| | | This thesis proposal aims to explore the use of the Progressive Hedging Algorithm (PHA) in choice-based optimization problems, with a particular focus on the pricing problem. PHA is a decomposition method well-suited to problems where decisions must be consistent across multiple scenarios. It operates by relaxing non-anticipativity constraints and iteratively enforcing them using a penalty mechanism.
The central objective is to assess how PHA performs when applied to pricing problems that incorporate customer choice behavior through discrete choice models. These models introduce nonlinear relationships between product prices and purchase probabilities, making the optimization problem particularly challenging.
The proposed method will be compared with existing approaches, including Lagrangian decomposition, spatial branch-and-Benders decomposition, and an exact breakpoint-based algorithm for park-and-ride pricing instances.
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