Leena Suhl

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.

Computing Sparse LU Factorizations for Large-Scale Linear Programming Bases

This paper discusses the computation of LU factorizations for large sparse matrices with emphasis on large-scale linear programming bases. We present new implementation techniques which reduce the computation times significantly. Numerical experiments with large-scale real life test problems were conducted. The software is compared with the basis factorization of MPSX/370, IBMs commercial LP system. INFORMS Journal on Computing , ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

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 partially integrated airline crew scheduling approach with time-dependent crew capacities and multiple home bases

Abstract Crew scheduling for airlines requires an optimally scheduled coverage of flights with regard to given timetables. We consider the crew scheduling and assignment process for airlines, where crew members are stationed unevenly among home bases. In addition, their availability changes dynamically during the planning period due to pre-scheduled activities, such as office and simulator duties, vacancy, or requested off-duty days. We propose a partially integrated approach based on two tightly coupled components: the first constructs chains of crew pairings spaced by weekly rests, where crew capacities at different domiciles and time-dependent availabilities are considered. The second component rearranges parts of these pairing chains into individual crew schedules with, e.g., even distribution of flight time. Computational results with real-life data from an European airline are presented.

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.

Aggregate production planning in the automotive industry with special consideration of workforce flexibility

We present a new mixed integer linear programming approach for the problem of aggregate production planning of flowshop production lines in the automotive industry. Our model integrates production capacity planning and workforce flexibility planning. In contrast to traditional approaches, it considers discrete capacity adaptations which originate from technical characteristics of assembly lines as well as from work regulations and shift planning. In particular, our approach takes change costs into account and explicitly represents a working time account via a linear approximation. A solution framework containing different primal heuristics and preprocessing techniques is embedded into a decision support system. Finally, we present an illustrative case study and computational results on problem instances of practically relevant complexity.

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.