Market static model for software development based on a transport problem with quadratic cost additions

Abstract

The authors propose to formulate a market continuous static model for software development based on the transport problem with quadratic cost additions. In contrast to the existing transport problem with fixed cost surcharges, the authors propose a statement that minimizes the sum of transportation costs, which may contain non-fixed additions proportional to the squares of the volumes of appointments. Thus, a quadratic formulation of the transport problem with non-fixed additions is proposed. It is shown that transport problem with quadratic additions can be reduced to a convex programming problem, which can be solved numerically by the subgradient method, or by the conjugate gradient method for the dual problem. The authors describe the interpretation of transport problem with quadratic additions as an assignment problem with non-fixed price discounts, taking into account the difference between the wholesale and retail prices. This makes possible to apply the set task to build digital platforms in the software development market for loading assignments to performers.