A dynamic-pricing label-setting algorithm for solving the elementary resource constrained shortest path problem - Vitale, Ignacio (2020)
The resource constrained elementary shortest-path problem is a problem used for solving vehicle-routing, production-scheduling and crew-scheduling applications. It occurs as a sub-problem used to implicitly generate the set of all feasible columns in a column-generation solution algorithm. In the problem there is a directed graph with a source node and a destination node, and each arc has a cost and a vector of weights specifying its requirements of resources. A minimum-cost source to destination directed path is sought such that the total consumption of resources does not exceed the resources vehicle-capacity. The problem is NP-hard in the strong sense. We propose a new label-setting heuristic algorithm based on the dynamic update of resources and prices vectors according the partial label-path and embed it into a column generation algorithm to solve some testing problems. Later we perform some numerical experiments in order to study its computational efficiency.