arXiv subjects

Robert Klein

Publications and source records attributed to Robert Klein.

4 recordsLinked to original sources

arXiv2026

A global framework to estimate urban spatial cycling patterns based on crowdsourced data

Cycling is a cornerstone of a sustainable mobility transition in cities. Cycling research depends on the data available, but it has been difficult to produce or access these data in comparable ways. Sports tracking platforms like Strava have been transformative in mass-tracking cycling patterns and data sharing through applications and data competitions. Nevertheless, access to data has remained limited. Here, we present a framework that draws on the openly accessible Strava Global Heatmap to estimate spatial patterns of relative cycling intensity on an urban scale. To refine the raw heatmap outputs, we weighted them with population and point of interest (POI) counts within varying buffers. The cycling patterns were validated in a global context, comparing the heatmap values with cycle count data from 29 cities. Both population and POI weighting delivered high correlations in most cases between the heatmap and the cycle counts, POI weighting performing better overall. The strongest associations between Strava heatmap and cycle counts were observed in European cities and along the North American east coast, with p>0.7 for all, and p>0.8 for most cities. Additionally, the performance of our approach improved with higher cycling modal share at the city level. We demonstrate that a POI-weighted Strava heatmap can accurately represent urban cycling patterns and provide estimates of categorical cycling volumes. Our approach can be applied with relatively low effort to support the planning for urban cycling if official counts are sparse. Furthermore, it can enable the use of consistent cycling data for large-scale urban cycling analyses.

physics.soc-ph↗

arXiv2024

From approximation error to optimality gap -- Explaining the performance impact of opportunity cost approximation in integrated demand management and vehicle routing

The widespread adoption of digital distribution channels both enables and forces more and more logistical service providers to manage booking processes actively to maintain competitiveness. As a result, their operational planning is no longer limited to solving vehicle routing problems. Instead, demand management decisions and vehicle routing decisions are optimized integratively with the aim of maximizing revenue and minimizing fulfillment cost. The resulting integrated demand management and vehicle routing problems (i-DMVRPs) can be formulated as Markov decision process models and, theoretically, can be solved via the well-known Bellman equation. Unfortunately, the Bellman equation is intractable for realistic-sized instances. Thus, in the literature, i-DMVRPs are often addressed via decomposition-based solution approaches involving an opportunity cost approximation as a key component. Despite its importance, to the best of our knowledge, there is neither a technique to systematically analyze how the accuracy of the opportunity cost approximation translates into overall solution quality nor are there general guidelines on when to apply which class of approximation approach. In this work, we address this research gap by proposing an explainability technique that quantifies and visualizes the magnitude of approximation errors, their immediate impact, and their relevance in specific regions of the state space. Exploiting reward decomposition, it further yields a characterization of different types of approximation errors. Applying the technique to a generic i-DMVRP in a full-factorial computational study and comparing the results with observations in existing literature, we show that the technique contributes to better explaining algorithmic performance and provides guidance for the algorithm selection and development process.

cs.AI↗

arXiv2024

Dynamic Demand Management for Parcel Lockers

In pursuit of a more sustainable and cost-efficient last mile, parcel lockers have gained a firm foothold in the parcel delivery landscape. To fully exploit their potential and simultaneously ensure customer satisfaction, successful management of the locker's limited capacity is crucial. This is challenging as future delivery requests and pickup times are stochastic from the provider's perspective. In response, we propose to dynamically control whether the locker is presented as an available delivery option to each incoming customer with the goal of maximizing the number of served requests weighted by their priority. Additionally, we take different compartment sizes into account, which entails a second type of decision as parcels scheduled for delivery must be allocated. We formalize the problem as an infinite-horizon sequential decision problem and find that exact methods are intractable due to the curses of dimensionality. In light of this, we develop a solution framework that orchestrates multiple algorithmic techniques rooted in Sequential Decision Analytics and Reinforcement Learning, namely cost function approximation and an offline trained parametric value function approximation together with a truncated online rollout. Our innovative approach to combine these techniques enables us to address the strong interrelations between the two decision types. As a general methodological contribution, we enhance the training of our value function approximation with a modified version of experience replay that enforces structure in the value function. Our computational study shows that our method outperforms a myopic benchmark by 13.7% and an industry-inspired policy by 12.6%.

cs.AI↗

arXiv1994

Mean values of Dedekind sums

For a positive integer k and an arbitrary integer h, the Dedekind sum s(h,k) was first studied by Dedekind because of the prominent role it plays in the transformation theory of the Dedekind eta-function, which is a modular form of weight 1/2 for the full modular group SL_2(Z). There is an extensive literature about the Dedekind sums. Rademacher [8] has written an introductory book on the subject.

math.NT↗