Multi-criteria models for healthcare operations need weights that express how stakeholders trade off patient waiting time, provider workload, and operating cost, but these weights are difficult to quantify. Teams of large language model (LLM) agents, each prompted to represent a stakeholder, have been used to supply them. We propose a framework for assessing the reliability of LLM-generated preferences as inputs to multi-objective optimization and quantifying how their uncertainty affects decisions. We study explicit preferences by asking agents to rate the importance of the criteria in an outpatient appointment scheduling problem, and implicit preferences by inferring trade-offs from the agents' pairwise choices between emergency department configurations. The computational experiments show that the explicit preferences respond to the clinic's operating conditions and differ across roles, but deliberation among the agents can erase these differences, whereas simple averaging preserves them. The pairwise choices used to reveal the agents' implicit preferences depend largely on which option is presented first, and we find limited evidence that a statistical model using contextual information alongside presentation order predicts the agents' choices on new comparison pairs better than a model using presentation order alone. We then formulate robust weighted-sum optimization models to account for preference uncertainty. In most cases, these models select different schedules or configurations from those obtained using average preference weights. These results indicate that LLM-generated preferences need an audit of this kind before they are used as optimization weights in healthcare decision support.

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