arXiv subjects

Stefan Waldherr

Publications and source records attributed to Stefan Waldherr.

4 recordsLinked to original sources

arXiv2026

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.

math.OC↗

arXiv2024

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.

math.OC↗

arXiv2021

The Customer is Always Right: Customer-Centered Pooling for Ride-Hailing Systems

Today's ride-hailing systems experienced significant growth and ride-pooling promises to allow for efficient and sustainable on-demand transportation. However, efficient ride-pooling requires a large pool of participating customers. To increase the customers' willingness for participation, we study a novel customer-centered pooling (CCP) mechanism, accounting for individual customers' pooling benefits. We study the benefit of this mechanism from a customer, fleet operator, and system perspective, and compare it to existing provider-centered pooling (PCP) mechanisms. We prove that it is individually rational and weakly dominant for a customer to participate in CCP, but not for PCP. We substantiate this analysis with complementary numerical studies, implementing a simulation environment based on real-world data that allows us to assess both mechanisms' benefit. To this end, we present results for both pooling mechanisms and show that pooling can benefit all stakeholders in on-demand transportation. Moreover, we analyze in which cases a CCP mechanism Pareto dominates a PCP mechanism and show that a mobility service operator would prefer CCP mechanisms over PCP mechanisms for all price segments. Simultaneously, CCP mechanisms reduce the overall distance driven in the system up to 32% compared to not pooling customers. Our results provide decision support for mobility service operators that want to implement and improve pooling mechanisms as they allow us to analyze the impact of a CCP and a PCP mechanism from a holistic perspective. Among others, we show that CCP mechanisms can lead to a win-win situation for operators and customers while simultaneously improving system performance and reducing emissions.

eess.SY↗

arXiv2018

Competitive Equilibria in Combinatorial Exchanges with Financially Constrained Buyers:Computational Hardness and Algorithmic Solutions

Advances in computational optimization allow for the organization of large combinatorial markets. We aim for allocations and competitive equilibrium prices, i.e. outcomes that are in the core. The research is motivated by the design of environmental markets, but similar problems appear in energy and logistics markets or in the allocation of airport time slots. Budget constraints are an important concern in many of these markets. While the allocation problem in combinatorial exchanges is already NP-hard with payoff- maximizing bidders, we find that the allocation and pricing problem becomes even $Σ_2^p$-hard if buyers are financially constrained. We introduce mixed integer bilevel linear programs (MIBLP) to compute core prices, and propose pricing functions based on the least core if the core is empty. We also discuss restricted but simpler cases and effective computational techniques for the problem. In numerical experiments we show that in spite of the computational hardness of these problems, we can hope to solve practical problem sizes, in particular if we restrict the size of the coalitions considered in the core computations.

cs.GT↗