Selecting Good a Priori Sequences for Vehicle Routing Problem with Stochastic Demand

In the vehicle routing problem with stochastic demand, the customers' demands vary from one collection/delivery period to the next. Under the assumption that they become known only upon arrival of the vehicle at their sites, our objective is to find a fixed a priori sequence that is used in every period. We present a priori sequences that achieve 2-, 2-, 3- and 5-approximation in the worst case on trees, cycles, cactus graphs, and general graphs, respectively, in the case where the demand of a customer must be serviced all at once. These approximation ratios are with respect to the optimal distance computed off-line, when all demands are non-zero and are known in advance. If the demand of a customer can be serviced in parts, we present a linear time algorithm to find an optimal solution for cycles.