Balancing supply and demand in free-floating one-way carsharing systems is a critical operational challenge. This paper presents a novel approach that integrates a binary logit model into a mixed integer linear programming framework to optimize short-term pricing and fleet relocation. Demand modeling, based on a binary logit model, aggregates different trips under a unified utility model and improves estimation by incorporating information from similar trips. To speed up the estimation process, a categorizing approach is used, where variables such as location and time are classified into a few categories based on shared attributes. This is particularly beneficial for trips with limited observations as information gained from similar trips can be used for these trips effectively. The modeling framework adopts a dynamic structure where the binary logit model estimates demand using accumulated observations from past iterations at each decision point. This continuous learning environment allows for dynamic improvement in estimation and decision-making. At the core of the framework is a mathematical program that prescribes optimal levels of promotion and relocation. The framework then includes simulated market responses to the decisions, allowing for real-time adjustments to effectively balance supply and demand. Computational experiments demonstrate the effectiveness of the proposed approach and highlight its potential for real-world applications. The continuous learning environment, combining demand modeling and operational decisions, opens avenues for future research in transportation systems.