Optimal Control for Dynamic Pricing and Advertising of Ticket Selling for the Sport and Entertainment Events

Document Type : Original Article


1 Professor, Tehran University.

2 Associate professor, Shahid Beheshti university.

3 Associate professor, Tehran university.

4 PHD student, Kish campus of Tehran university.


This article is the result of a research project in dynamic pricing and advertising to determine the number of sale tickets for a sporting or an entertainment event. For this purpose, a dynamic optimal control model was used to maximize the organizer's profit. To provide the best estimate, all potential variables and costs in ticket sales were considered. These included free ticket transfers, food and beverage sales, promotional goods, insurance, and other services (e.g., customer service) to ticket buyers. Using a piecewise continuous function (arrival intensity) we applied variables that are not controlled by organizers (e.g., impacts of seasonal change on demand) to determine the number of tickets for sale (capacity planning) and their dynamic and optimal price, considering the dynamic optimal advertising costs. Among the strengths of this study is the application of two piecewise continuous functions to analyze the effect of unsold tickets numbers on customers’ purchasing behavior. The impacts of such factors have not been studied in previous studies.


Main Subjects

  1. Adeli, M. & Zandieh, M. (2013). submit the multi-objective simulation optimization approach for the integrated sourcing model and inventory decisions. Journal of Industrial Management Perspective, 11(3), 89-110. (In Persian)
  2. Asgharizadeh, A. Mohaghar, A. & Taghavi, N (2015). Designing a model for probable mutibjective planning for optimal capacity of electricity energy. Journal of Industrial Management Perspective, 22(1), 67-90. (In Persian).
  3. Blondet, G. Le Duigou, J. & Boudaoud, N. (2019). A KBS for numerical design of experiments processes in mechanical engineering. Expert system with application, 122, 289-302.
  4. Blourian Tehrani, M. (2014). Pricing in simple words. Tehran, Corporate of commercial publishing. (In Persian)
  5. Feng, Y., & Gallego, G. (1995). Optimal starting times for end-of-season sales and optimal stopping times for promotional fares. Management Sciences, 41 (8), 1371–1391.
  6. Gallego, G., & van Ryzin, G., (1994). Optimal dynamic pricing of inventories with stochastic demand over finite horizons. Management Sciences, 40(8), 999–1020
  7. Helmes, K., Schlosser, R. & Weber, M. (2013). Dynamic advertising and pricing in a class of general new-product adoption models. European Journal of Operational Research, 229(2) 433-443.
  8. Intriligator, M, D. (2008). Mathematical optimization, and economic theory. (translated by Pourkazemi M.H.) Tehran. Publication of Shahid Beheshti. (In Persian).
  9. Jørgensen, S., Kort, P.M., & Zaccour, G. (2009). Optimal pricing and advertising policies for an entertainment event. Journal of Economic Dynamics and Control. 33(3), 583–596.
  10. Jørgensen, S., & Zaccour, G. (2019). Optimal pricing and advertising policies for a one-time entertainment event. Journal of Economic Dynamics and Control100, 395-416
  11. Klima, I. (1995). The Spirit of Prague (Deyhimi, kh). Tehran, publication of Ney. (In Persian).
  12. Kuper, S. (2006) Soccer against the enemy. (Translated by Ferdosipour, A). Tehran, Nashre Cheshmeh. (In Persian)
  13. Laudon, K. (2013). E-Commerce Marketing. (Arbab, H, R). Tehran. Publication of Ney. (In Persian).
  14. Pourkazemi, M, H. (2015). Dynamic Optimization, Optimal Control and its applications. Publication of Shahid Beheshti. (In Persian).
  15. Rajan, A., Rakesh and Steinberg, R. (1992). Dynamic pricing and ordering decisions by a monopolist. Management Sciences 38(2), 240–262.
  16. Sethi, S. P., Prasad, A. & He, X. (2008). Optimal advertising and pricing in a new-product adoption model. Journal of Optimization Theory and Applications 139(2), 351–360.
  17. Schlosser, R. (2015). A stochastic dynamic pricing and advertising model under risk aversion. Journal of Revenue Pricing Management, 14(6), 451–468.
  18. Schlosser, R. (2016), Joint Stochastic Dynamic Pricing and Advertising with Time-Dependent Demand. Journal of Economic Dynamics and Control, 73, Pages 439-452
  19. Taleizadeh, A., & Mohammadi, R. (2015). Optimization of sale price and advertising cost in a two-level supply chain includes one manufacturer and two retailers. Journal of Industrial Management Perspective, 18(2), 107-127. (In Persian).
  20. Weber, M. (2015). Optimal Inventory Control in the Presence of Dynamic Pricing and Dynamic Advertising, DISSERTATION, Humboldt-University, Germany.