A new queuing-based mathematical model for hotel capacity planning: a genetic algorithm solution

Document Type : Research Paper


1 PhD Student of Industrial Engineering, Imam Hossein Comprehensive University, Tehran, Iran.

2 Associate Professor of Department of Industrial Engineering, Imam Hossein Compressive University, Tehran, Iran.



This study presents a new mathematical optimization model using queuing theory to determine the hotel capacity in an optimal manner. For this purpose, a Knapsack model based on the queuing theory is proposed. In this regard, after simulating a hotel's reception system with the help of queuing models and using a limited two-dimensional Knapsack model, the capacity and an optimum number of rooms are obtained. Since the proposed model is too complex on large scales, a modified Genetic Algorithm (GA) approach enhanced by Taguchi method is employed to solve the problem. The obtained results indicate that unlike previous studies, the proposed models can be applied to different scenarios.


Main Subjects

[1]    Khalili, S., ZareMehrjerdi, Y., Fallahnezhad, M. S., & Mohammadzade, H. (2014). Hotel location problem using erlang queuing model under uncertainty. International journal of engineering-transactions c: aspects, 27(12), 1879-1887.‏
[2]    Demneh, M. T., Farmani, S., & Mamaliki, R. M. (2011). Investigating current challenges in Shiraz tourism industry in relation to limited residential centers. Journal of urban-regional studies and research, 2(8), 117-132.‏
[3]    Taylor, G. D. (1980). How to match plant with demand: a matrix for marketing. International journal of tourism management, 1(1), 56-60.‏
[4]    Klassen, K. J., & Rohleder, T. R. (2002). Demand and capacity management decisions in services. International journal of operations & production management‏, 22(5), 527-548.
[5]    Getz, D. (1983). Capacity to absorb tourism: Concepts and implications for strategic planning. Annals of tourism research, 10(2), 239-263.‏
[6]    Crandall, R. E., & Markland, R. E. (1996). Demand management‐today's challenge for service industries. Production and operations management, 5(2), 106-120.‏
 [7]   Pullman, M., & Rodgers, S. (2010). Capacity management for hospitality and tourism: A review of current approaches. International journal of hospitality management, 29(1), 177-187.‏
[8]    Khalili, S., & Lotfi, M. M. (2015). The optimal warehouse capacity: A queuing-based fuzzy programming approach. Journal of industrial and systems engineering, 8(2), 1-12.‏
[9]    Rao, A. K., & Rao, M. R. (1998). Solution procedures for sizing of warehouses. European journal of operational research, 108(1), 16-25.‏
[10]  Drake, R. E., & Wallach, M. A. (2019). Assessing the optimal number of psychiatric beds for a region. Administration and policy in mental health and mental health services research, 46(6), 696-700.‏
[11]  Zhu, T., Liao, P., Luo, L., & Ye, H. Q. (2020). Data-Driven models for capacity allocation of inpatient beds in a Chinese public hospital. Computational and mathematical methods in medicine.‏ https://doi.org/10.1155/2020/8740457
[12]  Bachouch, R. B., Guinet, A., & Hajri-Gabouj, S. (2012). An integer linear model for hospital bed planning. International journal of production economics, 140(2), 833-843.‏
[13]  Khalili, S., Ghodoosi, M., & Hasanpour, J. (2018). The optimal number of hospital beds under uncertainty: a costs management approach. Journal of optimization in industrial engineering, 11(2), 129-138.‏
[14]  Mehrolhasani, M. H., Khosravi, S., & Tohidi, M. (2016). Reallocation of shafa hospital beds in kerman using goal programming model. Electronic physician, 8(8), 2733.‏
[15]  e Oliveira, B. R. P., de Vasconcelos, J. A., Almeida, J. F. F., & Pinto, L. R. (2020). A simulation-optimization approach for hospital beds allocation. International journal of medical informatics, 141, 104 -174.‏
 [16] Kokangul, A. (2008). A combination of deterministic and stochastic approaches to optimize bed capacity in a hospital unit. Computer methods and programs in biomedicine, 90(1), 56-65.‏
[17]  Hwang, J., Gao, L., & Jang, W. (2010). Joint demand and capacity management in a restaurant system. European journal of operational research, 207(1), 465-472.‏
[18]  Gu, Z. (2003). Analysis of Las Vegas strip casino hotel capacity: an inventory model for optimization. Tourism management, 24(3), 309-314.‏
[19]  Chen, C. M., & Lin, Y. C. (2013). The influence of uncertain demand on hotel capacity. International journal of hospitality management, 34, 462-465.‏
 [20] Ben-David, N., Teitler-Regev, S., & Tillman, A. (2016). What is the optimal number of hotel rooms: Spain as a case study?  Tourism management57, 84-90. https://doi.org/10.1016/j.tourman.2016.05.016
[21]  Tavor, T., Gonen, L. D., & Spiegel, U. (2019). Optimal pricing and capacity under well-defined and well-known deterministic demand fluctuations. Rev. Eur. Stud., 11, 15. https://doi.org/10.5539/res.v11n2p15
 [22] Zhuang, W., Chen, J., & Fu, X. (2017). Joint dynamic pricing and capacity control for hotels and rentals with advanced demand information. Operations research letters, 45(5), 397-402.‏
[23]  Leisten, M. (2020). Volatility, uncertainty, and hotel capacity.‏ Retrieved from file:///C:/Users/jpour/Downloads/Volatility__Uncertainty__and_Hotel_Capacity.pdf
[24]  Madanoglu, M., & Ozdemir, O. (2016). Is better? The relationship between meeting space capacity and hotel operating performance. Tourism management, 52, 74-81.‏
[25]  Pan, C. M. (2007). Market demand variations, room capacity, and optimal hotel room rates. International journal of hospitality management, 26(3), 748-753.‏
[26]  Brunato, M., & Battiti, R. (2020). Combining intelligent heuristics with simulators in hotel revenue management. Annals of mathematics and artificial intelligence, 88(1-3), 71-90.‏
[27]  Nair, G. K. (2019). Dynamics of pricing and non-pricing strategies, revenue management performance and competitive advantage in hotel industry. International journal of hospitality management, 82, 287-297.‏
[28]  Pimentel, V., Aizezikali, A., & Baker, T. (2019). Hotel revenue management: Benefits of simultaneous overbooking and allocation problem formulation in price optimization. Computers & industrial engineering, 137, 106073.‏
[29]  Fadly, M., Ridwan, A. Y., & Akbar, M. D. (2019). Hotel room price determination based on dynamic pricing model using nonlinear programming method to maximize revenue. 2nd international conference on applied information technology and innovation (icaiti) (pp. 190-196). IEEE.‏ https://doi.org/10.1109/ICAITI48442.2019.8982154
[30]  Vives, A., Jacob, M., & Payeras, M. (2018). Revenue management and price optimization techniques in the hotel sector: A critical literature review. Tourism economics, 24(6), 720-752.‏
 [31] Khataei, M., Farzin, M. R., & Mousavi, A. (2008). Measuring the efficiency of selected hotels in Tehran: A DEA approach.‏ The economic research, 8(2) 1-24.
 [32] D. Feiz, h. taherian, and a. zarei. (2011). Service quality and customer satisfaction in hotel industry (case study: Mashhad hotels). Scientific journal management system, 3 (6), 123-149.
[33]  Gelenbe, E., Pujolle, G., Gelenbe, E., & Pujolle, G. (1998). Introduction to queueing networks (Vol. 2). New York: Wiley.‏
 [34] Magazine, M. J., & Chern, M. S. (1984). A note on approximation schemes for multidimensional knapsack problems. Mathematics of operations research, 9(2), 244-247.‏
[35]  Khoshfetrat, S., & Hosseinzadeh Lotfi, F. (2014). Introducing a nonlinear programming model and using genetic algorithm to rank the alternatives in analytic hierarchy process. Journal of applied research on industrial engineering, 1(1), 12-18.‏
 [36] Mirmohseni, S. M., Nasseri, S. H., & Khaviari, M. H. (2017). A new fuzzy hybrid dynamic programming for scheduling weighted jobs on single machine. Journal of applied research on industrial engineering, 4(2), 97-115.‏
[37]  Fabbri, G., & Greppi, M. (2018). An optimized heat sink for thermo photovoltaic panels. Journal of applied research on industrial engineering, 5(1), 1-9.‏
 [38] Ahmed, S. M., Biswas, T. K., & Nundy, C. K. (2019). An optimization model for aggregate production planning and control: a genetic algorithm approach. International journal of research in industrial engineering, 8(3), 203-224.‏
[39]  Molaei, S., & Cyrus, K. M. (2014). Robust design of maintenance scheduling considering engineering insurance using genetic algorithm. International journal of research in industrial engineering, 3(1), 39-48.‏
[40]  Holland, J. H. (1992). Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. MIT press.‏
[41]  Koza, J. R. (1992). Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence. U.S. Patent No. 5,136,686. Washington, DC: U.S. Patent and Trademark Office.‏ https://ieeexplore.ieee.org/servlet/opac?bknumber=6267401
[42]  Taguchi, G. (1986). Introduction to quality engineering: designing quality into products and processes (No. 658.562 T3).‏ Quality Resources. https://www.amazon.com/Introduction-Quality-Engineering-Designing-Processes/dp/9283310845