Bicriteria line balancing in robotic cells

In this study, we consider a production line that consists of a number of machines and material handling robot. The robot does not perform any operations on the parts but loads/unloads the machines and transports the parts between the machines. The parts to be processed are assumed to be identical. A specific number of operations are to be performed on these parts on the machines. The robot can be transport a single part at a time and can load/unload a single machine at a time. The decisions to be made include i-the determination of the number of the machines on the line, ii-the determination of the assignment of operations to the machines, and iii-the determination of the robot move sequence. This problem is handled as a bicriteria problem that includes the minimization of the cycle time and the minimization of the number of machines used on the line. Two solution approaches are considered: Prioritization of the objectives and determination of the pareto optimal solutions by parameterizing one of the objectives. Mathematical programming formulations are developed for both of these methods. Computational studies are performed using different parameter combinations and the results are analyzed in detail.