A low carbon multi-modal logistics network optimization: A novel neutrosophic mixed integer linear programming approach

This paper proposes a novel neutrosophic mixed integer linear programming (NMILP) model for designing a multi-period, multi-country, and multi-modal network in an uncertain environment. The uncertainty related to demand, production cost, transportation cost, carbon emission cost, capacity and delive...

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Bibliographic Details
Published in:Journal of environmental management Vol. 387; p. 125924
Main Authors: Kumar, Anurag, Mishra, Shraddha
Format: Journal Article
Language:English
Published: England Elsevier Ltd 01.07.2025
Subjects:
Carbon
Carbon regulation
Global logistics
Models, Theoretical
Multi-modal
Neutrosophic fuzzy
Programming, Linear
Uncertainty
Neutrosophic fuzzy
Global logistics
Multi-modal
Carbon regulation
ISSN:0301-4797, 1095-8630, 1095-8630
Online Access:Get full text
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Summary:This paper proposes a novel neutrosophic mixed integer linear programming (NMILP) model for designing a multi-period, multi-country, and multi-modal network in an uncertain environment. The uncertainty related to demand, production cost, transportation cost, carbon emission cost, capacity and delivery time is handled with triangular neutrosophic numbers. The proposed NMILP provides joint decision-making on several issues, including facility location, production allocation, the number of carrier trips required and transportation mode selection. The NMILP model aims to balance carbon emissions, delivery delays and overall network cost. We proposed a novel approach focusing on the concept of α,δ,andγ cuts (variation parameters for truth, indeterminacy, and falsity membership functions). This transformation changes the initial NMILP into a comparable interval mixed-integer linear programming model. This method allows for meaningful analysis and interpretation of results, providing best-case and worst-case optimal solutions. A key advantage of this approach lies in its flexibility, enabling decision-makers to experiment and adjust the required acceptance, indeterminacy, and falsity levels while analysing results. The proposed NMILP is validated using a representative case of a reasonable size. •The model integrates facility location, production planning, inventory management, and multi-modal distribution.•The model determines shipment frequency for each transportation mode to enhance supply chain efficiency.•Carbon emissions from production, storage, and transportation are regulated using the cap-and-trade mechanism.•The model balances total cost, delivery delays, and carbon emissions under a multi-period uncertain environment.•A neutrosophic programming approach is employed to address uncertainty and ensure supply chain resilience.
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ISSN:0301-4797
1095-8630
1095-8630
DOI:10.1016/j.jenvman.2025.125924