Linearization strategies for energy-aware optimization of single-truck, multiple-drone last-mile delivery systems

The increasing demand for rapid and sustainable parcel delivery has motivated the exploration of innovative logistics systems that integrate drones with traditional ground vehicles. Among these, the single-truck, multiple-drone last-mile delivery configuration has attracted significant attention due...

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Detalles Bibliográficos
Autores: Gordani, Ornela, Kalluci, Eglantina, Xhafa Xhafa, Fatos|||0000-0001-6569-5497
Tipo de recurso: artículo
Fecha de publicación:2026
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/452153
Acceso en línea:https://hdl.handle.net/2117/452153
https://dx.doi.org/10.3390/fi18010045
Access Level:acceso abierto
Palabra clave:Last-mile delivery
Drones
Single truck
Energy consumption
Gurobi solver
Linearization
Logistics
Smart cities
Àrees temàtiques de la UPC::Enginyeria de la telecomunicació
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network_acronym_str ES
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spelling Linearization strategies for energy-aware optimization of single-truck, multiple-drone last-mile delivery systemsGordani, OrnelaKalluci, EglantinaXhafa Xhafa, Fatos|||0000-0001-6569-5497Last-mile deliveryDronesSingle truckEnergy consumptionGurobi solverLinearizationLogisticsSmart citiesÀrees temàtiques de la UPC::Enginyeria de la telecomunicacióThe increasing demand for rapid and sustainable parcel delivery has motivated the exploration of innovative logistics systems that integrate drones with traditional ground vehicles. Among these, the single-truck, multiple-drone last-mile delivery configuration has attracted significant attention due to its potential to reduce both delivery time and environmental impact. However, optimizing such systems remains computationally challenging because of the nonlinear energy consumption behavior of drones, which depends on factors such as payload weight and travel time, among others. This study investigates the energy-aware optimization of truck–drone collaborative delivery systems, with a particular focus on the mathematical formulation as mixed-integer nonlinear problem (MINLP) formulations and linearization of drone energy consumption constraints. Building upon prior models proposed in the literature in the field, we analyze the MINLP computational complexity and introduce alternative linearization strategies that preserve model accuracy while improving performance solvability. The resulting linearized mixed-integer linear problem (MILP) formulations are solved using the PuLP software, a Python library solver, to evaluate the efficacy of linearization on computation time and solution quality across diverse problem instance sizes from a benchmark of instances in the literature. Thus, extensive computational results drawn from a standard dataset benchmark from the literature by running the solver in a cluster infrastructure demonstrated that the designed linearization methods can reduce optimization time of nonlinear solvers to several orders of magnitude without compromising energy estimation accuracy, enabling the model to handle larger problem instances effectively. This performance improvement opens the door to a real-time or near-real-time solution of the problem, allowing the delivery system to dynamically react to operational changes and uncertainties during deliveryPeer ReviewedMultidisciplinary Digital Publishing Institute (MDPI)20262026-01-0120262026-01-30journal articlehttp://purl.org/coar/resource_type/c_6501VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttps://hdl.handle.net/2117/452153https://dx.doi.org/10.3390/fi18010045reponame:UPCommons. Portal del coneixement obert de la UPCinstname:Universitat Politècnica de Catalunya (UPC)Inglésengopen accesshttp://purl.org/coar/access_right/c_abf2http://creativecommons.org/licenses/by/4.0/info:eu-repo/semantics/openAccessoai:upcommons.upc.edu:2117/4521532026-05-27T15:37:01Z
dc.title.none.fl_str_mv Linearization strategies for energy-aware optimization of single-truck, multiple-drone last-mile delivery systems
title Linearization strategies for energy-aware optimization of single-truck, multiple-drone last-mile delivery systems
spellingShingle Linearization strategies for energy-aware optimization of single-truck, multiple-drone last-mile delivery systems
Gordani, Ornela
Last-mile delivery
Drones
Single truck
Energy consumption
Gurobi solver
Linearization
Logistics
Smart cities
Àrees temàtiques de la UPC::Enginyeria de la telecomunicació
title_short Linearization strategies for energy-aware optimization of single-truck, multiple-drone last-mile delivery systems
title_full Linearization strategies for energy-aware optimization of single-truck, multiple-drone last-mile delivery systems
title_fullStr Linearization strategies for energy-aware optimization of single-truck, multiple-drone last-mile delivery systems
title_full_unstemmed Linearization strategies for energy-aware optimization of single-truck, multiple-drone last-mile delivery systems
title_sort Linearization strategies for energy-aware optimization of single-truck, multiple-drone last-mile delivery systems
dc.creator.none.fl_str_mv Gordani, Ornela
Kalluci, Eglantina
Xhafa Xhafa, Fatos|||0000-0001-6569-5497
author Gordani, Ornela
author_facet Gordani, Ornela
Kalluci, Eglantina
Xhafa Xhafa, Fatos|||0000-0001-6569-5497
author_role author
author2 Kalluci, Eglantina
Xhafa Xhafa, Fatos|||0000-0001-6569-5497
author2_role author
author
dc.subject.none.fl_str_mv Last-mile delivery
Drones
Single truck
Energy consumption
Gurobi solver
Linearization
Logistics
Smart cities
Àrees temàtiques de la UPC::Enginyeria de la telecomunicació
topic Last-mile delivery
Drones
Single truck
Energy consumption
Gurobi solver
Linearization
Logistics
Smart cities
Àrees temàtiques de la UPC::Enginyeria de la telecomunicació
description The increasing demand for rapid and sustainable parcel delivery has motivated the exploration of innovative logistics systems that integrate drones with traditional ground vehicles. Among these, the single-truck, multiple-drone last-mile delivery configuration has attracted significant attention due to its potential to reduce both delivery time and environmental impact. However, optimizing such systems remains computationally challenging because of the nonlinear energy consumption behavior of drones, which depends on factors such as payload weight and travel time, among others. This study investigates the energy-aware optimization of truck–drone collaborative delivery systems, with a particular focus on the mathematical formulation as mixed-integer nonlinear problem (MINLP) formulations and linearization of drone energy consumption constraints. Building upon prior models proposed in the literature in the field, we analyze the MINLP computational complexity and introduce alternative linearization strategies that preserve model accuracy while improving performance solvability. The resulting linearized mixed-integer linear problem (MILP) formulations are solved using the PuLP software, a Python library solver, to evaluate the efficacy of linearization on computation time and solution quality across diverse problem instance sizes from a benchmark of instances in the literature. Thus, extensive computational results drawn from a standard dataset benchmark from the literature by running the solver in a cluster infrastructure demonstrated that the designed linearization methods can reduce optimization time of nonlinear solvers to several orders of magnitude without compromising energy estimation accuracy, enabling the model to handle larger problem instances effectively. This performance improvement opens the door to a real-time or near-real-time solution of the problem, allowing the delivery system to dynamically react to operational changes and uncertainties during delivery
publishDate 2026
dc.date.none.fl_str_mv 2026
2026-01-01
2026
2026-01-30
dc.type.none.fl_str_mv journal article
http://purl.org/coar/resource_type/c_6501
VoR
http://purl.org/coar/version/c_970fb48d4fbd8a85
dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
format article
dc.identifier.none.fl_str_mv https://hdl.handle.net/2117/452153
https://dx.doi.org/10.3390/fi18010045
url https://hdl.handle.net/2117/452153
https://dx.doi.org/10.3390/fi18010045
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2

http://creativecommons.org/licenses/by/4.0/
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
http://purl.org/coar/access_right/c_abf2

http://creativecommons.org/licenses/by/4.0/
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute (MDPI)
publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute (MDPI)
dc.source.none.fl_str_mv reponame:UPCommons. Portal del coneixement obert de la UPC
instname:Universitat Politècnica de Catalunya (UPC)
instname_str Universitat Politècnica de Catalunya (UPC)
reponame_str UPCommons. Portal del coneixement obert de la UPC
collection UPCommons. Portal del coneixement obert de la UPC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.81155

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