Benders decomposition algorithm for MMAL balancing problem with express parallel line

Mixed-model assembly line (MMAL) could be a form of line capable of manufacturing numerous models of a product on one line. In this paper, a particular parallel MMAL balancing problem is studied in a make-to-order (MTO) production system. Customer’s satisfaction is examined in this paper by considering two parallel assembly lines: a main assembly line for normal orders and an express parallel line capable of quick assembling of models for priority orders. Furthermore, due to change of customer demands in MTO environment, the rebalancing problem is considered to maximize flexibility in the lead-time. To solve this multi-objective balancing problem, an integrated Benders Decomposition Algorithm (BDA) based on the LP-metric method is introduced. In large-size problems, the presented model is compared with the non-dominated sorting genetic algorithm (NSGA-II) and Multi-objective Particle Swarm Optimization (MOPSO) and the effectiveness of the proposed integrated BDA is investigated based on computational experiments. The percentage of gap from optimal solutions in the integrated BDA is zero and this gap changes from 0 to 4.2 in the NSGA-II algorithm and from 1 to 4.4 in the MOPSO algorithm. With regard to run times, the results obtained from NSGA-II are relatively superior in calculation time compared to the integrated BDA. However, the solution times for the integrated BDA are not large with respect to exact solutions of this algorithm and dimensions of problems.