A Fast Heuristic Algorithm for the Train Unit Assignment Problem

In this paper we study a railway optimization problem known as the Train Unit Assignment Problem. A train unit consists of a self-contained train with an engine and a set of wagons with passenger seats. Given a set of timetabled train trips, each with a required number of passenger seats, and a set of train units, each with a given number of available seats, the problem calls for the best assignment of the train units to the trips, possibly combining more than one train unit for a given trip, that fulfills the seat requests. We propose a heuristic algorithm based on the computation of a lower bound obtained by solving an Integer Linear Programming model that gives the optimal solution in a "peak period" of the day. The performance of the heuristic algorithm is computationally evaluated on real-world instances provided by a regional Italian Train Operator. The results are compared with those of existing methods from the literature, showing that the new method is able to obtain solutions of good quality in much shorter computing times

Almost 20 Years of Combinatorial Optimization for Railway Planning: from Lagrangian Relaxation to Column Generation

We summarize our experience in solving combinatorial optimization problems arising in railway planning, illustrating all of these problems as integer multicommodity flow ones and discussing the main features of the mathematical programming models that were successfully used in the 1990s and in recent years to solve them

A branch-and-price approach for solving the train unit scheduling problem

We propose a branch-and-price approach for solving the integer multicommodity flow model for the network-level train unit scheduling problem (TUSP). Given a train operator’s fixed timetable and a fleet of train units of different types, the TUSP aims at determining an assignment plan such that each train trip in the timetable is appropriately covered by a single or coupled train units. The TUSP is challenging due to its complex nature. Our branch-and-price approach includes a branching system with multiple branching rules for satisfying real-world requirements that are difficult to realize by linear constraints, such as unit type coupling compatibility relations and locations banned for coupling/decoupling. The approach also benefits from an adaptive node selection method, a column inheritance strategy and a feature of estimated upper bounds with node reservation functions. The branch-and-price solver designed for TUSP is capable of handling instances of up to about 500 train trips. Computational experiments were conducted based on real-world problem instances from First ScotRail. The results are satisfied by rail practitioners and are generally competitive or better than the manual ones

Optimising halting station of passenger railway lines

In many real life passenger railway networks, the types of stations and lines characterisethe halting stations of the train lines. Common types are Regional, Interregional or Intercity.This paper considers the problem of altering the halts of lines by both upgrading and downgrading stations, such that this results in less total travel time. We propose a combination of reduction methods, Lagrangian relaxation, and a problem-specific multiplier adjustment algorithm to solve the presented mixed integer linear programming formulation. A computational study of several real-life instances based on problem data of the Dutch passenger railway operator NS Reizigers is included.mathematical economics and econometrics ;

Railway Crew Rescheduling with Retiming

Railway operations are disrupted frequently, e.g. the Dutch railway network experiences about three large disruptions per day on average. In such a disrupted situation railway operators need to quickly adjust their resource schedules. Nowadays, the timetable, the rolling stock and the crew schedule are recovered in a sequential way. In this paper, we model and solve the crew rescheduling problem with retiming. This problem extends the crew rescheduling problem by the possibility to delay the departure of some trains. In this way we partly integrate timetable adjustment and crew rescheduling. The algorithm is based on column generation techniques combined with Lagrangian heuristics. In order to prevent a large increase in computational time, retiming is allowed only for a limited number of trains where it seems very promising. Computational experiments with real-life disruption data show that, compared to the classical approach, it is possible to find better solutions by using crew rescheduling with retiming.

A new approach to crew scheduling in rapid transit networks

We propose a new approach for the crew scheduling problem in rapid transit networks. With this approach we try to open a new branch for future research, providing a different way of facing the crew scheduling problem which makes integration with other planning problems easier than the traditional approach based on column generation for solving a set covering/partitioning problem. For solving this new model we develop a Lagrangian relaxation and we take advantage of an ad hoc decomposition based on time personnel clustering. We present some preliminary computational experiments for real case studies drawn from the main Spanish train operator, RENFE

A Lagrangian heuristic for a real-life integrated planning problem of railway transportation resources

International audienceRailway planning requires three scarce and heterogeneous resources: train paths (infrastructure), rolling stock and train drivers. In the current industrial approach at SNCF (French National Railway Company), these resources are essentially planned through a sequential approach which typically starts from (1) train paths and goes further on to (2) rolling stock and finally (3) train drivers. SNCF has already developed optimization tools for Steps (2) and (3). In this paper, we built upon the work previously presented at IAROR-RAILROME 2011. We presented a mixed integer linear programming model with coupling constraints for a simplified integrated problem of railway production resources. We also proposed a Lagrangian relaxation heuristic. In this approach, sub-problems were solved thanks to a standard mathematical programming solver. First numerical experiments were conducted on a reduced data set, extracted from an actual instance from a French region (Bretagne). The results obtained were promising but showed that the resolution with a standard solver was too costly in terms of computational times for real-world instances and that the model had to be improved for implementation in a Lagrangian relaxation framework. Since 2011, the mathematical model has been improved and numerous operational constraints have been integrated in order to tackle real-life integrated planning problems at SNCF. The Lagrangian relaxation heuristic has been updated consequently. As already mentioned, SNCF has already developed two independent optimization tools for planning rolling stock and train drivers. The Lagrangian approach has also been adapted so that the resulting sub-problems of this mathematical decomposition method can now be solved with the two dedicated tools. We thus can now address real-life instances and solve each sub-problem of the specific Lagrangian heuristic with proprietary software. Preliminary computational results show the interest of our method. Compared to a sequential approach, the Lagrangian heuristic leads to substantial cost reductions and generates good solutions in a reasonable CPU time. This is thus an interesting tool for human planners who want to experiment and quantitatively evaluate different scenarios (e.g. other train-path distribution, specific rolling stock, train drivers with other capabilities...)

Operations research in passenger railway transportation

In this paper, we give an overview of state-of-the-art OperationsResearch models and techniques used in passenger railwaytransportation. For each planning phase (strategic, tactical andoperational), we describe the planning problems arising there anddiscuss some models and algorithms to solve them. We do not onlyconsider classical, well-known topics such as timetabling, rollingstock scheduling and crew scheduling, but we also discuss somerecently developed topics as shunting and reliability oftimetables.Finally, we focus on several practical aspects for each of theseproblems at the largest Dutch railway operator, NS Reizigers.passenger railway transportation;operation research;planning problems

Routing in Point-to-Point Delivery Systems

This paper was also printed as a Working Paper at the Yale School of Organization and Management, Series B, No. 103.We develop an optimization-based approach for a point-to-point route planning problem that arises in many large scale delivery systems(for example, less-than-truckload freight, rail, mail and package delivery, communications). In these settings, a firm which must ship goods between many origin and destination pairs on a network needs to specify a route for each origin-destination pair so as to minimize transportation costs and/or transit times. Typically, the cost structure is very complicated. The approach discussed in this paper exploits the structure of the problem to decompose it into two smaller subproblems, each amenable to solution by a combination of optimization and heuristic techniques. One subproblem is an 'assignment' problem with capacity constraints. The other subproblem is a mixed-integer multicommodity flow problem. We propose solution methods based on Lagrangian relaxation for each subproblem. Computational results with these methods and with a heuristic procedure for the multicommodity flow problem on a problem met in practice are encouraging and suggest that mathematical programming methods can be successfully applied to large-scale problems in delivery systems planning and other problems in logistical system design

Crew Scheduling for Netherlands Railways: "destination: customer"

: In this paper we describe the use of a set covering model with additional constraints for scheduling train drivers and conductors for the Dutch railway operator NS Reizigers. The schedules were generated according to new rules originating from the project "Destination: Customer" ("Bestemming: Klant" in Dutch). This project is carried out by NS Reizigers in order to increase the quality and the punctuality of its train services. With respect to the scheduling of drivers and conductors, this project involves the generation of efficient and acceptable duties with a high robustness against the transfer of delays of trains. A key issue for the acceptability of the duties is the included amount of variation per duty. The applied set covering model is solved by dynamic column generation techniques, Lagrangean relaxation and powerful heuristics. The model and the solution techniques are part of the TURNI system, which is currently used by NS Reizigers for carrying out several analyses concerning the required capacities of the depots. The latter are strongly influenced by the new rules.crew scheduling;dynamic column generation;lagrange relaxation;railways;set covering model