# A novel approach to determine the cell formation using heuristics approach

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## Abstract

Cellular manufacturing is a vital part of lean manufacturing. It is an application of group technology. Three problems in cellular manufacturing are cell formation, machine layout and cell layout problems. However, these problems are NP-hard optimisation problems and cannot be solved using exact methods. A difficult part is to form the machine groups or cells, also called Cell Formation Problem and several techniques have been proposed to solve the same. In this paper, the Cell Formation Problem is solved using an integrated approach of heuristics along with Genetic Algorithm and Membership Index. Heuristics technique is used for domain selection which is used in Genetic Algorithm as the initial population. Genetic Algorithm is useful for optimising the results of machine assignment to cells, and Membership Index is used to assign parts to the cells. The performance is analysed using performance measures such as group technology efficiency and some exceptional elements. The proposed computational methodology is tested on standard problems of diverse size from literature papers using the hybrid approach. Results from test problems show that the proposed method is effective and efficient. The paper is useful from the practicality aspect and also relevant from current research and industry trends.

## Keywords

Cell formation Cellular manufacturing Genetic algorithm Heuristics Membership index Hybrid approach## Abbreviations

*X*_{a,b}Similarity coefficients between machines ‘a’ and ‘b’

- \( P_{pbr} \)
Processing time is taken by part ‘p’ on machine ‘b’ with process plan ‘r’

- \( P_{par} \)
Processing time is taken by part ‘p’ on the machine ‘a’ with process plan ‘r’

- \( o_{a} \)
Number of operations done on machine ‘a’

- \( o_{b} \)
Number of operations done on machine ‘b’

- \( M_{a} \)
Machine ‘a’ capacity

- \( M_{b} \)
Machine ‘b’ capacity

*N*_{op}Operations performed by a part

*V*_{p}Part volume of ‘p’ type part per period

*D*_{p}The part demand of ‘p’ type part per period

*A*_{abpr}= 1 if part ‘p’ for process plan ‘r’ visits both ‘a’ and ‘b’ machines; 0 otherwise

*B*_{abpr}= 1 if part ‘p’ for process plan ‘r’ visits both ‘a’ and ‘b’ machines; 0 otherwise

*R*Total of part routings which can be processed on both ‘a’ and ‘b’ machines

*u*Total number of machines

*v*Total number of parts

- \( V_{{A_{abpr} }} \)
Number of parts with process routings ‘r’, that can visit both ‘a’ and ‘b’ machines

- \( \frac{{P_{par} }}{{M_{a} }} \)
The ratio of processing time for part ‘p’ for machine ‘a’ capacity

- \( \frac{{P_{pbr} }}{{M_{b} }} \)
The ratio of processing time for part ‘p’ for machine ‘b’ capacity

- \( \frac{{o_{a} }}{{O_{amax} }} \)
Total operations on the machine ‘a’ concerning the maximum number of operations

- \( \frac{{o_{b} }}{{O_{bmax} }} \)
Total operations on the machine ‘b’ concerning the maximum number of operations

- \( \frac{{V_{p} }}{{D_{p} }} \)
Ratio of production volume rate to demand per part

- \( X_{{m,r_{c} }} \)
Similarity coefficient between machine m and group representative of the selected cell decision variable

- \( f_{m,c} \)
= 1 if machine ‘m’ is allocated to cell ‘c’; 0 otherwise

- \( \frac{{a_{pc} }}{{A_{c} }} \)
The proportion of machines required by part ‘p’ in cell ‘c’

- \( \frac{{a_{pc} }}{{A_{p} }} \)
The fraction of a number of machines necessary for part ‘p’ in cell ‘c’

- \( \frac{{P_{pc} }}{{P_{p} }} \)
The percentage of processing time required by part ‘p’ in cell ‘c’

- \( N_{op} \)
Number of operations (‘o’ = 1….. N

_{op})- \( q_{vpo} \)
0 if operations ‘o’ and ‘o + 1’ are performed in one cell; 1 otherwise

## Notes

## Supplementary material

## References

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