Bi-objective cyclic scheduling in a robotic cell with processing time windows and non-Euclidean travel times

This paper addresses bi-objective cyclic scheduling in a robotic cell with processing time windows. In particular, we consider a more general non-Euclidean travel time metric where robots travel times are not required to satisfy the well-known triangular inequality. We develop a tight bi-objective mixed integer programming (MIP) model with valid inequalities for the cyclic robotic cell scheduling problem with processing time windows and non-Euclidean travel times. The objective is to minimise the cycle time and the total robot travel distance simultaneously. We propose an iterative ε-constraint method to solve the bi-objective MIP model, which can find the complete Pareto front. Computational results both on benchmark instances and randomly generated instances indicate that the proposed approach is efficient in solving the cyclic robotic cell scheduling problems.