Optimal solution for the two-dimensional facility layout problem using a branch-and-bound algorithm

Facilities layout problem is one of the important issues affecting the productivity of manufacturing systems. This problem deals with the determination of optimum arrangement of manufacturing facilities with respect to different layout patterns. A two-dimensional layout is an arrangement fashion in which the manufacturing facilities are laid in a planar area. In this paper, a mixed-integer nonlinear mathematical programming model is proposed for determining the optimum layout of machines in a two-dimensional area. The parameters considered by the proposed model are (a) production capacity of machines, (b) multiple machines of each type (machine redundancy), (c) processing route of parts, (d) dimensions of machines. A technique is used to linearize the formulated nonlinear model. An algorithm based on branch-and-bound approach is proposed to obtain the optimal solution of the proposed mathematical programming model. A simple illustrative example is discussed to demonstrate the technique, and then small-, medium-, and large-sized problems are solved. Comparison of the layout obtained from the proposed model indicates that the proposed model considerably reduces the total distance traveled by products as compared to an optimum process layout configuration for small- and medium-sized problems. The paper concludes that the proposed branch-and-bound approach performs inefficient for large-sized problems. For large-sized problems, the proposed mathematical programming model should be solved through meta-heuristics like genetic algorithms, tabu search, etc.