Delay management including capacities of stations

The question of delay management (DM) is whether trains should wait for delayed feeder trains or should depart on time. Solutions to this problem strongly depend on the capacity constraints of the tracks making sure that no two trains can use the same piece of track at the same time. While these capacity constraints have been included in integer programming formulations for DM, the capacity constraints of the stations (only offering a limited number of platforms) have been neglected so far. This can lead to highly infeasible solutions. In order to overcome this problem we suggest two new formulations for DM both including the stations' capacities. We present numerical results showing that the assignment-based formulation is clearly superior to the packing formulation. We furthermore propose an iterative algorithm in which we improve the platform assignment with respect to the current delays of the trains at each station in each step. We will show that this subproblem asks for coloring the nodes of a graph with a given number of colors while minimizing the weight of the conflicts. We show that the graph to be colored is an interval graph and that the problem can be solved in polynomial time by presenting a totally unimodular IP formulation

Delay Management including Capacities of Stations

The question of delay management is whether trains should wait for delayed feeder trains or should depart on time. Solutions to this problem strongly depend on the available capacity of the railway infrastructure. While the limited capacity of the tracks has been considered in delay management models, the limited capacity of the stations has been neglected so far. In this paper, we develop a model for the delay management problem that includes the stations’ capacities. This model allows to reschedule the platform assignment dynamically. Furthermore, we propose an iterative algorithm in which we first solve the delay management model with a fixed platform assignment and then improve this platform assignment in each step. We show that the latter problem can be solved in polynomial time by presenting a totally unimodular IP formulation. Finally, we present an extension of the model that balances the delay of the passengers on the one hand and the number of changes in the platform assignment on the other. All models are evaluated on real-world instances from Netherlands Railways

Delay Management with Re-Routing of Passengers

The question of delay management is whether trains should wait for a delayed feeder train or should depart on time. In classical delay management models passengers always take their originally planned route. In this paper, we propose a model where re-routing of passengers is incorporated. To describe the problem we represent it as an event-activity network similar to the one used in classical delay management, with some additional events to incorporate origin and destination of the passengers. We present an integer programming formulation of this problem. Furthermore, we discuss the variant in which we assume fixed costs for maintaining connections and we present a polynomial algorithm for the special case of only one origin-destination pair. Finally, computational experiments based on real-world data from Netherlands Railways show that significant improvements can be obtained by taking the re-routing of passengers into account in the model

Min-ordering and max-ordering scalarization methods for multi-objective robust optimization

Several robustness concepts for multi-objective uncertain optimization have been developed during the last years, but not many solution methods. In this paper we introduce two methods to find min–max robust efficient solutions based on scalarizations: the min-ordering and the max-ordering method. We show that all point-based min–max robust weakly efficient solutions can be found with the max-ordering method and that the min-ordering method finds set-based min–max robust weakly efficient solutions, some of which cannot be found with formerly developed scalarization based methods. We then show how the scalarized problems may be approached for multi-objective uncertain combinatorial optimization problems with special uncertainty sets. We develop compact mixed-integer linear programming formulations for multi-objective extensions of bounded uncertainty (also known as budgeted or Γ-uncertainty). For interval uncertainty, we show that the resulting problems reduce to well-known single-objective problems