We present a branch-and-cut algorithm to solve the single-commodity, uncapacitated, fixed-charge network flow problem, which includes the Steiner tree problem, uncapacitated lot-sizing problems, and the fixed-charge transportation problem as special cases. The cuts used are simple dicut inequalities and their variants. A crucial problem when separating these inequalities is to find the right cut set on which to generate the inequalities. The prototype branch-and-cut system, bc-nd, includes a separation heuristic for the dicut inequalities and problem-specific primal heuristics, branching, and pruning rules. Computational results show that bc-nd is competitive compared to a variety of special purpose algorithms for problems with explicit flow costs. We also examine how general purpose MIP systems perform on such problems when provided with formulations that have been tightened a priori with dicut inequalities.

This article describes several heuristics for the construction of a rapid transit alignment. The objective is the maximization of the total origin-destination demand covered by the alignment. Computational results show that the best results are provided by a simple greedy extension heuristic. This conclusion is confirmed on the Sevilla data for scenarios when the upper bound for inter-station distance is greater than 1250 m. Otherwise, when those upper bounds are smaller (750 m and 1000 m), an insertion heuristic followed by a post-optimization phase yields the best results. Computational times are always insignificant.

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Rapid transit systems timetables are commonly designed to accommodate passenger demand in sections with the highest passenger load. However, disruptions frequently arise due to an increase in the demand, infrastructure incidences or as a consequence of fleet size reductions. All these circumstances give rise to unsupplied demand at certain stations, which generates passenger overloads in the available vehicles. The design of strategies that guarantee reasonable user waiting time with small increases of operation costs is now an important research topic. This paper proposes a tactical approach to determine optimal policies for dealing with such situations. Concretely, a short-turning strategy is analysed, where some vehicles perform short cycles in order to increase the frequency among certain stations of the lines and to equilibrate the train occupancy level. Turn-back points should be located and service offset should be determined with the objective of diminishing the passenger waiting time while preserving certain level of quality of service. Computational results and analysis for a real case study are provided.

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