Abstract
Building height is of crucial importance in architectural design. In this paper, we provide an integer optimization model to determine the number of stories in high-rise buildings. This model relies on the analysis of profit cash flow over time. The practical insights of our proposal are illustrated through a real-world case study involving a hypothetical development in Punta del Este, Uruguay. A sensitivity analysis of the parameters that exert a more significant impact on the optimal height is studied as well.
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Data Availability
No datasets were generated or analyzed during the current study.
Code Availability
The code is displayed in the Appendix.
Notes
Specifically, this pattern is more pronounced in markets where the credit or mortgage system for purchasing dwellings is not well-developed.
This approach is widely employed in decision analytical studies; for reference, see Clemen and Reilly [18].
We are assuming that the developer is risk neutral, but other preferences for risk could be used in this model (see Egozcue et al. [41]).
For insights into incentives related to this type of restriction and their impact on decision analysis, interested readers are referred to Thanassoulis et al. [42].
It is worth noting that our model offers flexibility, allowing for the consideration of other premium functional forms.
For guidance on creating a tornado diagram and conducting sensitivity analysis, one can refer to the detailed steps outlined by Eschenbach [47].
This approximation arises because we have defined the revenue collection period in months.
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Martin Egozcue wrote the whole work.
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Appendix
Appendix
To facilitate efficient computation of the optimal building height, we present a concise R code for the base-case scenario. This code leverages user-specified model parameters through well-defined functions to determine the number of floors that maximizes the project’s net present value (NPV). The code’s design allows for easy modification of revenue and cost functions and base-case assumptions, enabling users to explore various financial scenarios and their impact on the optimal building height. This facilitates efficient exploration of a range of financial scenarios and their corresponding optimal building. For the sake of simplifying notation in R, “a” replaces \(\nu \), “b” replaces \(\theta \), “e” replaces \(\rho \), “f” replaces \(\gamma \), and “g” replaces \(\delta \).
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Egozcue, M. An Integer Optimization Approach for Determining Building Height. Oper. Res. Forum 5, 56 (2024). https://doi.org/10.1007/s43069-024-00335-7
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DOI: https://doi.org/10.1007/s43069-024-00335-7