A bi-objective model for the integrated frequency-timetabling problem

The urban transport planning process has four basic activities: network design, timetable construction, vehicle scheduling and crew scheduling. In this work we focus on the urban bus timetable construction problem which has two sub-activities: bus frequency calculation and bus departures setting. Typically, these sub-activities are done sequentially, which has some drawbacks: to overcome these drawback we propose to integrate both these sub-activities. We take into consideration: multiple planning periods, synchronizations events (a synchronization occurs when two buses from different routes arrive to a node within a time window), fixed and variable operations costs and uncertain demand in each period

Multiperiod synchronization bus timetabling

The timetabling subproblem of bus transit network planning determines the departure times for all trips of the lines along the entire day. Most of the public transport networks consider planning periods identical for all lines. In this study we drop this strong assumption by introducing specific periods for each line, which is more realistic. Thus, we propose the multiperiod synchronization bus timetabling (MSBT) problem, which specifies the departure times of the trips of all lines where each line has its own planning periods along the day, with the objective of optimizing synchronization events: maximize passenger transfers and minimize bus bunching along the network. We propose an integer linear programming formulation for the MSBT problem and analyze the structural properties of this formulation by a constraint propagation methodology. These properties are the basis for different operators that lead to the design of efficient metaheuristics for solving the problem. We empirically obtain high-quality feasible solutions for real size instances and show that by considering a multiperiod approach, synchronization events of trips belonging to different planning periods are not ignored, as it is the case when several single period timetables are merged

Selecting Large Portfolios of Social Projects in Public Organizations

We address the portfolio selection of social projects in public organizations considering interdependencies (synergies) affecting project funds requirements and tasks. A mixed integer linear programming model is proposed incorporating the most relevant aspects of the problem found in the literature. The model supports both complete (all or nothing) and partial (a certain amount from a given interval of funding) resource allocation policies. Numerical results for large-scale problem instances are presented