. [42] advocated an overall systems Approach in 1973. The procedure they suggested doesn’t appear to have any definite methodology, but they recognize the need considering cell formation in the context of the total manufacturing system. Another development was the Salford method [34] , developed by the University of Salford. It is based on the assumption that every cell has at least one key machine i. e. A machine which is loaded by a greater variety of components than the rest of the machine which is loaded by a greater variety of components than the rest of the machines. By identifying such machines (bottlenecks), it is possible to identify groups, by selecting the other machines close to it and then identifying another key machine and repeating the same thing. This is continued till all machines are exhausted.

Here, machines are combined into groups and components into families based on (optimizing) some criteria. Prominent among the techniques used are two basic ones. Since these are complex processes with a great deal of programming details, we will just touch upon the developments in the field.

This is usually based on the minimum cost criteria and was first suggested by Urosevic and Solaja [31] in a primitively developed way. It was developed formally by Purcheck [37] for GT application. He defined his objective function as the minimization of exceptional components. Kusiak [37] while developing a generalized concept of GT, grouped machines together using the similarity of the components they process as the the criterion for maximizing objective function in the whole system. He called this his P-median model. In the same paper, he used integer programming for grouping the part-machine families. Kusiak and Vanelli [31] also used this method coupled with a graph theoretic approach (minimization of the inter cutest edges to form cells. In 1988, Choobineh [37] developed a model for the optimization of various costs (of intercell moves, machine duplications,etc.) in the construction of cells. Co and Arrar [1]have also used integer programming for their assignment problem of machines in the initial stages of their report.

These methods are robust in the sense that they try to optimize some definite parameters, which can be defined by the designer at will and thus provide and interactive approach to cell formation. The models developed can be easily changed to suit our criteria and standard LP packages can be used. But this method is criticized on grounds that can have it’s own specific solutuon. This is done at the large amount of inefficiency in computing and grouping that are there in LP programs. Also the maximizing criteria becomes the sole aim of the problem, ignoring, at the same time other important aspects of cells, often leading to poor overall solutions. The mathematical representation for modeling the system for programming involves a lot of approximations.

This method owes it,s existence to purcheck [34] , who has originated most of the methods in ‘it. Purcheck aimed at maximizing the scheduling flexibility and minimize the total cost of establishing the cells. In these methods the routings of the components are noted and are represented as sets and subsets are identified and grouped under the sets. This process of including subsets is further enhanced by adding additional machines (which are bottleneck) to each set to make the set hospitable to other sets to include many more components in it. Purcheck and Oliva Lopez [34] contributed further to the method by considering load balancing and other aspects in their simulation study. In recent times, John [23] worked on a similar approach using auxiliary cell formation which employed the consideration for operation sequences and other aspects.

The set-theoretic approaches are desirable in that they incorporate the operation sequences, and other parameters in them and are comprehensive, but are very cumbersome for large sized problem. Also they suffer from the drawback of having no fixed aim and hence not optimizing any desired value.

These techniques use iterative recordering procedures for permuting the rows (machines) and the columns (components) of a machine-part matrix. They have well defined procedures and are very amenable to computer application.

Roc was developed by king [2 ] in 1980. It is one of the most important techniques of machine-part cell clustering and has evoked enthusiastic response from researchers. It was further modified in 1982 by king and Nakornchai [2 ] to make it more suitable for large matrices, but the basic methodology’ remained the same. ROC has given rise to a variety of derivatives.

An important derivative of ROC is Modified ROC better known as MODROC, developed by Chandrasekharan and Rajgopalan [10] in 1986. It was an ingenious attempt to overcome the drawbacks of ROC and has been discussed in the next chapter. Next Askin and Subramaniam [28] developed a cost based heuristic involving a three phase algorithm – determination of the machine component cells using a combination of ROC and PFA, setting up of initial groups based on economic considerations, machine loading aspects. In recent times (late 1988), Co and Arrar [28] have developed a comprehensive expert system approach using Roc in the second stage. They have suggested a procedure of solving large (unmanageably) problems by starting with a 15x15 sub matrix and applying ROC to it. Rajgopal [28] , in his thesis has suggested an altered comprehensive form of ROC called ALTROC. This generates alternative blocks, among which the final solution is selected.

This method was first developed for the decomposition and data organization of large matrices by Mccormick et. al. [21] in 1972. It’s possibility for use in GT cell formation was first pointed by King [ 3] This method has several drawbacks as well as advantages, which will be discussed in detail in the next chapter.

This was originated by Chan and Milner [34] and is a heuristic technique of forming machine-component cells from a 0-1 machine component matrix. The ones are considered the positive cells and the zeros are the negative ones. The direct clustering algorithm goes through the matrix sequentially moving the rows with the leftmost positive cells on to the left of the matrix.

The procedure suggests that the method is just another form of the ROC procedure, but significant difference lies in the execution efficiency and the manner in which the cells are defined.

These methods have so far been the exclusive contribution of Rajagopalan and Chandrasekharan [12] . The initial article they wrote [11] was an ideal seed nonh ierarchical clustering algorithm. The problem is first formulated as a bipartite graph (with machines as one group and components as the other) then a non-hierarchical clustering method is adopted for grouping. An ideal seed algorithm, using Mcqueen,’s k-mean method ,is used for grouping. This method generates ideal seeds (identifies certain rows /Columns to cluster the closest ones together). Their second paper [32] on the subject follows a similar procedure of ideal seed clustering with an iterative procedure. Also Datar and Krishna [14] have developed a method of assigning weights to the various positions of the matrix and then seek to minimize the weights leading to a block-diagonal structure.

The ideal seed methods have been claimed to bring out the best natural clusters inherent in the system . They use a concept akin to similarity and hence ought to be reliable as methods. However, their procedure is complex and difficult to grasp and the computation

Most algorithms developed in the cellular manufacturing systems do not really give a generalized formula for the solution of different practical problems though they are best for the solution of incidence matrices in their own realms. So evaluation of the block diagonal machine-part matrix is important. These measures include grouping measures, performance measures and simulated models. (Seiffoddini and Djassemi 1996) [7]. The best way to evaluate the solutions obtained from different algorithms is to choose an absolute quantitative scale. If a such a quantitative scale is generated, it would be easier to compare the results of individuals objectively and in case of forming blocks, such quantitative measure can be considered as the objective functions, which has to be maximized.

Chandrasekharan and Rajagopalan (1986) [7] first proposed a quantitative measure of goodness of a solution, named grouping efficiency, which is the weighted average of two functions and it is defined as

where h _l is the ratio of numbers of 1s in the diagonal blocks to the total number of elements (both 0s and 1s) in the diagonal block, h ₂the ratio of numbers of 0s in the off diagonal blocks to the total number of elements (both 0s and 1s) in the off diagonal block, and q is a weighing factor(0£ q£ 1). If e is the total number of ones in a machine-part incidence matrix, o is the total number of zeros in a machine-part incidence matrix, e_l is the number of 1s in the diagonal block and e_v is the number of voids in the diagonal blocks, then grouping efficiency is expressed as

Kumar and Chandrasekharan (1990) [7] proposed another measure named grouping efficacy which has overcome the weaker discriminatory power of grouping efficiency measure putting equal weightage on the number of voids and the number of exceptional elements. This measure is defined as

where e is the total number of ones in a machine-part incidence matrix,, e_o the number of exceptional elements (i,e number of ones in the off-diagonal blocks), e_v the number of voids, (i,e, number of zeros) in the diagonal block, y the ratio of the number of exceptional elements to the total number of operations, and f is the ratio of the number of voids in the diagonal blocks to the total number of operations.

0 otherwise

It is the ratio of the total number of operations that are performed within the suggested cells to total number of operations in the systems.

T_ij= Processing time of part j on machine I

The Quality Index (QI) for a block diagonal machine component matrix is calculated as

Seifoddini and Djassemi (1996) [6] developed a simulated model for the performance evaluation of five different measures; bond energy measure, grouping efficiency, grouping efficacy, grouping capability measure and quality index. It is used to determine which measures predict more accurately the performance of the machine-part incidence matrix solution where the average flow time and in process inventories are used as variables to show the comparison of the measures graphically. They found that the efficiency of all these measures is 100% for a certain value of mean flow time and efficiency of all these measures begins to fall as the value of mean flow time increases, but the steepest fall occurs with QI measure. Grouping capability index and grouping efficiency measures give similar values of efficiency as grouping efficacy and bond-energy measures do give the similar results. Among these five measures, quality index gives the highest efficiency for a range of mean flow time. Seifoddini and Djassemi (1996) [6] claimed that QI is the measure of independence of machine-part groups, since independent machines are ideal for the formation of CMS, a high value of QI is expected to lead to a high performance level in the corresponding CMS

A distinct trend in the manufacturing research evident in the literature is the use of performance measures in developing models and optimizing various industrial operations. It has wide application in various types of manufacturing system, data collection and preparation. This approach has been adopted in capacity planning, facility planning and flexible manufacturing loading. It is clear in a CMS that the goodness of solution of a machine-part incidence matrix depends mostly on the perfection of forming a standard block diagonalized matrix. Many other factors like production volume, CPU time, machining requirements of parts, processing time may have influence on the goodness of a solution, but fortunately they are not taken into consideration in almost all the measures. Another important factor cost, is also not introduced effectively in any of the efficiency measures mentioned here.