The robust Vehicle Routing Problem

We consider a Vehicle Routing Problem (VRP) under uncertainty and seek to find efficient solutions in practice. Routing problems contain a fairly high degree of uncertainty in real life; thus pre-planned optimal routes are no longer of practical use. Current methods to address the uncertainty in VRP either make require strong assumptions or increase the complexity of the deterministic model significantly. In this study, we propose a routing model that uses robust optimization to represent uncertainty in demand and travel times, we adapt this model for a real life courier delivery problem, we develop a heuristic for this large scale problem, and we evaluate the quality of this solution procedure in practice.; To develop the routing model, we first experimentally compare the robustness of VRP formulations. We then adapt the most suitable VRP formulation and develop a robust counterpart of VRP (RVRP) with demand and travel time uncertainty that can be solved efficiently. The RVRP is not more difficult to solve than VRP; in fact the RVRP with demand uncertainty is simply a single instance of VRP with modified demand data. We show experimentally that the solution of this RVRP when compared to the solution of the deterministic VRP protects against the unmet demand at the expense of slightly increased cost, especially when the network is clustered.; We combine robust optimization with scenario based stochastic optimization to address a real life courier delivery problem, a variant of VRP with time windows. We use robust optimization for uncertainty in service times and time windows, and we represent uncertainty in demand using stochastic optimization with recourse. Our model maximizes number of customers serviced and similarity of daily routes while minimizing route lengths and total penalty. We develop a two-phase insertion based heuristic balancing these objectives. Our experiments show that our heuristic improves similarity of routes and total penalty at the expense of increasing route lengths compared to independent deterministic solutions for each demand outcome. Our solution for real life problem is also better than the current practice.