Graph theory-based approach to optimize single-product flow-line configurations of RMS

Generating economical and distinctive configurations for a given demand period is an important optimization problem for reconfigurable manufacturing systems (RMS) at both initial design and reconfiguration stages. This paper presents a graph model to optimize capital cost of singe-product flow-line (SPFL) configurations of RMS. The parameters of the SPFL configuration include number of workstations, number and type of machines and assigned operations for each workstation. The full topological sorting and graph augmentation procedures are developed to derive a combined machine graph from the operation precedence graph of a specific product. Then a two-phase optimization approach is proposed. In the first phase, the optimal and K-1 suboptimal configurations are generated by solving a constrained K-shortest paths problem on the machine graph. In the second phase, a dissimilarity index is introduced to measure the dissimilarity between every pair of found configurations. Subsequently p distinctive ones out of K configurations are obtained using the algorithms for p-dispersion problem. Case studies illustrate the effectiveness of our approach and show some superiority of our approach compared to existing approaches. Computational experience shows that the approach is fit for small-to-medium size problems of configuration generation. The approach is also applied to optimizing SPFL in mechanical production.