Optimal price-controlled demand response with explicit modeling of consumer preference dynamics

This paper describes a new approach to modeling consumers' utility preferences in price-controlled demand systems, such as the demand for mobile service or electric energy. Relaxing the assumption that the consumer group size is infinite and individual utility preferences are static, we explicitly model their dynamics through a non-uniform and time varying probability distribution characterized by a well-defined dynamically changing parameter. This parameter is embedded into a stochastic dynamic programming problem used to solve for the optimal price policy. An analytic characterization of the optimal policy is derived based on the differential cost function which leads to an assisted value iteration approach that reduces computational complexity. Numerical results are provided to verify and elaborate that optimal policies conform to claims established in rigorous analytic investigations.