Heatmap Design for Probabilistic Driver Repositioning in Crowdsourced Delivery

Aliaa Alnaggar (), Fatma Gzara () and James Bookbinder ()
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Aliaa Alnaggar: Mechanical, Industrial, and Mechatronics Engineering Department, Toronto Metropolitan University, Toronto, Ontario M5B 2K3, Canada
Fatma Gzara: Management Science and Engineering Department, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada
James Bookbinder: Management Science and Engineering Department, University of Waterloo, Waterloo, Ontario N2L 3G1, Canada

Transportation Science, 2025, vol. 59, issue 1, 81-103

Abstract: This paper proposes the use of heatmaps as a control lever to manage the probabilistic repositioning of independent drivers in crowdsourced delivery platforms. The platform aims to maximize order fulfillment by dynamically matching drivers and orders and selecting heatmaps that trigger the probabilistic flow of unmatched drivers to balance driver supply and delivery requests across the service region. We develop a Markov decision process (MDP) model to sequentially select matching and heatmap decisions in which the repositioning behavior of drivers is captured by a multinomial logit discrete choice model. Because of the curse of dimensionality and the endogenous uncertainty of driver repositioning, the MDP model is solved using a rolling-horizon stochastic lookahead policy. This policy decomposes matching and heatmap decisions into two optimization problems: a two-stage stochastic programming upper bounding problem for matching decisions and a mixed-integer programming problem for heatmap decisions. We also propose a simple policy for efficiently solving large-scale problems. An extensive computational study on instances derived from the Chicago ride-hailing data set is conducted. Computational experiments demonstrate the value of heatmaps in improving order fulfillment beyond the level achieved by matching alone (up to 25%) and identify conditions that affect the benefit of using heatmaps to guide driver repositioning.

Keywords: crowdsourced delivery; probabilistic repositioning; Markov decision process; approximate dynamic programming; endogenous uncertainty (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:59:y:2025:i:1:p:81-103

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