An exact algorithm for the vehicle routing problem with stochastic demands
The classical deterministic Vehicle Routing Problem (VRP) can be defined as follows. Let G = (V, E) be an undirected graph where V = {l_brace}v{sub 1}, {center_dot}{center_dot}, v{sub n}{r_brace} is a set of vertices representing cities or customers, and E = {l_brace}(v{sub i}, V{sub j}) : i < j; v{sub i}, v{sub j} {element_of} V{r_brace} is an edge set. With each vertex v{sub i}(i {>=} 2) (v{sub i}, v{sub j}) is associated a non-negative cost (distance, travel time) c{sub ij}. Vertex v{sub 1} represents a depot at which are based m identical vehicle of capacity Q > 0. Depending on the version of the problem considered, the value of m is either fixed, or bounded above by a constant {<=} m. The VRP consists of determining vehicle routes in such a way that (i) all routes start and end at the depot; (ii) each vertex other than the depot is visited exactly once; (iii) the total demand of any given route does not exceed Q; (iv) the total distance traveled by all vehicles is minimized. In the Stochastic Vehicle Routing Problem (SVRP), the demand associated with vertex v{sub i} is a random variable {xi}{sub i}. As a result, it is no longer possible to assume that vehicle routes may be followed as planned. The SRVP is modeled in two stages. In the first stage, a priori vehicle routes satisyfing conditions (i) and (ii) are constructed, without full information on the demands. In the second stage, when this information becomes available, routes are followed as planned, until the accumulated demand attains or exceeds the vehicle capacity. In this case, failure is said to occur and a recourse action is taken: the vehicle returns to the depot to unload, and resumes its visits at the point of failure. The SVRP consists of determining an a priori set of routes so as to minimize the expected cost of the second stage solution. The corresponding model can be solved using the relaxation approach in Laporte and Louveaux.
- OSTI ID:
- 36238
- Report Number(s):
- CONF-9408161--
- Country of Publication:
- United States
- Language:
- English
Similar Records
New exact algorithms for the vehicle routing problem
A New Upper Bound for Laplacian Graph Eigenvalues