Topics in Integrated Vehicle and Crew Scheduling in Public Transport

The talk deals with new models and OR techniques for an integrated approach to vehicle and crew scheduling. These techniques include explotation of network ow structures using Lagrangian relaxations and column generation, and, in particular, new algorithms for vehicle scheduling and the column generation pricing problem. Computational results obtained with real life problems will be presented as well. The design of an optimal, or cost eeective, telecommunications network is a complex, multi-faceted task. Typical problem domains consider topology, connectivity and routing decisions. Restricting attention to an optimal topology, for example, if we consider an n node network, allowing for k possible bandwidths for each link, the space of potential topologies is (k + 1) (n(n?1)=2). The term (k + 1) is included in order to allow for a link of zero capacity, i.e. not present, to be represented. For the values, n = 10 and k = 3, this evaluates to 1:2x10 27 possible designs. Even for this small problem, the search space is extremely large. If we extend this simple formulation to include the routing decision and the (ring) design, considerations which must be taken into account in any realistic solution, the problem becomes much more complex. In such cases, enumeration of all potential designs is impractical and eeective search techniques need to be employed. One such technique is the genetic algorithm 1]. The actual problem that we wish to solve is as follows: determine (a) the routes used by all traac in the network, (b) the link capacities (c) and the multi-ring topology of the network such that the overall cost of the network is minimized. Cost here is taken to mean the weighted sum of parameters of interest such as the link length, the monetary cost of providing link bandwidth, and the deviation of each link's utilization from the average (in order to balance link use, i.e. spread link usage as much as possible). In addition, cost will include a term dependent upon the multi-ring topology of the network, the main objective of this aspect is to minimise interring traac as such traac requires specialised hardware in real networks. The corresponding weighting factors used in this multiple objective optimisation problem are determined by the priorities of the global design problem and, in turn, determine the trade-oos that GA search process is willing to accept in the nal design that is generated. Network survivability is considered crucial in …