The first step in the process of designing a cellular manufacturing system is called cell formation. Most approaches to cell formation utilize a machine-component incidence matrix, which is derived and oversimplified from the information included in the routing sheets of the parts to be manufactured. A typical machine-component incidence matrix is shown in Figure 6.1. The aji, which is the (j,i)th entry of
this matrix, is 1 if the part i requires processing on machine j and aji is otherwise 0. Many attempts have
been made to convert this form of matrix to a block diagonal form, as shown in Figure 6.2. Each block in Figure 6.2 represents a potential manufacturing cell. Not all incidence matrices can be decomposed to a complete block diagonal form. This problem can come from both exceptional elements and bot- tleneck machines. There are two possible ways to deal with exceptional elements. One way is to investigate alternative routings for all exceptional elements and choose a process route that does not need any machine from another cell. However, this solution cannot be achieved in most cases. Another way is subcontracting the exceptional elements to other companies. If there are not many exceptional elements, this way seems more reasonable, although it may incur extra handling costs and create problems with production planning and control.
In the presence of bottleneck machines, the system cannot be decomposed into independent cells, and some intercellular movements are inevitable. The impact of bottleneck machines on the system is increas- ing usage of material handling devices due to parts moving amongst the cells. Obviously a high number of intercellular movements will lead to an increase in material handling costs. Therefore, to decrease the
FIGURE 6.1 An init ial ma chine–component matrix.
PARTS 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 1 1 1 1 1 1 1 2 1 1 1 1 1 1 3 1 1 1 1 1 4 1 1 1 1 1 5 1 1 1 6 1 1 1 1 7 1 1 1 1 1 8 1 1 1 1 9 1 1 1 1 1 1 10 1 1 1 1 11 1 1 1 1 1 12 1 1 1 1 1 1 13 1 1 1 1 1 1 14 1 1 1 1 15 1 1 1 1 1 16 1 1 1 1 1 17 1 1 1 1 1 1 1 18 1 1 1 1 1 1 19 1 1 1 1 1 20 1 1 1 1 1 21 1 22 1 1 1 1 1 1 1 1 23 1 1 1 1 24 1 1 1 1 1 1 1 1 25 1 1 1 26 1 1 1 1 1 1 27 1 1 1 1 1 28 1 1 1 1 29 1 1 1 1 30 1 1 1 1 1 1 1 M A C H I N E S
number of intercellular movements, some or all bottleneck machines should be duplicated. However, duplicating of bottleneck machines is not always economical. To justify which machine is to be duplicated, some subproblems including clustering procedure,intracell layout, and intercell layout of machines should be considered simultaneously in any attempt to optimize the design.
The above discussion indicates that the design of cellular manufacturing systems can be divided into two major stages: cell formation and system layout. The activities in the cell formation stage include constructing a group technology database of parts and their process routings, finding the most suitable routings among parts’ alternative routings, grouping machines into machine groups, and forming parts into part families dedicated to the machine groups. In the system layout stage, the activities are selecting candidates for machine duplication, designing intercellular and intracellular layout, and detailed design. As in any design process, the design of cellular manufacturing systems should take into consideration all relevant production parameters, design constraints, and design objectives. The relevant production parameters are process routings of parts, parts’ production volume or annual demand, parts’ alternative routings, processing time of each operation, and machine capacity or machine availability. There are also some constraints that should be considered while designing a cellular manufacturing system, such as minimum and/or maximum cell size, minimum and/or maximum number of cells, and maximum number of each machine type. In design optimization, there are many design objectives with regard to a cellular manufacturing system that can be considered individually or combinatorially. The design objectives may include minimizing intercellular movements, minimizing set-up time, minimizing machine load variation or maximizing machine utilization, and minimizing the system’s costs. Some of these objectives can be conflicting. The goal of attaining all of these objectives, and at the same time satisfying the relevant design constraints, is a challenging task and may not be achievable because of conflicting objectives.
Many analytical, heuristic, cost-based and artificial intelligence techniques have been developed for solving the cell formation problem. Some examples are branch and bound method [Kusiak et al., 1991], nonlinear integer programming [Adil et al., 1996], cellular similarity [Luong, 1993], fuzzy technique [Lee et al., 1991], and simulated annealing [Murthy and Srinivasan, 1995]. There are also a number of review papers in this area. Waghodekar and Sahu [1983] provide an exhaustive bibliography of papers on group technology that appeared from 1928 to 1982. They also have classified the bibliography into four cate- gories relating to both design and operational aspects. Another extensive survey with regard to different aspects of cellular manufacturing systems can be found in Wemmerlov and Hyer [1987]. Kusiak and Cheng [1991] have also reviewed some applications of models and algorithms for the cell formation
FIGURE 6.2 A block diag onal f orm (BDF) o f machine–component matrix.
PARTS 9 27 21 39 24 14 18 1 13 35 16 11 2 31 20 26 3 10 12 22 29 23 15 4 17 19 28 25 8 5 33 38 30 40 6 7 32 37 34 36 6 1 1 1 1 14 1 1 1 1 18 1 1 1 1 1 1 11 1 1 1 1 1 8 1 1 1 19 1 1 1 1 1 20 1 1 1 1 1 9 1 1 1 1 1 1 15 1 1 1 1 1 16 1 1 1 1 1 10 1 1 1 1 12 1 1 1 1 1 1 13 1 1 1 1 1 1 17 1 1 1 1 1 1 1 21 1 1 1 1 1 1 1 1 22 1 1 1 1 1 1 1 1 24 1 1 1 1 1 1 1 1 2 1 1 1 1 1 1 7 1 1 1 1 1 1 30 1 1 1 1 1 1 1 26 1 1 1 1 1 1 1 28 1 1 1 1 1 29 1 1 1 5 1 1 1 23 1 1 1 1 4 1 1 1 1 1 27 1 1 1 1 25 1 1 1 3 1 1 1 1 1 M A C H I N E S
process. A review of current works in literature has revealed several drawbacks in the existing methods for designing cellular manufacturing systems. These drawbacks can be summarized as follows:
• Most methods work only with binary data or binary machine-component matrix. These approaches are far from real situations in industry, as they do not take all relevant production data into consideration in the design process. For example, production volumes, process sequences, processing times, and alternative routings are neglected in the majority of methods.
• Most methods are not able to handle design constraints such as minimum or maximum cell size or the maximum number of each machine type.
• Most methods are heuristic, and there is no optimization in the design process. Although many attempts have been made to optimize the design process using traditional optimization techniques such as integer programming, their scope of application is very limited as they can only deal with problems of small scale.
This chapter presents an integrated methodology for cellular manufacturing system design based on genetic algorithms. This methodology takes into account all relevant production data in the design process. Other features of this methodology include design optimization and the ability to handle design constraints such as cell size and machine duplication.