Dynamic optimization of tourism resource utilization: An optimal control model for balancing economic growth and environmental conservation
Published: September 16, 2026
Abstract
This study develops an intertemporal optimal control model for tourism resource exploitation, with resource quality as the state variable and visitor volume and conservation investment intensity as control variables. Applying the Pontryagin maximum principle, the study establishes a modified golden rule for tourism destinations, proves saddle-point stability of the steady state, and derives the optimal environmental charge as the product of the degradation coefficient and the resource shadow price. Numerical simulations show that the optimal resource level is 40.14% above the maximum sustainable yield level, with 16.11% fewer visitors but 69.57% higher net benefits. Open access eliminates the destination’s entire present value while attracting 11.69% fewer visitors. Conservation investment equal to 7.74% of revenue raises resource quality by 20.6%, visitor volume by 30.5%, and present value by 35.0%.
Keywords
optimal controltourism resourcessustainable developmentPontryagin maximum principleenvironmental charge
References
1.
Thủ tướng Chính phủ. (2020). Quyết định số 147/QĐ-TTg ngày 22/01/2020 phê duyệt Chiến lược phát triển du lịch Việt Nam đến năm 2030.
2.
Butler, R. W. (1980). The concept of a tourist area cycle of evolution: Implications for management of resources. Canadian Geographer, 24(1), 5-12.
3.
Casagrandi, R., & Rinaldi, S. (2002). A theoretical approach to tourism sustainability. Conservation Ecology, 6(1), 13.
4.
Cerina, F. (2007). Tourism specialization and environmental sustainability in a dynamic economy. Tourism Economics, 13(4), 553-582.
5.
Clark, C. W. (1990). Mathematical bioeconomics: The optimal management of renewable resources (2nd ed.). John Wiley & Sons.
6.
Coccossis, H., & Mexa, A. (2004). The challenge of tourism carrying capacity assessment: Theory and practice. Ashgate.
7.
Conrad, J. M. (2010). Resource economics (2nd ed.). Cambridge University Press.
8.
Dasgupta, P., & Heal, G. M. (1979). Economic theory and exhaustible resources. Cambridge University Press.
9.
Gordon, H. S. (1954). The economic theory of a common-property resource: The fishery. Journal of Political Economy, 62(2), 124-142.
10.
Hardin, G. (1968). The tragedy of the commons. Science, 162(3859), 1243-1248.
11.
Johnston, R. J., & Tyrrell, T. J. (2005). A dynamic model of sustainable tourism. Journal of Travel Research, 44(2), 124-134.
12.
Lozano, J., Gómez, C. M., & Rey-Maquieira, J. (2008). The TALC hypothesis and economic growth theory. Tourism Economics, 14(4), 727-749.
13.
Mananyi, A. (1998). Optimal management of ecotourism. Tourism Economics, 4(2), 147-169.
14.
Marsiglio, S. (2015). Economic growth and environment: Tourism as a trigger for green growth. Tourism Economics, 21(1), 183-204.
15.
Marsiglio, S. (2017). On the carrying capacity and the optimal number of visitors in tourism destinations. Tourism Economics, 23(3), 632-646.
16.
O’Reilly, A. M. (1986). Tourism carrying capacity: Concept and issues. Tourism Management, 7(4), 254-258.
17.
Palmer, T., & Riera, A. (2003). Tourism and environmental taxes, with special reference to the “Balearic ecotax”. Tourism Management, 24(6), 665-674.
18.
Piga, C. A. G. (2003). Pigouvian taxation in tourism. Environmental and Resource Economics, 26(3), 343-359.
19.
Pintassilgo, P., & Silva, J. A. (2007). “Tragedy of the commons” in the tourism accommodation industry. Tourism Economics, 13(2), 209-224.
20.
Pontryagin, L. S., Boltyanskii, V. G., Gamkrelidze, R. V., & Mishchenko, E. F. (1962). The mathematical theory of optimal processes. Interscience Publishers.
21.
Quốc hội. (2017). Luật số 09/2017/QH14: Luật Du lịch, ban hành ngày 19/6/2017.
22.
Schubert, S. F. (2010). Coping with externalities in tourism: A dynamic optimal taxation approach. Tourism Economics, 16(2), 321-343.
23.
Seierstad, A., & Sydsæter, K. (1987). Optimal control theory with economic applications. North-Holland.
