A graph-pair representation and linear programming embedded genetic algorithm for unequal-sized layout of cellular manufacturing systems

Abstract

Purpose

This paper aims to deal with intra and inter-cell layout problems in cellular manufacturing systems. The model is organized to minimize the total handling cost, i.e. intra and inter-cell handling costs in a continuous environment.

Design/methodology/approach

The research was conducted by developing a mixed integer mathematical model. Due to the complexity and NP-hard nature of the cellular manufacturing layout problem, which mostly originated from binary variables, a “graph-pair” representation is used for every machine set and cells each of which manipulates the relative locations of the machines and cells both in left-right and below-up direction. This approach results in a linear model as the binary variables are eliminated and the relative locations of the machines and cells are determined. Moreover, a genetic algorithm as an efficient meta-heuristic algorithm is embedded in the resulting linear programming model after graph-pair construction.

Findings

Various numerical examples in both small and large sizes are implemented to verify the efficiency of the linear programming embedded genetic algorithm.

Originality/value

Considering the machine and cell layout problem simultaneously within the shop floor under a static environment enabled managers to use this concept to develop the models with high efficiency.