A novel competitive exact approach to solve assembly line balancing problems based on lexicographic order of vectors

The assembly line balancing problem (ALBP) is an eminent NP-hard topic that is discussed in mass production systems with low diversity. Primarily, two types of ALBPs are discussed in the literature as type I, which aims to find the minimum number of workstations for a given cycle time, and type II, which assigns some tasks to a given number of workstations such that the maximum workstation load is minimized. To solve ALBPs, various exact, heuristic, and metaheuristic methods have been proposed. However, these methods lose their efficiency when handling large-size problems. Therefore, researchers have focused on proposing heuristic and metaheuristic algorithms to solve large-size problems, especially when they deal with real-life case problems in the industry. This study aims to present a novel and competitive exact method for solving ALBP type II based on the lexicographic order of vectors for feasible solutions. To evaluate the performance of the developed method, a group of highly used standard test problems in the literature is utilized, and the results are compared and discussed in detail. The computational results in this study specify that the developed solution approach performs efficiently and yields the best global solution of all the ALB test problems, which proves the proposed method's potential and its competitive advantage.