A vehicle routing problem with stochastic demand
Operations Research
Algorithms for Capacitated Vehicle Routing
SIAM Journal on Computing
A Capacitated Vehicle Routing Problem on a Tree
ISAAC '98 Proceedings of the 9th International Symposium on Algorithms and Computation
The Finite Capacity Dial-A-Ride Problem
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
On the vehicle routing problem
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
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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.