Abstract
We consider a vehicle routing problem with multiple trips and time windows (VRPMTTW) in which a mobile robot transports materials from a central warehouse to multiple demanding places. The robot needs to strictly satisfy the time windows at demanding places and it can run multiple trips. How to effectively scheduling the robot is a key problem in operations of Smart Nations and intelligent automated manufacturing. In the literature three-index mixed integer programming models are developed. However, these three-index models are difficult to solve in reasonable time for real problems due to computational complexity of integer programming. We propose an innovative two-index mixed integer programming model. The numerical results show our model can successfully obtain optimal solutions fast for cases where the existing literature has not found the optimal solution yet. To our best knowledge, it is the first two-index model for this type of problems.