Dynamic programming algorithms for the elementary shortest path problem with resource constraints

When vehicle routing problems with additional constraints (e.g. capacities or time windows) are solved via column generation and branch-and-price, it is common that the pricing problem requires the computation of a minimum cost constrained path on a graph with costs on the arcs and prizes on the nodes. The pricing problem is usually solved via dynamic programming in two possible ways: requiring elementary paths or allowing paths with cycles. We experimentally compare these two strategies and we evaluate the effectiveness of some algorithmic ideas to improve their performance.