Formulations of the robust pickup and delivery problem with time windows

This work addresses the pickup and delivery problem with time windows considering uncertainties on demand and travel time through robust optimisation. This approach does not require previous knowledge of probability distributions and use the parameter's variation interval to guarantee feasible solutions for the most relevant realisations. We propose mathematical formulations to incorporate the anticipated uncertainties based on dualisation and linearisation of recursive equations. The computational experimentation results for different uncertainty scenarios show that the developed formulations are effective to solve small instances, highlighting as more efficient the models based on the linearisation of recursive equations.