Solving resource constrained shortest path problems with LP-based methods

• The resource constrained shortest path problem is addressed by LP-based branch-and-bound methods.
• New cutting planes along with separation algorithms are provided.
• NP-hardness of the separation problem for a known class of cutting planes is proved.
• New variable-fixing and primal heuristic methods are developed.
• Detailed tests are reported on each of the above components.

In the resource constrained shortest path problem (RCSPP) there is a directed graph along with a source node and a destination node, and each arc has a cost and a vector of weights specifying its requirements from a set of resource types with finite capacities. A minimum cost source–destination directed path is sought such that the total consumption of the arcs from each resource type does not exceed the capacity of the resource. In this paper we investigate LP-based branch-and-bound methods and introduce new cutting planes, separation procedures, variable fixing, and primal heuristic methods for solving RCSPP to optimality. We provide detailed computational experiments, and a comparison to other methods in the literature.