Optimal multi-degree cyclic scheduling of multiple robots without overlapping in robotic flowshops with parallel machines

•This paper considers scheduling robotic flowshops with parallel machines and multiple robots in multi-degree cycles.•The principle without overlapping is applied to avoid collisions among robots.•A mixed integer linear programming (MILP) model (the first one) is formulated to obtain optimal solutions.•An example illustrates the application of the MILP model.•The example illustrates that solutions in multi-degree cycles outperform those in 1-degree cycles.

This paper considers scheduling robotic flowshops with parallel machines and multiple robots. Robots share the same track and cannot crossover each other. To avoid conflicts among robots, the principle without overlapping is applied. Identical parts with time window constraints are produced. It is challenging to obtain better cyclic schedules to improve the throughput. Moreover, multi-degree cycles are considered to obtain better schedules comparing to simple cycles, i.e. 1-degree cycles. To our knowledge, this is the first work to deal with the multi-degree cyclic scheduling in this complicated scenario. This is the main contribution of this research. The objective is to maximize the throughput of the flowshop by obtaining optimal schedules. As for given degree cycles, it is equivalent to minimizing the cycle time. Operations in robotic flowshops considering multi-degree cycles are analyzed in detail. Based on the analyses, a mixed integer linear programming model is formulated for this challengeable problem. A numerical example modified from the previous work is used to illustrate the model proposed, which is solved by CPLEX. Results show the benefits of the model, especially considering multi-degree cycles.