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