Natalia Kliewer

A time–space network based exact optimization model for multi-depot bus scheduling

Abstract The vehicle scheduling problem, arising in public transport bus companies, addresses the task of assigning buses to cover a given set of timetabled trips with consideration of practical requirements, such as multiple depots and vehicle types as well as depot capacities. An optimal schedule is characterized by minimal fleet size and minimal operational costs including costs for unloaded trips and waiting time. This paper discusses the multi-depot, multi-vehicle-type bus scheduling problem (MDVSP), involving multiple depots for vehicles and different vehicle types for timetabled trips. We use time–space-based instead of connection-based networks for MDVSP modeling. This leads to a crucial size reduction of the corresponding mathematical models compared to well-known connection-based network flow or set partitioning models. The proposed modeling approach enables us to solve real-world problem instances with thousands of scheduled trips by direct application of standard optimization software. To our knowledge, the largest problems that we solved to optimality could not be solved by any existing exact approach. The presented research results have been developed in co-operation with the provider of transportation planning software PTV AG. A software component to support planners in public transport was designed and implemented in context of this co-operation as well.

An overview on vehicle scheduling models

The vehicle scheduling problem, arising in public transport bus companies, addresses the task of assigning buses to cover a given set of timetabled trips with consideration of practical requirements such as multiple depots and vehicle types as well as further extensions. An optimal schedule is characterized by minimal fleet size and/or minimal operational costs. Various publications were released as a result of extensive research in the last decades on this topic. Several modeling approaches as well as specialized solution strategies were presented for the problem and its extensions. This paper discusses the modeling approaches for different kinds of vehicle scheduling problems and gives an up-to-date and comprehensive overview on the basis of a general problem definition. Although we concentrate on the presentation of modeling approaches, also the basic ideas of solution approaches are given.

A Time-Space Network Approach for the Integrated Vehicle-and Crew-Scheduling Problem with Multiple Depots

This paper discusses the integrated vehicle-and crew-scheduling problem in public transit with multiple depots. It is well known that the integration of both planning steps discloses additional flexibility that can lead to gains in efficiency, compared to sequential planning. We present a new modeling approach that is based on a time-space network representation of the underlying vehicle-scheduling problem. The integrated problem is solved with column generation in combination with Lagrangian relaxation. The column generation subproblem is modeled as a resource-constrained shortest-path problem based on a novel time-space network formulation. Feasible solutions are generated by a heuristic branch-and-price method that involves fixing service trips to depots. Numerical results show that our approach outperforms other methods from the literature for well-known test problems.

Solving large multiple-depot multiple-vehicle-type bus scheduling problems in practice

Abstract.We consider the multiple-depot multiple-vehicle-type scheduling problem (MDVSP) which arises in public transport bus companies and aims to assign buses to cover a given set of timetabled trips with consideration of practical requirements, such as multiple depots and vehicle types as well as depot capacities. An optimal schedule is characterized by minimal fleet size and minimal operational costs including costs for empty movements and waiting time. It is well-known that the MDVSP is NP-hard.Although progress has recently been made in solving large practical MDVSP to optimality with time-space network models, current optimization technology sets limits to the model size that can be solved. In order to approach very large practical instances we propose a two-phase method which produces close to optimal solutions. This modeling approach enables us to solve real-world problem instances with thousands of scheduled trips by direct application of standard optimization software. Furthermore, we introduce the concept of depot groups for the case that a bus may return in the evening into another depot than where it started in the morning.

A note on the online nature of the railway delay management problem

Unavoidable disruptions induce the necessity of delay management in timetable-driven passenger rail traffic. Minimizing the negative consequences of delays becomes one of the most relevant challenges for the economic success, as it directly affects the timeliness of passengers, which is a core indicator of customer satisfaction. In this article, we evaluate and compare various delay management strategies in a passenger railway network. A simulator has been implemented to generate delays and perform operations control decisions to resolve connection conflicts induced through passenger connections involving delayed trains. We compare dispatching strategies based on mathematical optimization with simple rule-based strategies. Simulation runs with a timetable from the long-distance passenger traffic of German Railways show that, due to the online nature of this decision problem, a simple waiting time rule strategy can outperform a strategy where the operations are reoptimized online after each disruption.

Design of Customer-oriented Dispatching Support for Railways

Traditionally, dispatching strategies in railways mainly concentrate on maintaining timeliness of trains and ensuring passenger connections. Although customer-orientation is getting more and more important today, little is explicitly known about the effects of various dispatching strategies into customer satisfaction. In this paper, we discuss the design of dispatching support systems for railway passenger traffic from the viewpoint of passenger orientation. We have implemented simulation and optimization based tools and validated them using extensive data from German Rail. We report on three systems: A coarse simulator based on global waiting time rules, a detailed agent-based simulator, and an exact optimization system. The system environment can be used offline, and partially online as well, to test and evaluate dispatching strategies. The focus of the paper is on the system design and its validation for the purposes of railway dispatching. The numerical results are still preliminary and have to be extended in subsequent studies.

Multiple depot vehicle and crew scheduling with time windows for scheduled trips

This paper examines time windows for scheduled trips in multiple depot vehicle and crew scheduling problems that arise in public bus transportation. In practice, the two planning tasks vehicle scheduling and crew scheduling are traditionally solved sequentially with the implicit understanding that the scheduled time for timetabled trips remains fixed. In order to improve cost efficiency two concepts have been developed over the last years: In order to obtain better flexibility when scheduling crews, vehicle and crew scheduling problems are tackled simultaneously. In order to extend flexibility while scheduling vehicles, variable trip departure and arrival times are considered. Obviously the combination of both concepts promises the largest savings, but probably leads to bursting computational times due to growing problem complexity.In this paper we combine both concepts by extending the integrated vehicle and crew scheduling problem with the possibility to shift scheduled trips within defined time windows. We examine the tradeoffs between solution quality and computational time for different solution approaches.

Mathematical models and solution methods for optimal container terminal yard layouts

In this paper, we introduce an integer linear program for planning the layout of container yards. We concentrate on a special layout class of container yards which we call yard layout with transfer lanes. For those layouts typically rubber tired gantry cranes are used for stacking operations and trucks for horizontal transports. We show that the optimization model can be formulated as a special type of a resource constrained shortest path problem for which the LP relaxation always has at least one integer optimal solution. This model is restricted to a rectangular storage yard which allows a linear formulation. For an arbitrary shaped container yard we adopt the model and develop a variable neighborhood descent (VND) heuristic for solving non-rectangular instances. Concerning the rectangular case, we show that the VND heuristic achieves optimal solutions for 38% of the realistic test instances.

Planning Container Terminal Layouts Considering Equipment Types and Storage Block Design

Currently, several container terminals are being expanded, redesigned or newly built. In all those cases the layout of the container terminal has to be designed. We discuss different technologies which can be used for container terminal operation and describe their impact on the terminal layout. Different container terminal layout categories are defined. For a layout which is typical for the use of automated rail-mounted gantry cranes we propose a procedure to calculate promising storage yard configurations. The results show that smaller block widths lead to higher yard performances, but also to higher cost. Using the proposed block design problem, we are able to calculate all non-dominated solutions, which enables terminal planners to choose a solution for their specific situation. Moreover, we analyze the impact of the reefer racks distribution on the yard performance. The results show that an equal distribution of reefer racks over the existing storage blocks allows the best workload distribution.

A Crew Scheduling Approach for Public Transit Enhanced with Aspects from Vehicle Scheduling

This paper presents a new approach for solving the crew scheduling problem in public transit. The approach is based on interaction with the corresponding vehicle scheduling problem. We use a model of the vehicle scheduling problem which is based on a time-space network formulation. An advantage of this procedure is that it produces a bundle of optimal vehicle schedules, implicitly given by the solution flow. In our approach, we give this degree of freedom to the crew scheduling phase, where a vehicle schedule is selected that is most consistent with the objectives of crew scheduling.