Efficient Circulation of Railway Rolling Stock

Abstract

Railway rolling stock is one of the most significant cost sources for operators of passenger trains. The efficient circulation of rolling stock is therefore one of the main objectives pursued in practice. This paper focuses on the determination of appropriate numbers of train units of different types together with their efficient circulation on a single line. In order to utilize the train units on this line in an efficient way, they are coupled to or uncoupled from the trains in certain stations according to the passengers' seat demand in peak hours and off-peak hours. Since coupling and uncoupling train units has to respect specific rules related to the shunting possibilities in the stations, it is important to take into account the order of the train units in the trains. This aspect strongly increases the complexity of the rolling stock circulation problem. This paper presents a solution approach based on an Integer Programming model. The approach is applied to a real life case study based on the timetable of NS Reizigers, the main Dutch operator of passenger trains.

Solving a real-world train-unit assignment problem

“…Besides the (customary) column-generation based procedure to solve the LP relaxation, the heuristic method has three main components: (1) a diving rule to fix the value of some of the variables following the current LP optimal solution, reoptimizing the LP after the addition of these TUAP heur begin initialize the current LP as a reduced version of LP (7)- (11), with (9) replaced by (20), with only a subset of the variables; repeat solve the current LP by a general-purpose LP solver, letting x be the optimal primal solution, (α, β, γ) the optimal dual solution, and z the corresponding value; apply the constructive heuristic procedure based on (α, β, γ); refine the solution found by the constructive heuristic procedure, possibly updating the incumbent solution; if there are dual constraints violated by (α, β, γ) then add some of the corresponding primal variables to the current LP; else fix the value of some of the primal variables by changing the associated bounds; until the current LP is infeasible or z ≥ value of the incumbent solution; end. fixing constraints, (2) a simple constructive heuristic procedure based on the current dual LP solution that is applied at each iteration of the column-generation based procedure, and (3) a refinement procedure that is applied to improve each solution produced by the constructive heuristic procedure in (2). The general structure of the method is outlined in Fig.…”

“…There are a few references that consider the assignment of TUs: [1,2,15,23,25]. Most of them consider the case in which there is a very small number of distinct TU types (two in most cases).…”

“…In [1], Abbink et al present an ILP formulation with the objective of minimizing the seat shortages during the rush hours. Alfieri et al [2] propose an ILP model for the case of multiple TU types, aimed at satisfying the seat requests while minimizing the travel distance. The problem is solved by decomposition into subproblems.…”

Improving robustness of rolling stock circulations in rapid transit networks

“…Alfieri et al [1] propose an integer programming model so as to determine the RS circulation for multiple RS material types on a single line and on a single day; they use the concept of a transition graph to deal with the RS circulations; this concept is based on the assumption that for each trip, the next trip is known a priori. The objective is to minimize the number of train units such that the given passenger demand is satisfied.…”

“…The approach is tested on real-life examples from Nederlandse Spoorwegen (NS), the main operator of passenger trains in the Netherlands. The model described by Alfieri et al [1] is extended by Fioole et al [16], to include combining and splitting trains, as happens at several locations in the Dutch timetable. They use an extended set of variables to locally obtain an improved description of the convex hull of the integer solutions.…”