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Collaborative truck multi-drone pollution routing problem with pickup and delivery under variable truck speeds: a cost minimisation approach.

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Title: Collaborative truck multi-drone pollution routing problem with pickup and delivery under variable truck speeds: a cost minimisation approach.
Authors: Alizadeh, Arash1 (AUTHOR), Srinivas, Sharan1 (AUTHOR) SrinivasSh@missouri.edu, Noble, James1 (AUTHOR), Otto, Alena2 (AUTHOR)
Source: International Journal of Production Research. Jul2026, Vol. 64 Issue 14, p6025-6057. 33p.
Subjects: Drone aircraft delivery, Vehicle routing problem, Energy consumption, Cost control, Delivery of goods, Metaheuristic algorithms, Speed limits
Abstract: Collaborative truck-drone systems offer significant potential for reducing cost and emissions in last-mile logistics. However, prior studies often assume constant truck speeds, oversimplify fuel and drone energy use, and overlook differences between labor- and energy-dominant cost structures. This study introduces the Truck Multi-Drone Pollution Routing Problem with Pickup and Delivery under Variable Truck Speeds (TMD-PRP-PDVS), a generalisation of the PRP that integrates multi-drone coordination, segment-specific truck speed control, and realistic cost modelling. It is the first to unify variable truck speeds and coordinated truck-drone operations within a PRP framework for comparative analysis across distinct cost environments. A mixed-integer programming model is developed to minimise total cost, comprising truck fuel consumption, drone energy usage, and driver labor cost. For larger instances, an Adaptive Large Neighborhood Search heuristic is proposed with an embedded local search procedure that refines truck speeds at the route-segment level in polynomial time. Computational results show that drone deployment reduces total cost by about 40%, while speed optimisation yields an additional 7-11% on average and up to 18% in some cases. Case studies on real-world networks demonstrate applicability across contrasting cost regimes. The findings highlight the joint influence of truck speed regulation, drone deployment, and cost structures. [ABSTRACT FROM AUTHOR]
Copyright of International Journal of Production Research is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Collaborative truck multi-drone pollution routing problem with pickup and delivery under variable truck speeds: a cost minimisation approach.
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Production+Research%22">International Journal of Production Research</searchLink>. Jul2026, Vol. 64 Issue 14, p6025-6057. 33p.
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  Data: <searchLink fieldCode="DE" term="%22Drone+aircraft+delivery%22">Drone aircraft delivery</searchLink><br /><searchLink fieldCode="DE" term="%22Vehicle+routing+problem%22">Vehicle routing problem</searchLink><br /><searchLink fieldCode="DE" term="%22Energy+consumption%22">Energy consumption</searchLink><br /><searchLink fieldCode="DE" term="%22Cost+control%22">Cost control</searchLink><br /><searchLink fieldCode="DE" term="%22Delivery+of+goods%22">Delivery of goods</searchLink><br /><searchLink fieldCode="DE" term="%22Metaheuristic+algorithms%22">Metaheuristic algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Speed+limits%22">Speed limits</searchLink>
– Name: Abstract
  Label: Abstract
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  Data: Collaborative truck-drone systems offer significant potential for reducing cost and emissions in last-mile logistics. However, prior studies often assume constant truck speeds, oversimplify fuel and drone energy use, and overlook differences between labor- and energy-dominant cost structures. This study introduces the Truck Multi-Drone Pollution Routing Problem with Pickup and Delivery under Variable Truck Speeds (TMD-PRP-PDVS), a generalisation of the PRP that integrates multi-drone coordination, segment-specific truck speed control, and realistic cost modelling. It is the first to unify variable truck speeds and coordinated truck-drone operations within a PRP framework for comparative analysis across distinct cost environments. A mixed-integer programming model is developed to minimise total cost, comprising truck fuel consumption, drone energy usage, and driver labor cost. For larger instances, an Adaptive Large Neighborhood Search heuristic is proposed with an embedded local search procedure that refines truck speeds at the route-segment level in polynomial time. Computational results show that drone deployment reduces total cost by about 40%, while speed optimisation yields an additional 7-11% on average and up to 18% in some cases. Case studies on real-world networks demonstrate applicability across contrasting cost regimes. The findings highlight the joint influence of truck speed regulation, drone deployment, and cost structures. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  Data: <i>Copyright of International Journal of Production Research is the property of Taylor & Francis Ltd and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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RecordInfo BibRecord:
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    Identifiers:
      – Type: doi
        Value: 10.1080/00207543.2026.2626537
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      – Code: eng
        Text: English
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        PageCount: 33
        StartPage: 6025
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      – SubjectFull: Drone aircraft delivery
        Type: general
      – SubjectFull: Vehicle routing problem
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      – SubjectFull: Energy consumption
        Type: general
      – SubjectFull: Cost control
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      – SubjectFull: Delivery of goods
        Type: general
      – SubjectFull: Metaheuristic algorithms
        Type: general
      – SubjectFull: Speed limits
        Type: general
    Titles:
      – TitleFull: Collaborative truck multi-drone pollution routing problem with pickup and delivery under variable truck speeds: a cost minimisation approach.
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          Name:
            NameFull: Alizadeh, Arash
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            NameFull: Srinivas, Sharan
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            NameFull: Noble, James
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            NameFull: Otto, Alena
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            – D: 15
              M: 07
              Text: Jul2026
              Type: published
              Y: 2026
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