Modeling Contexts in Trade-off Total Cost and Customer Satisfaction VRP via Large Language Models

The Vehicle Routing Problem (VRP) is among the most extensively studied combinatorial optimization problems in operations research. As a critical variant, the Sustainable Vehicle Routing Problem (SVRP) integrates multidimensional cost considerations, including environmental, economic, and social dimensions. When modeling optimization problems, it is crucial to acknowledge that decision-making does not take place in a vacuum or in isolation from reality. Currently, systematic a priori and a posteriori modeling methods based on fuzzy propositions provide conditions for embedding contextual constraints into mathematical models, yet manual construction of such models remains challenging. To address this, this study proposes an automatic modeling method based on large language model (LLM), designs a dedicated prompt template to embed the context constraints, and realizes the output of complete code from natural language input, and meanwhile extends the a priori modeling method to the constrained multi-objective optimization framework to construct a Bi-objective SVRP centered on both customer satisfaction and total cost based on the original SVRP. Experiments are conducted under the sustainability and fairness contexts of decision-makers, drivers, and customers, with ten generation tests performed on four different LLMs, achieving a maximum solvability rate of 0.9 for a single instance; after transferring the optimal results to four data instances, most results still maintain solvability, with true values ranging from near 0 to fully meeting the threshold requirements, and supplementary experiments also analyze differences in parameters, operational costs, and algorithms. Finally, multiple experiments validate the effectiveness of the proposed method and simultaneously reveal the discrepancies introduced by different LLMs and algorithms.