Advanced OR and AI Methods in Transportation

In this paper the classical Vehicle Routing Problem (VRP) is extended to cover the more realistic case of uncertainty about customer demands. This case is modelled as a VRP with stochastic demands and tackled with a heuristic solution approach based on Ant Colony Optimization (ACO). The main issues studied in this paper are the modelling of the uncertainty (i) in terms of its influence on the performance of the algorithm and (ii) in terms of the structure and quality of the solutions with respect to di#erent risk measures

A Tabu Search Algorithm for the Split Delivery

can be greater than the capacity of the vehicles. This case have already been studied in [1] and [2] where the authors have proved that the problem is NP-hard when the capacity of the vehicles is greater than or equal to 3 and they have shown that, under specific conditions on the distances, the problem is reducible in polynomial time to a new problem where each customer has a demand that is lower than the capacity of the vehicles, with a possible reduction on the number of customers. We now show that for this problem there always exists an optimal solution where the quantity delivered by each vehicle when visiting a customer is an integer number. We then present a tabu search algorithm to solve the SDVRP which we call the SPLITABU. The algorithm starts from an initial feasible solution and then it moves to neighbor solutions, always remaining in the set of feasible solutions. At each iteration the algorithm tries to remove a customer from the routes where it is visited (if a custome