# Performance criteria for comparing performance of methods to solve cell formation, machine layout and cell layout problem

Researchers have developed their methods to solve cell formation, machine layout and cell layout problem. Researchers have also compared performance of their methods with other methods available in the literature by selecting appropriate performance criteria. Commonly used performance criteria for comparing performance of methods to solve cell formation, machine layout & cell layout problem are depicted in figure 1 and explained as follows.

Figure 1: Performance criteria for cell formation, machine layout and cell layout problem

1. Commonly used performance criteria for comparing performance of methods to solve cell formation problem are as follows.

## 1.1 Grouping efficiency

Grouping efficiency was suggested by Chandrasekharan and Rajagopalan in 1986 which can be used as a measure to compare the solutions of cell formation problem. Grouping efficiency is the weighted average of two functions. It is defined as follows.

GE = qp1 + (1-q) p2

Where, p1 is the ratio of number of 1s in the diagonal blocks to the total number of elements in the diagonal block. Total number of elements means both 0s and 1s. P2 is the ratio of number of 0s in the off diagonal blocks to the total number of elements in the off diagonal block. q is a weighting factor on [0, 1]. In most past work, the value of q is fixed as 0.5.

## 1.2 Grouping efficacy

Kumar and Chandrasekharan was suggested another measure in 1990 named grouping efficacy which puts equal weight on the number of voids and the number of exceptional elements thus overcoming the weak discriminating power of grouping efficiency measure. It is defined as follows.

GF (e – eo) / (e + ev)

Where, e is the total number of 1s in a machine-part incidence matrix, eo is the number of exceptional elements and ev is the number of void elements.

2. Commonly used performance criteria for comparing performance of methods to solve machine layout problem are as follows.

## 2.1 Percentage of variation with optimum solution

Researchers have used percentage of variation with optimum solution as a performance criterion to compare performance of their developed method with other methods available in the literature. Most effective method is one which has lowest value of this performance criterion. This performance criterion is used when optimum solution of machine layout problem is known in advance or it is already found using one of the exact solution methods.

## 2.2 Total distance travelled by all parts

Researchers have also used total distance travelled by all parts as a performance criterion to compare performance of their developed method with other methods available in the literature. Total distance travelled by all parts is the objective function value of machine layout problem. And objective of machine layout problem is to minimize total distance travelled by all parts. So most effective method is one which has minimum value of this performance criterion. If optimum solution of machine layout problem is not known in advance then also this performance criterion can be used.

3. Commonly used performance criteria for comparing performance of methods to solve cell layout problem are as follows.

## 3.1 Percentage of deviation with best-known solution

Researchers have used percentage of deviation with best-known solution as a performance criterion to compare performance of their developed method with other methods available in the literature. This performance criterion is used in such situations where optimum solution of cell layout problem is not available but best-known solution is available in the literature. Most effective method is one which has lowest percentage of deviation with best-known solution.

## 3.2 Total inter-cell flow of materials

Researchers have also used total inter-cell flow of materials as a performance criterion for comparing performance of their developed method with other methods available in the literature. One of the objectives of cell layout problem is to minimize total inter-cell flow of materials. So most effective method is one which has minimum value of this performance criterion. If optimum solution of cell layout problem is not known in advance then also this performance criterion can be used.