A machine learning optimization approach for last-mile delivery and third-party logistics

Aug 5, 2026

Third-party logistics supports efficient delivery by letting firms buy carrier services rather than operate costly vehicle fleets, yet carrier capacity must be reserved in advance under demand uncertainty. The problem is formulated as variable cost and size bin packing with stochastic items, representing two-stage tactical capacity planning and operational recourse. Because exact solvers fail on realistic instances, a machine-learning-based heuristic is proposed and tested numerically. Experiments show strong solution quality in short run times and improved performance versus an efficient progressive hedging variant, with managerial takeaways from a Turin parcel-delivery case study.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages15

Reading Time38 min

AccessFree to download

Introduction

Problem formulation and methodology

Variable cost and size bin packing with stochastic items

Two-stage tactical and operational phases

Proposed machine-learning heuristic

Numerical experiments and comparisons

Progressive hedging benchmark

Managerial insights

POLITECNICO DI TORINO Repository ISTITUZIONALE A machine learning optimization approach for last-mile delivery and third-party logistics Original A machine learning optimization approach for last-mile delivery and third-party logistics / Bruni, MARIA ELENA; Fadda, Edoardo; Fedorov, Stanislav; Perboli, Guido. -In: COMPUTERS & OPERATIONS RESEARCH. -ISSN 0305-0548. -STAMPA. -157:(2023), pp. 1-14. [10 . 1016/j.cor.2023. 106262] Availability: This version is available at: 11583/2978470 since: 2023-05-12T14:15:09Z Publisher: Elsevier Published DOI:10.1016/j.cor.2023.106262 Terms of use: This article is made available under terms and conditions as specified in the corresponding bibliographic description in the repository Publisher copyright (Article begins on next page) 11 February 2024 Computers & Operations Research 157 (2023) 106262 | A machine learning optimization approach for last-mile delivery and third-party logistics
Maria Elena Brunia, Edoardo Faddab,∗, Stanislav Fedorov c, Guido Perbolid,ea DIMEG, University of Calabria, Rende, Italy
b DISMA, Politecnico di Torino, Torino, Italy
c DAUIN & CARS@Polito, Politecnico di Torino, Turin, Italy d DIGEP & CARS@Polito, Politecnico di Torino, Turin, Italy e Arisk S.p.A., Milan, Italy | | | | | --- | --- | --- | --- | | A R T I C L E I N F O | | A B S T R A C T | | | Keywords: Metaheuristics Machine learning
Variable cost and size bin packing
Third-party logistics Last-mile delivery Capacity planning | | Third-party logistics is now an essential component of efficient delivery systems, enabling companies to purchase carrier services instead of an expensive fleet of vehicles. However, carrier contracts have to be booked in advance without exact knowledge of what orders will be available for dispatch. The model describing this problem is the variable cost and size bin packing problem with stochastic items. Since it cannot be solved for realistic instances by means of exact solvers, in this paper, we present a new heuristic algorithm able to do so based on machine learning techniques. Several numerical experiments show that the proposed heuristics achieve good performance in a short computational time, thus enabling its real-world usage. Moreover, the comparison against a new and efficient version of progressive hedging proves that the proposed heuristic achieves better results. Finally, we present managerial insights for a case study on parcel delivery in Turin, Italy. | | 1. Introduction The growth of the urban population and rising living standards have led to a dramatic increase in the demand for services and goods. These conditions have paved the way to a competitive environment where companies fight for market share by continuously providing flexibility in delivering options while maintaining high resource efficiency. Consequently, the entire last-mile delivery sector is impacted, making it the most challenging in the entire logistic chain (Perboli et al., 2021a; Sergi et al., 2021). Several management solutions have been developed to achieve the desired efficiency level and hedge against the risks coming from realworld uncertainty. The most important is third-party logistics (3PL), which is an organization’s use of third-party businesses to outsource elements on the distribution, warehousing, and/or fulfillment services side (Perboli et al., 2017b). The adoption of 3PL translates into the advantage of reducing fleet investment while maintaining the same quality of service. This work focuses on the usage of 3PL for logistic tasks, i.e., we consider a company booking containers from a thirdparty logistic company to deliver goods. A practical example of such a decision is when service providers secure long-term distance contracts with the carriers (Crainic et al., 2016). In this context, the primary ∗ Corresponding author. E-mail address: edoardo.fadda@polito.it (E. Fadda). decision is related to the volume of bins to b

FAQs

What optimization problem is addressed in the paper?

The paper models capacity reservation for third-party logistics as the variable cost and size bin packing problem with stochastic items.

Why are heuristic methods needed instead of exact solvers?

Exact solvers cannot handle realistic problem instances within acceptable time, so heuristics are required.

How does the proposed approach perform compared with progressive hedging?

Numerical experiments indicate the proposed machine-learning-based heuristic achieves better results than an efficient progressive hedging version while keeping short computational times.

Aug 5, 2026

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