Mathematical models and simulated annealing algorithms for the robotic assembly line balancing problem

Robots are used in assembly lines because of their higher flexibility and lower costs. The purpose of this paper is to develop mathematical models and simulated annealing algorithms to solve the robotic assembly line balancing (RALB-II) to minimize the cycle time.

Four mixed-integer linear programming models are developed and encoded in CPLEX solver to find optimal solutions for small-sized problem instances. Two simulated annealing algorithms, original simulated annealing algorithm and restarted simulated annealing (RSA) algorithm, are proposed to tackle large-sized problems. The restart mechanism in the RSA methodology replaces the incumbent temperature with a new temperature. In addition, the proposed methods use iterative mechanisms for updating cycle time and a new objective to select the solution with fewer critical workstations.

The comparative study among the tested algorithms and other methods adapted verifies the effectiveness of the proposed methods. The results obtained by these algorithms on the benchmark instances show that 23 new upper bounds out of 32 tested cases are achieved. The RSA algorithm ranks first among the algorithms in the number of updated upper bounds.

Four models are developed for RALBP-II and their performance is evaluated for the first time. An RSA algorithm is developed to solve RALBP-II, where the restart mechanism is developed to replace the incumbent temperature with a new temperature. The proposed methods also use iterative mechanisms and a new objective to select the solution with fewer critical workstations.