MODEL FORMATION PLANS FOR THE DEVELOPMENT OF URBAN AREAS

We consider the problem of optimal (at a cost) development of the area, taking into account the restrictions on the required area of residential premises, and on the area of the land plot allocated for the construction of residential buildings. The problem of optimal development of the area was considered for the case of linear dependence of the construction cost on the number of houses of each type. The results are summarized for the case of concave dependencies of construction costs on the number of houses of each type. We consider such special cases when the amount of living space for all houses is equal or the area required for building a house is also equal for all houses. Initially, an algorithm for solving the problem for the continuous case is considered. In this variant, it is proved that the optimal solution to the problem will be a solution in which from the number of projects included in the production program for only one project the number of houses may be less than the maximum allowed, chosen for reasons of architectural diversity. The conditions are determined when the results of this statement will be valid for the integer solution. To solve the problem, the use of the branch and bound method is proposed. The main difficulty in implementing this scheme is the need to obtain lower bounds for the problem being solved. For this purpose, it is proposed to use the procedure of convexing cost functions directed to the execution of the intended production program.

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