【公开学术报告】Event Ticket Pricing With Capacity Constraints And Price Restrictions

Event ticket pricing with capacity constraints and price restrictions

Guest Speaker:            Yunke LI (University of Miami)

Date & Time:               9:30-11:00, Thur. 24th, Nov. 2022

Zoom Meeting:            85379990146（Password: 144970）

Click the Link:             https://us02web.zoom.us/j/85379990146

ABSTRACT

We study a ticket pricing problem facing managers of live events. Managers must maximize revenues by simultaneously determining prices for multiple categories of tickets (because their demands are interdependent) while incorporating contextual restrictions on capacity and prices. Focusing on the context of a single live event, we define the managers decision problem and refer to it as the Event Ticket Pricing (ETP) Problem and formulate it as a constrained non-linear optimization problem. Different from existing literature and recognizing the importance of incorporating key practical considerations, the ETP problem incorporates constraints based on capacity considerations and pricing restrictions. The ETP problem model is robust and can embed many demand functions. To better understand the impact of the nature of product differentiation on this revenue optimization, we solved the ETP problem considering two types of demand, stemming from vertically and horizontally-dlifferentiated ticket categories. To isolate the impact of individual constraints, for each case, we apply convex optimization techniques to investigate a series of optimization problems com-structed by progressively adding constraint classes. When the products are vertically-differentiated, we prove that the optimal solution has a sold-out threshold structure, in which only products with quality higher than a certain threshold are sold out. Extending the logic of the unconstrained optimal solution, we find that the not-sold-out products will have zero demand with capacity constraint only, but can generate positive sales when including price restrictions. When the products are horizontally-differentiated, the sold-out, threshold structure remains optimal. Importantly, this structure is in contrast to the well-known “equal markup” result that applies in the unconstrained context, confirming the importance of incorporating practically relevant considerations. With constraints, rather than an equal markup, we find that the prices are non-increasing in their quality. Finally, to understand the value of flexibility in seat capacities, we show how the optimal sales, prices, and revenue are affected when possible flexible changes are made to the ticket categories offered in the collection. Among other applications, our results can provide useful insights for live entertainment promotion planners to optimize the ticket pricing decision facing capacity constraints and price restrictions.

Key words: live entertainment events; multi-product pricing; vertical and horizontal product differentiation; constrained optimization