arXiv subjects

Marie Schmidt

Publications and source records attributed to Marie Schmidt.

9 recordsLinked to original sources

arXiv2026

The relief distribution problem with trucks and drones under incomplete demand information

Disaster relief operations often take place under uncertainty regarding the extent of damage across locations. In this paper, we study the delivery of relief aid in the aftermath of disasters when delivery vehicles are assisted by surveillance drones and the demand for relief supplies is initially unknown. We introduce a stylized problem that arises in many emergency supply delivery settings -- the relief distribution problem (RDP). In RDP, emergency vehicles, referred to as trucks, must distribute relief supplies on a network, starting from the depot to potential delivery locations, whose demand is initially unknown. The trucks are assisted by surveillance drones, which cannot deliver relief supplies, but scout delivery locations to see whether relief supplies are needed or not. The objective is to visit all location by any vehicle, deliver supplies to all damaged ones, and minimizing the completion time of the relief operation. We study two natural policies for the online problem RDP which we evaluate in two ways: the competitive ratio quantifies the performance in comparison to an optimal solution obtained under full information on damages, the drone-impact is the ratio of the algorithm's performance to the best outcome achievable without drones. Through theoretical analysis and computational experiments, we characterize the operational trade-offs between these policies and derive insights for the effective deployment of drones in disaster response.

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arXiv2026

Solving the Line-Based Dial-a-Ride Problem by Generating Stopping Patterns

In the line-based dial-a-ride problem (liDARP), vehicles operate along a predefined bus line, with the possibility of skipping stations and turning when empty. Motivated by the practical observation that tight passenger time windows often limit pooling in on-demand services, we introduce a new variant of this transportation system by removing all temporal constraints, which we call the liDARP without TWs. We introduce a new MILP formulation for the liDARP without TWs, which constructs feasible tours as sequences of stopping patterns; first, we consider a fundamental single-vehicle, single-pass special case. Based on our insights, we develop a branch-and-price algorithm where the pricing problem generates profitable stopping patterns. For practical applications, we additionally propose a root node heuristic, using the stopping patterns generated at the root node. Computational experiments show that our branch-and-price algorithm is competitive, finding solutions with a MIP gap of less than 5% for large instances in 60 minutes. Further, the root node heuristic scales to instances with up to 100 requests, outperforming the state-of-the-art and reaching optimality gaps of less than 5% within 15 minutes. This method is highly effective in generating solutions for practical applications, where solving large problems quickly is more valuable than reaching optimality.

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arXiv2025

Mobility to Campus -- a Framework to Evaluate and Compare Different Mobility Modes

The transport sector accounts for about 20% of German CO2 emissions, with commuter traffic contributing a significant part. Particularly in rural areas, where public transport is inconvenient to use, private cars are a common choice for commuting and most commuters travel alone in their cars. Consolidation of some of these trips has the potential to decrease CO2 emissions and could be achieved, e.g., by offering ridesharing (commuters with similar origin-destination pairs share a car) or ridepooling (commuters are picked up by shuttle services). In this study, we present a framework to assess the potential of introducing new mobility modes like ridesharing and ridepooling for commuting towards several locations in close vicinity to each other. We test our framework on the case of student mobility to the University of W\"urzburg, a university with several campus locations and a big and rather rural catchment area, where existing public transport options are inconvenient and many students commute by car. We combine data on student home addresses and campus visitation times to create demand scenarios. In our case study, we compare the mobility modes of ridesharing and ridepooling to the base case, where students travel by car on their own. We find that ridesharing has the potential to greatly reduce emissions, depending on the percentage of students willing to use the service and their willingness to walk to the departure location. The benefit of ridepooling is less clear, materializing only if the shuttle vehicles are more energy efficient than the student cars.

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arXiv2025

Visualization of Event Graphs for Train Schedules

Train timetables can be represented as event graphs, where correspond to a train passing through a location at a certain point in time. A visual representation of an event graph is important for many applications such as dispatching and (the development of) dispatching software. A common way to represent event graphs are time-space diagrams. In such a diagram, key locations are visualized on the y-axis and time on the x-axis of a coordinate system. A train's movement is then represented as a connected sequence of line segments in this coordinate system. This visualization allows for an easy detection of infrastructure conflicts and safety distance violations. However, time-space diagrams are usually used only to depict event graphs that are restricted to corridors, where an obvious ordering of the locations exists. In this paper, we consider the visualization of general event graphs in time-space diagrams, where the challenge is to find an ordering of the locations that produces readable drawings. We argue that this means to minimize the number of turns, i.e., the total number of changes in y-direction. To this end, we establish a connection between this problem and Maximum Betweenness. Then we develop a preprocessing strategy to reduce the instance size. We also propose a parameterized algorithm and integer linear programming formulations. We experimentally evaluate the preprocessing strategy and the integer programming formulations on a real-world dataset. Our best algorithm solves every instance in the dataset in less than a second. This suggests that turn-optimal time-space diagrams can be computed in real time.

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arXiv2024

The Complexity of Counting Turns in the Line-Based Dial-a-Ride Problem

Dial-a-Ride problems have been proposed to model the challenge to consolidate passenger transportation requests with a fleet of shared vehicles. The line-based Dial-a-Ride problem (LiDARP) is a variant where the passengers are transported along a fixed sequence of stops, with the option of taking shortcuts. In this paper we consider the LiDARP with the objective function to maximize the number of transported requests. We investigate the complexity of two optimization problems: the LiDARP, and the problem to determine the minimum number of turns needed in an optimal LiDARP solution, called the MinTurn problem. Based on a number of instance parameters and characteristics, we are able to state the boundary between polynomially solvable and NP-hard instances for both problems. Furthermore, we provide parameterized algorithms that are able to solve both the LiDARP and MinTurn problem.

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arXiv2024

The Line-Based Dial-a-Ride Problem

On-demand ridepooling systems offer flexible services pooling multiple passengers into one vehicle, complementing traditional bus services. We propose a transportation system combining the spatial aspects of a fixed sequence of bus stops with the temporal flexibility of ridepooling. In the line-based Dial-a-Ride problem (liDARP), vehicles adhere to a fixed, ordered sequence of stops in their routes, with the possibility of taking shortcuts and turning if they are empty. We propose three MILP formulations for the liDARP with a multi-objective function balancing environmental aspects with customer satisfaction, comparing them on a real-world bus line. Our experiments show that the formulation based on an Event-Based graph is the fastest, solving instances with up to 50 requests in under one second. Compared to the classical DARP, the liDARP is computationally faster, with minimal increases in total distance driven and average ride times.

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arXiv2024

Planning and Optimizing Transit Lines

For all line-based transit systems like bus, metro and tram, the routes of the lines and the frequencies at which they are operated are determining for the operational performance of the system. However, as transit line planning happens early in the planning process, it is not straightforward to predict the effects of line planning decisions on relevant performance indicators. This challenge has in more than 40 years of research on transit line planning let to many different models. In this chapter, we concentrate on models for transit line planning including transit line planning under uncertainty. We pay particular attention to the interplay of passenger routes, frequency and capacity, and specify three different levels of aggregation at which these can be modeled. Transit line planning has been studied in different communities under different names.The problem can be decomposed into the components line generation, line selection, and frequency setting. We include publications that regard one of these individual steps as well as publications that combine two or all of them. We do not restrict to models build with a certain solution approach in mind, but do have a focus on models expressed in the language of mathematical programming.

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arXiv2023

Approaches for Biobjective Integer Linear Robust Optimization

Real-world optimization problems often do not just involve multiple objectives but also uncertain parameters. In this case, the goal is to find Pareto-optimal solutions that are robust, i.e., reasonably good under all possible realizations of the uncertain data. Such solutions have been studied in many papers within the last ten years and are called robust efficient. However, solution methods for finding robust efficient solutions are scarce. In this paper, we develop three algorithms for determining robust efficient solutions to biobjective mixed-integer linear robust optimization problems. To this end, we draw from methods for both multiobjective optimization and robust optimization: dichotomic search for biobjective mixed-integer optimization problems and an optimization-pessimization approach from (single-objective) robust optimization, which iteratively adds scenarios and thereby increases the uncertainty set. We propose two algorithms that combine dichotomic search with the optimization-pessimization method as well as a dichotomic search method for biobjective linear robust optimization that exploits duality. On the way we derive some other results: We extend dichotomic search from biobjective linear problems to biobjective linear minmax problems and generalize the optimization-pessimization method from single-objective to multi-objective robust optimization problems. We implemented and tested the three algorithms on linear and integer linear instances and discuss their respective strengths and weaknesses.

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arXiv2017

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

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 algorithm of Bertsimas and Sim (2003) 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.

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