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A logistics ratio-optimised inventory routing problem with lateral transhipment using mixed-integer robust fractional programming.

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Title: A logistics ratio-optimised inventory routing problem with lateral transhipment using mixed-integer robust fractional programming.
Authors: Xingyu, Man1 (AUTHOR) manxingyu@outlook.com, Daofang, Chang2 (AUTHOR), Peng, Zheng2 (AUTHOR), Wanke, Han3 (AUTHOR)
Source: International Journal of Production Research. Dec2025, Vol. 63 Issue 24, p10381-10412. 32p.
Subjects: Logistics, Fractional programming, Economic uncertainty, Scarcity, Optimization algorithms, Cross-docking (Logistics), Inventory control, Mixed integer linear programming
Abstract: This study addresses a single-period multi-product inventory routing problem (IRP) considering reactive lateral transhipment with the optimisation objective of logistics ratio, defined as logistics cost per unit of product value. The problem is modelled in two stages: in the first stage, the distribution is planned based on imperfect forecasted demand. In the second stage, actual demand is revealed, and reactive lateral transhipment is executed based on first-stage decisions. We develop a basic fractional programming (BFP) model with deterministic demand for both stages. Considering demand uncertainty, we extend a robust fractional programming (RFP) model and a two-stage robust fractional programming (TSRFP) model for first-stage IRP and propose structural uncertainty sets. We apply Dinkelbach's algorithm and the robust counterpart transformation to tackle the RFP model. We employ the column and constraint generation algorithm to address the TSRFP model with Dinkelbach's algorithm. The results indicate that the proposed TSRFP is suits scenarios with high stockout penalties and at medium demand uncertainty levels. Managers can select between TSRFP, RFP, and BFP to optimise inventory management based on demand uncertainty and product attributes. [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: A logistics ratio-optimised inventory routing problem with lateral transhipment using mixed-integer robust fractional programming.
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  Data: <searchLink fieldCode="JN" term="%22International+Journal+of+Production+Research%22">International Journal of Production Research</searchLink>. Dec2025, Vol. 63 Issue 24, p10381-10412. 32p.
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  Data: <searchLink fieldCode="DE" term="%22Logistics%22">Logistics</searchLink><br /><searchLink fieldCode="DE" term="%22Fractional+programming%22">Fractional programming</searchLink><br /><searchLink fieldCode="DE" term="%22Economic+uncertainty%22">Economic uncertainty</searchLink><br /><searchLink fieldCode="DE" term="%22Scarcity%22">Scarcity</searchLink><br /><searchLink fieldCode="DE" term="%22Optimization+algorithms%22">Optimization algorithms</searchLink><br /><searchLink fieldCode="DE" term="%22Cross-docking+%28Logistics%29%22">Cross-docking (Logistics)</searchLink><br /><searchLink fieldCode="DE" term="%22Inventory+control%22">Inventory control</searchLink><br /><searchLink fieldCode="DE" term="%22Mixed+integer+linear+programming%22">Mixed integer linear programming</searchLink>
– Name: Abstract
  Label: Abstract
  Group: Ab
  Data: This study addresses a single-period multi-product inventory routing problem (IRP) considering reactive lateral transhipment with the optimisation objective of logistics ratio, defined as logistics cost per unit of product value. The problem is modelled in two stages: in the first stage, the distribution is planned based on imperfect forecasted demand. In the second stage, actual demand is revealed, and reactive lateral transhipment is executed based on first-stage decisions. We develop a basic fractional programming (BFP) model with deterministic demand for both stages. Considering demand uncertainty, we extend a robust fractional programming (RFP) model and a two-stage robust fractional programming (TSRFP) model for first-stage IRP and propose structural uncertainty sets. We apply Dinkelbach's algorithm and the robust counterpart transformation to tackle the RFP model. We employ the column and constraint generation algorithm to address the TSRFP model with Dinkelbach's algorithm. The results indicate that the proposed TSRFP is suits scenarios with high stockout penalties and at medium demand uncertainty levels. Managers can select between TSRFP, RFP, and BFP to optimise inventory management based on demand uncertainty and product attributes. [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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        Value: 10.1080/00207543.2025.2551240
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      – Code: eng
        Text: English
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      – SubjectFull: Logistics
        Type: general
      – SubjectFull: Fractional programming
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      – SubjectFull: Economic uncertainty
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      – SubjectFull: Scarcity
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      – SubjectFull: Optimization algorithms
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      – SubjectFull: Cross-docking (Logistics)
        Type: general
      – SubjectFull: Inventory control
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      – SubjectFull: Mixed integer linear programming
        Type: general
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      – TitleFull: A logistics ratio-optimised inventory routing problem with lateral transhipment using mixed-integer robust fractional programming.
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            NameFull: Xingyu, Man
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            NameFull: Daofang, Chang
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            NameFull: Peng, Zheng
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              Text: Dec2025
              Type: published
              Y: 2025
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