We study the Chva´tal rank of two linear relaxations of the stable set polytope, the edge constraint and the clique constraint stable set polytope. For some classes of graphs whose stable set polytope is given by 0/1valued constraints only, we present either the exact value of the Chva´tal rank or upper bounds (of the order of their largest cliques and stable sets), which improve the bounds previously known from the literature (of the order of the graph itself).
We discuss an optimization model for the line planning problem in public transport in order to minimize operation costs while guaranteeing a certain level of quality of service, in terms of available transport capacity. We analyze the computational complexity of this problem for tree network topologies as well as several categories of line operations that are important for the Quito Trolebús system. In practice, these instances can be solved quite well, and significant optimization potentials can be demonstrated.
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