THE STUDY OF OPTIMAL STRATEGY FOR SELLING TICKETS FOR A SPORTING EVENT

摘要

How to sell tickets optimally for a sporting event is a challenging problem in sports management. At Claflin University, we have regular sport events on campus. In our sport management, the goals are to maximize the income from selling tickets, and to attract more people to attend the sporting event, but we may not be able to realize these two goals at the same level. We are able to affect the tickets sale by increasing or decreasing its price. Furthermore, we have several constraints, like the capacity of a gymnasium or stadium, the acceptable price of tickets to sellers and buyers, etc. Based on the properties of this problem, the optimal control model will be adopted to help design selling strategy for some sport event. The typical solution method for optimal control model is based on solving Pontryagin Maximum Principle. Because of its nonlinearity, we analyze the Principle for our model, and develop a numerical algorithm to solve it. And at last, based on the numerical results, applicable strategy for selling tickets has been given.