A New Mathematical Model for Cell Layout Problem considering Rotation of Unequal Dimensions of Cells and Machines

One of the main concepts in group technology (GT) is the cellular manufacturing system (CMS) with three main problems of cell formation (CF), cell layout (CL), and cell scheduling (CS). This paper studies the cell layout problem (CLP), aiming to find the optimal layout of machines within each cell (intracellular layout) and the optimal layout of cells in each workshop (intercellular layout). To adapt to reality, the dimensions of the cells and machines (inside each cell) were considered unequal, and also the cells and machines could rotate. We believe that a cellular layout that assumes unequal dimensions of the cells and machines can be used for batch production. This kind of production has a wide variety of low to medium demand. Furthermore, a cellular layout can be applied in CMSs and also in noncontinuous industries that have a job shop layout. Our main contribution is considering the possibility of rotating the cells and machines inside the cells. For this purpose, a mixed nonlinear programming model was developed to solve the CLP with the minimum cost of intracellular and intercellular material flows. The proposed nonlinear model was first converted into a linear model, and then a problem was generated and solved with GAMS software to validate the resulting linear model. This model finds the best layout of cells within the workshop and the best layout of machines inside each cell. Then, because of the NP-hardness of the CLP and the fact that even exact methods cannot solve large-scale examples in an acceptable computational time, an imperialist competitive algorithm (ICA) was designed and used to solve the problem. To evaluate the efficiency of the proposed algorithm, its numerical results in small dimensions were compared with the results of GAMS software. In large dimensions, 30 random problems were created, and the results of ICA were compared with the results of the particle swarm optimization (PSO) algorithm and genetic algorithm (GA). Finally, the parameters of the three meta-heuristic algorithms were set by the Taguchi method. Numerical results indicated that ICA was superior to both the PSO algorithm and GA. It could also achieve efficient solutions in a shorter computational time.