An Inverse Robust Optimisation Approach for a Class of Vehicle Routing Problems under Uncertainty

There is a trade-off between the total penalty paid to customers (TPC) and the total transportation cost (TTC) in depot for vehicle routing problems under uncertainty (VRPU). The trade-off refers to the fact that the TTC in depot inevitably increases when the TPC decreases and vice versa . With respect to this issue, the vehicle routing problem (VRP) with uncertain customer demand and travel time was studied to optimise the TPC and the TTC in depot. In addition, an inverse robust optimisation approach was proposed to solve this kind of VRPU by combining the ideas of inverse optimisation and robust optimisation so as to improve both the TPC and the TTC in depot. The method aimed to improve the corresponding TTC of the robust optimisation solution under the minimum TPC through minimising the adjustment of benchmark road transportation cost. According to the characteristics of the inverse robust optimisation model, a genetic algorithm (GA) and column generation algorithm are combined to solve the problem. Moreover, 39 test problems are solved by using an inverse robust optimisation approach: the results show that both the TPC and TTC obtained by using the inverse robust optimisation approach are less than those calculated using a robust optimisation approach.