A Robust VRPHTW Model with Travel Time Uncertainty

Vehicle routing problem with hard time window(VRPHTW) is extremely strict in travel time. However, the travel time is usually uncertain due to some stochastic factors such as weather and other road conditions. It is an important issue to take travel time uncertainty into consideration in VRPHTW. This paper develops a robust VRPHTW model to cope with time uncertainty. We use robustness method of Bertismas to consider the maximum change of uncertain travel time in the degree of robustness set by decision maker. The probability that the optimal solution violates constraints is derived. The violated probability shows that the robustness of VRPHTW model can reach a satisfactory-level. Finally, one modified max-min ant system algorithm is proposed to solve this problem and one numerical example is conducted to illustrate the model and the algorithm. Both theory analysis and numerical example show the effectiveness of the proposed robust model.