Approximation Algorithms for VRP with Stochastic Demands.

We consider the vehicle routing problem with stochastic demands (VRPSD). We give randomized approximation algorithms achieving approximation guarantees of 1 + α for split-delivery VRPSD, and 2 + α for unsplit-delivery VRPSD; here is the best approximation guarantee for the traveling salesman problem. These bounds match the best known for even the respective deterministic problems [Altinkemer, K., B. Gavish. 1987. Heuristics for unequal weight delivery problems with a fixed error guarantee. Oper . Res. Lett. 6(4) 149-158; Altinkemer, K., B. Gavish. 1990. Heuristics for delivery problems with constant error guarantees. Transportation Res. 24(4) 294-297]. We also show that the "cyclic heuristic" for split-delivery VRPSD achieves a constant approximation ratio, as conjectured in Bertsimas [Bertsimas, D. J. 1992. A vehicle routing problem with stochastic demand. [ABSTRACT FROM AUTHOR]