A Novel Simulated Annealing Algorithm Proposal for the Resource Constrained Assembly Line Balancing Problem

The Assembly Line Balancing Problem is the assignment of tasks to workstations according to their precedence relationships, subject to certain constraints, and optimizing a defined performance measure. However, recent approaches, aiming to increase line efficiency and resource utilization, have focused on minimizing the number or cost of the limited resources used during task assignment. This advanced decision problem is termed the Resource-Constrained Assembly Line Balancing Problem. In this study, which addresses the single-model, straight Resource-Constrained Assembly Line Balancing Problem, the mathematical model of the problem was developed based on established literature examples. The primary objective is to simultaneously optimize the cycle time and the total number of resources used in the stations. The mathematical model was coded and analyzed using the GAMS 24.2.1 software. However, the long solution times required to reach an optimum solution as the problem size increases presented a constraint. To overcome this limitation, a metaheuristic approach capable of generating acceptable quality solutions in a short time, the Simulated Annealing algorithm, was proposed. The developed algorithm was coded and implemented using MATLAB R2021a software. The effectiveness of the proposed method was tested on existing datasets presented in the literature. Datasets with 2 resources and 4 resources were used for the comparison of the methods. GAMS, SA, and Rule-Based SA were compared, and the superior performance of the proposed Rule-Based SA method was determined using the Wilcoxon Signed-Rank Test. Especially as the problem size grew, the proposed method was shown to yield good solutions within reasonable time frames.