This paper introduces a decomposition of the Elementary Shortest Path Problem with Resource Constraints(ESPPRC), where the path is combined by smaller sub paths. We show computationals result by comparing different approaches for the decomposition and compare the best of these with existing algorithms. We show that the algorithm for many instances outperforms a bidirectional labeling algorithm.

Increasing competition in the air transport market has intensified active airlines’ efforts to keep their market share by attaching due importance to cost management aimed at reduced final prices. Crew costs are second only to fuel costs on the cost list of airline companies. So, this paper attempts to investigate the cockpit crew pairing problem. The set partitioning problem has been used for ...

The shortest path problem is considered with yet another extension. The transit times b(x,y,u) and the arc costs c(x,y,u) on arc (x,y) vary as a function of the departure time u at the beginning vertex of the arc. The problem considered is to find the shortest path between a pair of nodes such that the total traverse time is lesser than some specified value T. Waiting times at nodes are conside...

The shortest path problem in which the (s, t)-paths P of a given digraph G = (V,E) are compared with respect to the sum of their edge costs is one of the best known problems in combinatorial optimization. The paper is concerned with a number of variations of this problem having different objective functions like bottleneck, balanced, minimum deviation, algebraic sum, k-sum and k-max objectives,...

With their paper ”Symmetry helps: Bounded bi-directional dynamic programming for the elementary shortest path problem with resource constraints” [Discrete Optimization 3, 2006, pp. 255–273] Righini and Salani introduced bounded bidirectional dynamic programming (DP) as an acceleration technique for solving variants of the shortest path problem with resource constraints (SPPRC). SPPRCs must be s...

The resource constrained shortest path problem (CSP) asks for the computation of a least cost path obeying a set of resource constraints. The problem is NP-complete. We give theoretical and experimental results for CSP. In the theoretical part we present the hull approach, a combinatorial algorithm for solving a linear programming relaxation and prove that it runs in polynomial time in the case...

When delivering multimedia services over Internet, different media types are impacted by resource limitations in a different way. While an interactive audio service calls for low-latency communication, video streams should be routed over network paths with sufficient capacity. However, in current networks flows towards the same destination follow the same path, which may lead to a suboptimal re...