Marie Schmidt

Delay Management Including Capacities of Stations

The question of delay management is whether passenger trains should wait for delayed feeder trains or should depart on time. Solutions to this problem strongly depend on the available capacity of the railway infrastructure. Although the limited capacity of the tracks has been considered in delay management models, the limited capacity of the stations has been neglected so far. In this paper, we develop a model for the delay management problem that includes the capacities of the stations. This model allows rescheduling the platform track assignment. Furthermore, we propose an iterative heuristic in which we first solve the delay management model with a fixed platform track assignment, and then improve this platform track assignment in each step. We show that the latter problem can be solved in polynomial time by describing it as a minimum cost flow model. Finally, we present an extension of the model that balances the delay of the passengers on one hand and the number of changes in the platform track assignment on the other. All models are evaluated on real-world instances from Netherlands Railways.

The price of robustness in timetable information

In timetable information in public transport the goal is to search for a good passengers path between an origin and a destination. Usually, the travel time and the number of transfers shall be minimized. In this paper, we consider robust timetable information, i.e. we want to identify a path which will bring the passenger to the planned destination even in the case of delays. The classic notion of strict robustness leads to the problem of identifying those changing activities which will never break in any of the expected delay scenarios. We show that this is in general a strongly NP-hard problem. Therefore, we propose a conservative heuristic which identifies a large subset of these robust changing activities in polynomial time by dynamic programming and so allows us to find strictly robust paths efficiently. We also transfer the notion of light robustness, originally introduced for timetabling, to timetable information. In computational experiments we then study the price of strict and light robustness: How much longer is the travel time of a robust path than of a shortest one according to the published schedule? Based on the schedule of high-speed trains within Germany of 2011, we quantitatively explore the trade-off between the level of guaranteed robustness and the increase in travel time. Strict robustness turns out to be too conservative, while light robustness is promising: a modest level of guarantees is achievable at a reasonable price for the majority of passengers.

Timetabling with passenger routing

Customer-oriented optimization of public transport needs data about the passengers in order to obtain realistic models. Current models take passengers’ data into account by using the following two-phase approach: In a first phase, routes for the passengers are determined. In a second phase, the actual planning of lines, timetables, etc., takes place using the knowledge on which routes passengers want to travel from the results of the first phase. However, the actual route a passenger will take strongly depends on the timetable, which is not yet known in the first phase. Hence, the two-phase approach finds non-optimal solutions in many cases. In this paper we study the integrated problem of determining a timetable and the passengers’ routes simultaneously. We investigate the computational complexity of the problem and present solution approaches which are tested on close-to-real-world data.

Bi-objective robust optimisation

It is important, in practice, to find robust solutions to optimisation problems. This issue has been the subject of extensive research focusing on single-objective problems. Recently, researchers also acknowledged the need to find robust solutions to multi-objective problems and presented some first results on this topic. In this paper, we deal with bi-objective optimisation problems in which only one objective function is uncertain. The contribution of our paper is three-fold. Firstly, we introduce and analyse four different robustness concepts for bi-objective optimisation problems with one uncertain objective function, and we propose an approach for defining a meaningful robust Pareto front for these types of problems. Secondly, we develop an algorithm for computing robust solutions with respect to these four concepts for the case of discrete optimisation problems. This algorithm works for finite and for polyhedral uncertainty sets using a transformation to a multi-objective (deterministic) optimisation problem and the recently published concept of Pareto robust optimal solutions (Iancu & Trichakis, 2014). Finally, we apply our algorithm to two real-world examples, namely aircraft route guidance and the shipping of hazardous materials, illustrating the four robustness concepts and their solutions in practical applications.

Optimization Approaches for the Traveling Salesman Problem with Drone

The fast and cost-effcient home delivery of goods ordered online is logistically challenging. Many companies are looking for new ways to cross the last-mile to their customers. One technology-enabled opportunity that recently has received much attention is the use of a drone to support deliveries. An innovative last-mile delivery concept in which a truck collaborates with a drone to make deliveries gives rise to a new variant of the traveling salesman problem (TSP) that we call the TSP with drone. In this paper, we formulate this problem as an MIP model and develop several fast route first-cluster second heuristics based on local search and dynamic programming. We prove worst-case approximation ratios for the heuristics and test their performance by comparing the solutions to the optimal solutions for small instances. In addition, we apply our heuristics to several artificial instances with different characteristics and sizes. Our numerical analysis shows that substantial savings are possible with this concept in comparison to truck-only delivery.

Integrating Routing Decisions in Network Problems

This article gives an overview on some of the results of the author’s PhD thesis [11]. The thesis deals with the problem of integrating passengers’ routing decisions in the optimization process in public transportation problems, in particular the problems of line planning, timetabling and timetabling, where the objective is the minimization of the passengers’ overall travel time. In this article we concentrate on some aspects of integrating routing decisions in the delay management problem.

Recoverable robust timetable information

Timetable information is the process of determining a suitable travel route for a passenger. Due to delays in the original timetable, in practice it often happens that the travel route cannot be used as originally planned. For a passenger being already en route, it would hence be useful to know about alternatives that ensure that his/her destination can be reached. In this work we propose a recoverable robust approach to timetable information; i.e., we aim at finding travel routes that can easily be updated when delays occur during the journey. We present polynomial-time algorithms for this problem and evaluate the performance of the routes obtained this way on schedule data of the German train network of 2013 and simulated delay scenarios.

Integrating Routing Decisions in Public Transportation Problems

This book treats three planning problems arising in public railway transportation planning: line planning, timetabling, and delay management, with the objective to minimize passengers travel time. While many optimization approaches simplify these problems by assuming that passengers route choice is independent of the solution, this book focuses on models which take into account that passengers will adapt their travel route to the implemented planning solution. That is, a planning solution and passengers routes are determined and evaluated simultaneously. This work is technically deep, with insightful finding regarding complexity and algorithmic approaches to public transportation problems with integrated passenger routing. It is intended for researchers in the fields of mathematics, computer science, or operations research, working in the field of public transportation from an optimization standpoint. It is also ideal for students who want to gain intuition and experience in doing complexity proofs and designing polynomial-time algorithms for network problems. The book models line planning, timetabling and delay management as combined design and routing problems on networks. In a complexity analysis, the border between NP-hard and polynomially solvable problems is illustrated. Based on that, the insights gained are used to develop solution approaches for the considered problems. Besides integer programming formulations, a heuristic method iterating planning and routing step is proposed to solve the problems.

Simultaneous optimization of delay management decisions and passenger routes

The task of delay management is to decide whether connecting trains should wait for delayed feeder trains or depart on time in order to minimize the passengers’ delay. To estimate the effect of the wait-depart decisions on the travel times, most delay management models assume that passengers’ routes are predefined. However, in practice, passengers can adapt their routes to the wait-depart decisions and arising changes in the timetable. For this reason, in this paper we assume that passengers’ demand is given in form of pairs of origins and destinations (OD-pairs) and take wait-depart decisions and decisions on passengers’ routes simultaneously.This approach, called delay management with re-routing, was introduced in Dollevoet et al. (Transp. Sci. 46(1):74–89, 2012) and we build our research upon the results obtained there. We show that the delay management problem with re-routing is strongly NP-hard even if there is only one OD-pair. Furthermore, we prove that even if there are only two OD-pairs, the problem cannot be approximated with constant approximation ratio unless P=NP. However, for the case of only one OD-pair we propose a polynomial-time algorithm. We show that our algorithm finds an optimal solution if there is no reasonably short route from origin to destination which requires a passenger to enter the same train twice. Otherwise, the solution found by the algorithm is a 2-approximation of an optimal solution and the estimated travel time is a lower bound on the objective value.

Multi-objective minmax robust combinatorial optimization with cardinality-constrained uncertainty

Abstract In this paper, we develop two approaches to find minmax robust efficient solutions for multi-objective combinatorial optimization problems with cardinality-constrained uncertainty. First, we extend an existing algorithm for the single-objective problem to multi-objective optimization. We propose also an enhancement to accelerate the algorithm, even for the single-objective case, and we develop a faster version for special multi-objective instances. Second, we introduce a deterministic multi-objective problem with sum and bottleneck functions, which provides a superset of the robust efficient solutions. Based on this, we develop a label setting algorithm to solve the multi-objective uncertain shortest path problem. We compare both approaches on instances of the multi-objective uncertain shortest path problem originating from hazardous material transportation.