An uncertain programming model for fixed charge transportation problem with item sampling rates

This paper analyzes the transportation issue involving multiple objectives and items with fixed costs amid uncertainty, which aims to increase net profit while minimizing carbon emissions, to determine an optimal product shipping strategy. This paper introduces the use of uncertain theory to address the transportation dilemma, considering various challenges such as potential uncertainties during the actual transport process. It involves defining variables such as supply, demand and the rate of product sampling qualification as uncertain factors, constructing mathematical models, and deriving the corresponding model as well as the respective equivalent form by means of uncertainty theory. A linear weighted method is adopted to reflect the significance of each objective as identified by policymakers and suggest a sparrow optimization algorithm combined with butterfly search for numerical experiments to discover the optimal solution. This demonstrates the practicality and effectiveness of the proposed models.