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 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 $\alpha ,\delta ,\text{and}\gamma$ 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.