A Robust Scenario Approach for the Vehicle Routing Problem with Uncertain Travel Times

We consider a vehicle routing problem with uncertain travel times in which a penalty is incurred for each vehicle that exceeds a given time limit. A traditional stochastic programming approach would require precise knowledge of the underlying probability distributions of random data. In a novel approach presented here, we assume that only rough information on future travel times is available, leading to the multiple range forecasts of travel times and the probabilities of each range being realized. In this setting, we replace the point estimates of travel times on a scenario by range estimates. For each scenario, we then find the robust routes that protect the solution against the worst case within the given ranges, and finally we find the routes with the minimum expected cost. We propose a branch-and-cut algorithm to solve the problem and report computational results on both randomly generated and the well-known Solomon's instances. The results demonstrate that our approach is a favorable one when exact information of probability distributions is not available

A Robust Scenario Approach for the Vehicle Routing Problem with Uncertain Travel Times

International audienceWe consider a vehicle routing problem with uncertain travel times in which a penalty is incurred for each vehicle that exceeds a given time limit. A traditional stochastic programming approach would require precise knowledge of the underlying probability distributions of random data. In a novel approach presented here, we assume that only rough information on future travel times is available, leading to the multiple range forecasts of travel times and the probabilities of each range being realized. In this setting, we replace the point estimates of travel times on a scenario by range estimates. For each scenario, we then find the robust routes that protect the solution against the worst case within the given ranges, and finally we find the routes with the minimum expected cost. We propose a branch-and-cut algorithm to solve the problem and report computational results on both randomly generated and the well-known Solomon's instances. The results demonstrate that our approach is a favorable one when exact information of probability distributions is not available

Exact Algorithms for a Bandwidth Packing Problem with Queueing Delay Guarantees

The bandwidth packing problem (BWP) concerns the selection of calls from a given set and the assignment of one path to each selected call. The ultimate aim of the BWP is to maximize profit while the routings of the selected calls observe the capacity constraints of the links. Here, we additionally consider queueing delays in the network, which may cause a deterioration in the quality of service to users if they exceed the acceptable limits. The integer programming formulation for the BWP with the queueing delay restriction contains a nonlinear constraint that is intrinsic to the model. We apply the Dantzig-Wolfe decomposition to this nonlinear constraint, and since the Dantzig-Wolfe decomposition has exponentially many variables, we propose the branch-and-price procedure to find optimal solutions. We also propose a generalized Dantzig-Wolfe reformulation based on the aggregation of variables, which makes our branch-and-price algorithm more competitive. Computational results on cases of randomly generated networks and some real-life telecommunication networks demonstrate that our algorithm performs well for large networks