This paper tackles a generalization of the weight constrained shortest path problem in a directed network (WCSPP) in which replenishment arcs, that reset the accumulated weight along the path to zero, appear in the network. Such situations arise, for example, in airline crew pairing applications, where the weight represents duty hours, and replenishment arcs represent crew overnight rests, and also in aircraft routing, where the weight represents time elapsed, or flight time, and replenishment arcs represent maintenance events. In this paper, we introduce the weight constrained shortest path problem with replenishment (WCSPP-R), develop preprocessing methods, extend existing WCSPP algorithms, and present new algorithms that exploit the inter-replenishment path structure. We provide the results of computational experiments investigating the benefits of preprocessing and comparing several variants of each algorithm, on both randomly generated data, and data derived from airline crew scheduling applications.

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