A bi-objective mathematical model for dynamic cell formation problem considering learning effect, human issues, and worker assignment

One of the important aspects neglected in the literature related to cell formation problem is human issues. In this study, a bi-objective mathematical model is developed in which human issues and dynamic cell formation are taken into consideration simultaneously. The rst objective function deals with costs associated with machines and human issues. The costs of human issues relate to salary, hiring, ring, reward/penalty policy, and worker assignment. The second objective function takes into account labor utilization as a criterion for reward/penalty policy. Since the available time in different real conditions is not constant, we include learning effect to consider the real workers time. The nature of dynamic cell formation problem is NP-hard, and thus a Linear Programming embedded Genetic Algorithm (LP-GA) is employed to solve the model. In order to improve the performance of the applied GA, its parameters are tuned by means of Central Composite Design (CCD) method. Moreover, to validate the LP-GA, some test problems are solved and the results are compared with those obtained from an exact method and GA. The computational results show that the near optimal solutions yielded by LP-GA are better than GA in large-sized problems.