Models and two-phase bee algorithms for multi-objective U-shaped disassembly line balancing problem

Disassembly is the first and vital step in recycling and remanufacturing end-of-life products. Disassembly lines are utilized frequently due to high productivity and suitability. This research studies the disassembly line balancing problem on the U-shaped disassembly lines, which have higher flexibility than the traditional straight disassembly lines. A mixed-integer linear programming (MILP) model is developed to formulate the AND/OR precedence relationships with the objective of minimizing the number of stations. This model is also extended to a mixed-integer nonlinear programming model to optimize four objectives. To tackle this NP-hard problem effectively, a two-phase artificial bee colony algorithm and a bee algorithm are proposed and improved. In these algorithms, the first phase selects the stations with less loads on the last two stations for the purpose of achieving the optimal number of stations. The second phase hierarchically optimizes multiple objectives to achieve better line balances. Case studies show that the proposed MILP model obtains optimal solutions in terms of station number for the small-size instances, and the U-shaped disassembly lines obtain better fitness values than the straight disassembly lines. The comparative study demonstrates that the proposed methodologies perform competing performances in comparison with other 13 re-implemented algorithms, including tabu search algorithm, iterated local search algorithm, genetic algorithm, particle swarm optimization, three artificial bee colony algorithms and the original bee algorithm.