Tags: Contrasting EssaySports Studies Gcse CourseworkResearch On Bermuda TriangleAn Unforgettable Event In My Life EssaySociology Term Paper ThesisExcel Template For Business PlanEssay On Hitler'S Rise To PowerEnglish Comp 2 EssaysMaths Homework IdeasPositive Ambition Essay
Finally, we report extensive computational results on a railway corridor in which the sectors possess the basic feature of railway networks.
Peeters and Kroon  focused on the efficient circulation of train units within a certain scope of railway line given the timetable and the passengers’ seat demand and a branch-and-price algorithm is described.  present a solution approach based on an integer multicommodity flow model to determine the appropriate numbers of train units of different types together with their efficient circulation on a single line.  present two integer linear programming (ILP) formulations together with their relaxations (the linear programming (LP) relaxation and Lagrangian based approach, resp.) to assign the train units to the trips with minimum cost.
When the high-speed railway system is running, many disturbances can occur and that would lead to the irregularities of the operations of the train units.
In order to avoid such events to some extent, it is reasonable to find a plan that is insensitive to these disruptions; that is, the plan is able to cope with relatively small disruptions without structural changes, which is also known as the robustness scheduling, or to react immediately to those disruptions by applying a recovery strategy to the plan defined previously, which is also known as the rescheduling process (see, e.g., [8–10]).
Cadarso and Marín  formulate a multicommodity flow model for the rolling stock problem in rapid transit networks.
Due to the complexity, the lower bound is computed through a polynomial approximation algorithm which is a modification from the one solving the degree constraint minimum 1-tree problem.
Then, a branching strategy is designed to cope with the maintenance constraints.
Empty movements and shunting operations are considered and the robustness is introduced by selectively avoiding empty train movements and these operations.
Cadarso and Marín  presents a model to study the robust determining of the best sequence for each rolling stock in the train network.
Locomotives are often scheduled on a fixed sector and could be viewed as an assignment problem which could be solved by Hungarian algorithm.  formulated the locomotive-scheduling problem as a multicommodity flow problem with side constraints on a weekly space-time network.
Each locomotive type defines a commodity in the network.