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A critical factor in the success of decision support systems is the accuratemodeling of user preferences. Psychology research has demonstrated that usersoften develop their preferences during the elicitation process, highlightingthe pivotal role of system-user interaction in developing personalized systems.This paper introduces a novel approach, combining Large Language Models (LLMs)with Constraint Programming to facilitate interactive decision support. Westudy this hybrid framework through the lens of meeting scheduling, atime-consuming daily activity faced by a multitude of information workers. Weconduct three studies to evaluate the novel framework, including a diary study(n=64) to characterize contextual scheduling preferences, a quantitativeevaluation of the system's performance, and a user study (n=10) with aprototype system. Our work highlights the potential for a hybrid LLM andoptimization approach for iterative preference elicitation and designconsiderations for building systems that support human-system collaborativedecision-making processes.

"I Want It That Way": Enabling Interactive Decision Support Using Large Language Models and Constraint Programming