arXiv subjects

Markus Leitner

Publications and source records attributed to Markus Leitner.

9 recordsLinked to original sources

arXiv2026

An exact algorithm for vehicle routing problems with temporal dependency constraints

Temporal dependencies between customer visits, such as synchronization constraints, pose a fundamental challenge in vehicle routing. These dependencies, which arise in applications such as home healthcare routing, aircraft scheduling, and technician routing, introduce inter-route constraints that make the resulting problems significantly harder to solve. We present an exact solution method for vehicle routing problems with temporal dependencies capable of handling all types of temporal dependencies studied in the literature, unlike most existing approaches that target specific subclasses. Our approach is based on a fragment-based formulation in which routes are represented as sequences of a new type of fragment, designed to handle temporal dependency constraints. This formulation is solved via a price-cut-and-enumerate algorithm that computes a lower bound using alternating column-and-row generation, obtains an initial upper bound, and iteratively refines both bounds through fragment enumeration and branch-and-cut, supported by several new classes of valid inequalities. Computational experiments show that our method significantly outperforms state-of-the-art benchmark methods and is able to solve previously intractable instances while covering a wider range of temporal dependencies.

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arXiv2025

Pricing, bundling, and driver behavior in crowdsourced delivery

Challenges in last-mile delivery have encouraged solutions like crowdsourced delivery, in which occasional drivers undertake delivery tasks along their pre-planned trips in exchange for compensation. A key challenge is that drivers' acceptance behavior towards offered tasks is uncertain and influenced by task properties and compensation. The current literature lacks formulations that address this challenge with a joint and exact approach. Hence, we formulate an integrated optimization problem that maximizes total expected cost savings by offering bundles of tasks to occasional drivers. We simultaneously determine the optimal set of bundles, their assignment to drivers, and personalized compensations for each bundle-driver pair while considering bundle- and compensation-dependent acceptance probabilities, captured via generic logistic functions. The vast number of potential bundles, combined with incorporating acceptance probabilities leads to a mixed-integer nonlinear program (MINLP) with exponentially many variables. We address these complexities by exploiting properties of the problem, leading to an exact linearization of the MINLP tackled via a tailored exact column generation algorithm. Our algorithm uses a variant of the elementary shortest path problem with resource constraints that features a non-linear and non-additive objective function as subproblem, for which we develop tailored dominance and pruning strategies. We introduce several heuristic and exact variants, and perform an extensive experiments evaluating the performance and the solution structures. The results demonstrate the efficiency of these algorithms for instances with up to 120 tasks and 60 drivers, and highlight the advantages of integrated decision-making over sequential approaches. The sensitivity analysis indicates that sensitivity to compensation is the most influential factor in shaping the bundle structure.

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arXiv2024

A Two-Step Warm Start Method Used for Solving Large-Scale Stochastic Mixed-Integer Problems

Two-stage stochastic programs become computationally challenging when the number of scenarios representing parameter uncertainties grows. Motivated by this, we propose the TULIP-algorithm ("Two-step warm start method Used for solving Large-scale stochastic mixed-Integer Problems"), a two-step approach for solving two-stage stochastic (mixed) integer linear programs with an exponential number of constraints. In this approach, we first generate a reduced set of representative scenarios and solve the root node of the corresponding integer linear program using a cutting-plane method. The generated constraints are then used to accelerate solving the original problem with the full scenario set in the second phase. We demonstrate the generic effectiveness of TULIP on two benchmark problems: the Stochastic Capacitated Vehicle Routing Problem and the Two-Stage Stochastic Steiner Forest Problem. The results of our extensive numerical experiments show that TULIP yields significant computational gains compared to solving the problem directly with branch-and-cut.

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arXiv2024

Task-splitting in home healthcare routing and scheduling

This paper introduces the concept of task-splitting into home healthcare (HHC) routing and scheduling. It focuses on the design of routes and timetables for caregivers providing services at patients' homes. Task-splitting is the division of a (lengthy) patient visit into separate visits that can be performed by different caregivers at different times. The resulting split parts may have reduced caregiver qualification requirements, relaxed visiting time windows, or a shorter/longer combined duration. However, additional temporal dependencies can arise between them. To incorporate task-splitting decisions into the planning process, we introduce two different mixed integer linear programming formulations, a Miller-Tucker-Zemlin and a time-indexed variant. These formulations aim to minimize operational costs while simultaneously deciding which visits to split and imposing a potentially wide range of temporal dependencies. We also propose pre-processing routines for the time-indexed formulation and two heuristic procedures. These methods are embedded into the branch-and-bound approach as primal and improvement heuristics. The results of our computational study demonstrate the additional computational difficulty introduced by task-splitting possibilities and the associated additional synchronization, and the usefulness of the proposed heuristic procedures. From a planning perspective, our results indicate that integrating task-splitting decisions into the planning process reduces staff requirements, decreases HHC operational costs, and allows caregivers to spend relatively more time on tasks aligned with their qualifications.

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arXiv2023

The role of individual compensation and acceptance decisions in crowdsourced delivery

One of the recent innovations in urban distribution is crowdsourced delivery, where deliveries are made by occasional drivers who wish to utilize their surplus resources (unused transport capacity) by making deliveries in exchange for some compensation. The potential benefits of crowdsourced delivery include reduced delivery costs and increased flexibility (by scaling delivery capacity up and down as needed). The use of occasional drivers poses new challenges because (unlike traditional couriers) neither their availability nor their behavior in accepting delivery offers is certain. The relationship between the compensation offered to occasional drivers and the probability that they will accept a task has been largely neglected in the scientific literature. Therefore, we consider a setting in which compensation-dependent acceptance probabilities are explicitly considered in the process of assigning delivery tasks to occasional drivers. We propose a mixed-integer nonlinear model that minimizes the expected delivery costs while identifying optimal assignments of tasks to a mix of professional and occasional drivers and their compensation. We propose an exact two-stage solution algorithm that allows to decompose compensation and assignment decisions for generic acceptance probability functions and show that the runtime of this algorithm is polynomial under mild conditions. Finally, we also study a more general case of the considered problem setting, show that it is NP-hard and propose an approximate linearization scheme of our mixed-integer nonlinear model. The results of our computational study show clear advantages of our new approach over existing ones. They also indicate that these advantages remain in dynamic settings when tasks and drivers are revealed over time and in which case our method constitutes a fast, yet powerful heuristic.

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arXiv2022

Grasping the Inconspicuous

Transparent objects are common in day-to-day life and hence find many applications that require robot grasping. Many solutions toward object grasping exist for non-transparent objects. However, due to the unique visual properties of transparent objects, standard 3D sensors produce noisy or distorted measurements. Modern approaches tackle this problem by either refining the noisy depth measurements or using some intermediate representation of the depth. Towards this, we study deep learning 6D pose estimation from RGB images only for transparent object grasping. To train and test the suitability of RGB-based object pose estimation, we construct a dataset of RGB-only images with 6D pose annotations. The experiments demonstrate the effectiveness of RGB image space for grasping transparent objects.

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arXiv2021

An Exact Method for Fortification Games

A fortification game (FG) is a three-level, two-player Stackelberg game, also known as defender-attacker-defender game, in which at the uppermost level, the defender selects some assets to be protected from potential malicious attacks. At the middle level, the attacker solves an interdiction game by depreciating unprotected assets, i.e., reducing the values of such assets for the defender, while at the innermost level the defender solves a recourse problem over the surviving or partially damaged assets. Fortification games have applications in various important areas, such as military operations, design of survivable networks, protection of facilities, or power grid protection. In this work, we present an exact solution algorithm for FGs, in which the recourse problems correspond to (possibly NP-hard) combinatorial optimization problems. The algorithm is based on a new generic mixed-integer linear programming reformulation in the natural space of fortification variables. Our new model makes use of fortification cuts that measure the contribution of a given fortification strategy to the objective function value. These cuts are generated on-the-fly by solving separation problems, which correspond to (modified) middle-level interdiction games. We design a branch-and-cut-based solution algorithm based on fortification cuts, their lifted versions, and other speed-up techniques. We present a computational study using the knapsack fortification game and the shortest path fortification game. For the latter one, we include a comparison with a state-of-the-art solution method from the literature. Our algorithm outperforms this method and allows us to solve previously unsolved instances to optimality.

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arXiv2021

An Exact Method for (Constrained) Assortment Optimization Problems with Product Costs

We study the problem of optimizing assortment decisions in the presence of product-specific costs when customers choose according to a multinomial logit model. This problem is NP-hard and approximate solutions methods have been proposed in the literature to obtain both lower and upper bounds in a tractable manner. We propose the first exact solution method for this problem and show that provably optimal assortments of instances with up to one thousand products can be found, on average, in about two tenths of a second. In particular, we propose a bounding procedure based on the approximation method of Feldman and Topaloglu (2015a) to provide tight lower and upper bounds at a fraction of their computing times. We show how these bounds can be used to effectively identify an optimal assortment. We also describe how to adapt our approach to handle cardinality or space/resource capacity constraints on the assortment as well as assortment optimization under a mixed-multinomial logit model. In both cases, our solution method provides significant computational boosts compared to exact methods from the literature.

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arXiv2020

PyraPose: Feature Pyramids for Fast and Accurate Object Pose Estimation under Domain Shift

Object pose estimation enables robots to understand and interact with their environments. Training with synthetic data is necessary in order to adapt to novel situations. Unfortunately, pose estimation under domain shift, i.e., training on synthetic data and testing in the real world, is challenging. Deep learning-based approaches currently perform best when using encoder-decoder networks but typically do not generalize to new scenarios with different scene characteristics. We argue that patch-based approaches, instead of encoder-decoder networks, are more suited for synthetic-to-real transfer because local to global object information is better represented. To that end, we present a novel approach based on a specialized feature pyramid network to compute multi-scale features for creating pose hypotheses on different feature map resolutions in parallel. Our single-shot pose estimation approach is evaluated on multiple standard datasets and outperforms the state of the art by up to 35%. We also perform grasping experiments in the real world to demonstrate the advantage of using synthetic data to generalize to novel environments.

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