Determining the vulnerability of urban areas is one of the requirements that must be met before urban development to manage urban growth efficiently. This study aims to assess the vulnerability of urban areas using the data envelopment analysis method. We determined the physical growth of Yazd City in central Iran, utilizing the satellite images of 1976, 1984, 1993, 2006, and 2013. We studied the city’s growth in three districts as well as different directions in different years. Afterwards, this study identified the geomorphological indicators influential on the development of the districts. The CRS(Constant Return to Scale) additive model was designed and proposed to investigate different districts’ vulnerability and identify the areas with the highest and lowest vulnerability degrees. Finally, we introduced the districts with the least vulnerability as a pattern for the sustainable growth of the city. The modelling results show that District 1 in 1976 had the highest vulnerability (Z*0 = 0). Despite having the smallest area (input), this district has the highest unsuitable performance in terms of the geomorphological indicators. The performance of other units was found appropriate. Finally, the Districts 3 and 2 in 2013, with the ranks of 13 and 14, were recognized as the units with the least vulnerability and the highest sustainability, respectively.Therefore, we can recommend it for the sustainable and smart growth of the city to the government.
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