Event ticket pricing with capacity constraints and price restrictions
研究了在需求相互依赖、容量约束和价格限制下，如何为多类门票定价以最大化收益，并分析了产品差异化对定价策略的影响。
Motivated by ticket pricing challenges facing live event managers, we study how to maximize revenue when setting prices for multiple ticket categories with interdependent demand, realistic capacity constraints, and pricing restrictions. We define this decision problem as the Event Ticket Pricing (ETP) problem and formulate it as a constrained nonlinear optimization model. To examine how the nature of product differentiation (i.e., differentiation across ticket categories) affects seat portfolio pricing and revenue outcomes, we analyze the ETP problem under two demand specifications: vertically and horizontally differentiated ticket categories. For each case, we isolate the role of different constraints by developing and solving a sequence of problems with progressively added restrictions. This approach enables us to identify structural properties that either fully characterize the optimal solution or guide the development of efficient algorithms. Under vertical differentiation, we prove that the optimal solution has a sold-out threshold structure , with only high-quality categories sold out. The treatment of partially sold products depends on the active constraints. Sales vanish under capacity constraints alone but become positive once pricing restrictions are introduced, producing solutions distinct from the unconstrained benchmark. Under horizontal differentiation, the threshold structure persists, but the addition of constraints breaks the well-known “equal markup” rule, yielding prices that are non-increasing in quality. Finally, we study how flexible adjustments in seat capacities reshape optimal outcomes. These results underscore the importance of incorporating realistic constraints and offer practical guidance for live event planners.