International audienceThis article tackles the multi-trip vehicle routing problem with time windows and limited duration. A trip is a timed route such that a succession of trips can be assigned to one vehicle. We provide an exact two-phase algorithm to solve it. The first phase enumerates possible ordered lists of clients which match the maximum trip duration criterion. The second phase uses a Branch and Price scheme to generate and choose a best set of trips so that all customers are visited. We propose a set covering formulation as the column generation master problem, where columns (variables) represent trips. The sub-problem selects appropriate timing for trips and has a pseudo-polynomial complexity. Computational results on Solomon's benchmarks are presented. The computational times obtained with our new algorithm are much lower than the ones recently obtained in the only two studies published on this problem to date

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International audienceWe explore in this paper some complexity issues inspired by the contig scaffolding problem in bioinformatics. We focus on the following problem: given an undirected graph with no loop, and a perfect matching on this graph, find a set of cycles and paths covering every vertex of the graph, with edges alternatively in the matching and outside the matching, and satisfying a given constraint on the numbers of cycles and paths. We show that this problem is NP-complete, even in planar bipartite graphs. Moreover, we show that there is no subexponential-time algorithm for several related problems unless the Exponential-Time Hypothesis fails. Lastly, we also design two polynomial-time approximation algorithms for complete graphs