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arXiv · 2507.03634

Pricing, bundling, and driver behavior in crowdsourced delivery

Alim Buğra Çınar·Claudia Archetti·Wout Dullaert·Markus Leitner·Stefan Waldherr
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Abstract

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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Alim Buğra Çınar, Claudia Archetti, Wout Dullaert, Markus Leitner, Stefan Waldherr. 2025-07-04. Pricing, bundling, and driver behavior in crowdsourced delivery. https://arxiv.org/abs/2507.03634

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