A General Variable Neighborhood Search approach based on a p-median model for cellular manufacturing problems

One of the practical application in cellular manufacturing systems is the cell formation problem (CFP). Its main idea is to group machines into cells and parts into part families in a way that the number of exceptional elements and the number of voids are minimized. In literature, it is proved that p-median is an efficient mathematical programming model for solving CF problems. In the present work, we develop a modified p-median based model dedicated to solve CFP respecting the objective of minimizing the sum of dissimilarities of machines. For this aim, we applied a General Variable Neighborhood Search algorithm and we collaborated it with an Estimation of Distribution Algorithm maximizing the group capability index and the grouping efficacy evaluation criteria. Thirty CF problems are taken from the literature and tested by our proposed algorithm and the experimental study demonstrated that the proposed method guided by p-median model provides high quality cells in speed running times and beats other state-of-the-art algorithms particularly for CF instances with large sizes.