Robust Solution Approach for the Dynamic and Stochastic Vehicle Routing Problem

The dynamic and stochastic vehicle routing problem (DSVRP) can be modelled as a stochastic program (SP). In a two-stage SP with recourse model, the first stage minimizes the a priori routing plan cost and the second stage minimizes the cost of corrective actions, performed to deal with changes in the inputs. To deal with the problem, approaches based either on stochastic modelling or on sampling can be applied. Sampling-based methods incorporate stochastic knowledge by generating scenarios set on realizations drawn from distributions. In this paper we proposed a robust solution approach for the capacitated DSVRP based on sampling strategies. We formulated the problem as a two-stage stochastic program model with recourse. In the first stage the a priori routing plan cost is minimized, whereas in the second stage the average of higher moments for the recourse cost calculated via a set of scenarios is minimized. The idea is to include higher moments in the second stage aiming to compute a robust a priori routing plan that minimizes transportation costs while permitting small changes in the demands without changing solution structure. Additionally, the approach allows managers to choose between optimality and robustness, that is, transportation costs and reconfiguration. The computational results on a generic dynamic benchmark dataset show that the robust routing plan can cover unmet demand while incurring little extra costs as compared to the preplanning. We observed that the plan of routes is more robust; that is, not only the expected real cost, but also the increment within the planned cost is lower.