Multi-objective scheduling and assembly line balancing with resource constraint and cost uncertainty: A “box” set robust optimization

Assembly lines are flow-oriented production systems that are of great importance in the industrial production of standard, high-volume products and even more recently, they have become commonplace in producing low-volume custom products. The main goal of designers of these lines is to increase the efficiency of the system and therefore, the assembly line balancing to achieve an optimal system is one of the most important steps that have to be considered in the design of assembly lines. The purpose of the assembly line balancing is to assign tasks to the workstation called the station, so that prerequisite relationships, cycle times, and other assembly line constraints to be met and a number of line performance criteria to be optimized. In this study, considering the social responsibility related objective function, a mathematical model is proposed for scheduling and balancing the cost-oriented assembly line that has resource constraints with cost uncertainty. The box set robust optimization is applied and the obtained model is solved with the augmented epsilon constraint in the GAMS and some test problems and their results are presented. Finally, the cost parameter has been changed in a robust optimization approach and the obtained results have been analyzed for different costs.