Optimizing Service Operations via LLM-Powered Multi-Agent Simulation

2026-04-05

AI Summary

This study addresses the challenge of optimizing service system performance in the presence of complex and difficult-to-model participant behavioral responses. The authors propose a large language model–based multi-agent simulation framework (LLM-MAS), which formulates the design problem as a stochastic optimization problem with decision-dependent uncertainty. By leveraging prompt engineering to orchestrate agent interactions, the framework simultaneously performs zeroth-order gradient estimation and updates design parameters within a single simulation trajectory. This approach uniquely integrates LLM-driven multi-agent simulation with steady-state performance optimization, incorporating variance reduction techniques and controlled Markov chain modeling. Empirical evaluations in sustainable supply chain and tournament design scenarios demonstrate substantial improvements over black-box optimization baselines, enabling both efficient evaluation of existing designs and discovery of high-performing configurations overlooked by conventional methods.

Abstract

Service system performance depends on how participants respond to design choices, but modeling these responses is hard due to the complexity of human behavior. We introduce an LLM-powered multi-agent simulation (LLM-MAS) framework for optimizing service operations. We pose the problem as stochastic optimization with decision-dependent uncertainty: design choices are embedded in prompts and shape the distribution of outcomes from interacting LLM-powered agents. By embedding key numerical information in prompts and extracting it from LLM-generated text, we model this uncertainty as a controlled Markov chain. We develop an on-trajectory learning algorithm that, on a single simulation run, simultaneously constructs zeroth-order gradient estimates and updates design parameters to optimize steady-state performance. We also incorporate variance reduction techniques. In a sustainable supply chain application, our method outperforms benchmarks, including blackbox optimization and using LLMs as numerical solvers or as role-playing system designers. A case study on optimal contest design with real behavioral data shows that LLM-MAS is both as a cost-effective evaluator of known designs and an exploratory tool that can uncover strong designs overlooked by traditional approaches.

Problem

• service operations
• human behavior
• decision-dependent uncertainty
• stochastic optimization
• multi-agent simulation

Innovation

• LLM-powered multi-agent simulation
• decision-dependent uncertainty
• zeroth-order optimization
• controlled Markov chain
• on-trajectory learning