Enumerative algorithms for choice-based pricing under capacity constraints

The choice-based pricing problem (CPP) consists in optimizing product prices while accounting for consumer preferences and potential capacity constraints. Demand is typically modeled using a discrete choice model (DCM). We introduce the Breakpoint Heuristic Algorithm (BHA) to address the CPP with and without capacity constraints as well as an extension of the Breakpoint Exact Algorithm (BEA) to handle capacities, together with valid inequalities for the QCQP-L (quadratically constrained quadratic program with linear objective) formulation of the uncapacitated CPP, allowing us to speed up the exact Branch the ILS matches all known optima, and the BHA maintains an average gap below 0.03%. • Breakpoint Heuristic Algorithm (BHA) solves choice-based pricing problems with and without capacity. • BHA and ILS deliver near-optimal solutions drastically faster than exact meth- ods for large-scale CPP. • BHA can be used to guide exact Branch and Bound methods together with valid inequalities. • BHA outperforms CMA-ES in computational time and solution quality for choice-based pricing. • Mixed-logit pricing problems solved faster with BHA and ILS than with spe- cialized methods.