A Bilevel Approach for Compensation and Routing Decisions in Last-Mile Delivery

Martina Cerulli (), Claudia Archetti (), Elena Fernández () and Ivana Ljubić ()
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Martina Cerulli: Department of Computer Science, University of Salerno, 84084 Fisciano, Italy
Claudia Archetti: Department of Information Systems, Decision Sciences and Statistics, ESSEC Business School, 95021 Cergy Pontoise, France
Elena Fernández: Department of Statistics and Operational Research, Universidad de Cádiz, 11510 Puerto Real, Spain
Ivana Ljubić: Department of Information Systems, Decision Sciences and Statistics, ESSEC Business School, 95021 Cergy Pontoise, France

Transportation Science, 2024, vol. 58, issue 5, 1076-1100

Abstract: In last-mile delivery logistics, peer-to-peer logistic platforms play an important role in connecting senders, customers, and independent carriers to fulfill delivery requests. As the carriers are not under the platform’s control, the platform has to anticipate their reactions while deciding how to allocate the delivery operations. Indeed, carriers’ decisions largely affect the platform’s revenue. In this paper, we model this problem using bilevel programming. At the upper level, the platform decides how to assign the orders to the carriers; at the lower level, each carrier solves a profitable tour problem to determine which offered requests to accept, based on her own profit maximization. Possibly, the platform can influence carriers’ decisions by determining also the compensation paid for each accepted request. The two considered settings result in two different formulations: the bilevel profitable tour problem with fixed compensation margins and with margin decisions, respectively. For each of them, we propose single-level reformulations and alternative formulations where the lower-level routing variables are projected out. A branch-and-cut algorithm is proposed to solve the bilevel models, with a tailored warm-start heuristic used to speed up the solution process. Extensive computational tests are performed to compare the proposed formulations and analyze solution characteristics.

Keywords: bilevel programming; profitable tour problem; last-mile delivery; peer-to-peer transportation platforms (search for similar items in EconPapers)
Date: 2024
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Persistent link: https://EconPapers.repec.org/RePEc:inm:ortrsc:v:58:y:2024:i:5:p:1076-1100

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