In this study, we consider the proportion of a rectangular city consisting of buildings which locate on dense lattice points. Each travelling route is supposed to consist of vertical route in building(s) and recti-linear route on the surface of the earth. The study is to find the shapes of the city which minimizes three values : (i) the average; (ii) the variance; (iii) the maximum value, of travelling time of residents. For many-to-many uniform trip pattern and many-to-one uniform trip pattern, the optimal proportions are derived. After deriving the mathematical results, we apply it to evaluate an existing rectangular city, Shibam, famous skyscraper in a desert in Yemen. To our surprise, the proportion of Shibam is almost equal to the optimal solution derived from our mathematical programing model.
