In this article, a simulation model of a natural gas transport network based on the minimization of its operating costs was developed. For this, a system of equations that determine these costs and the conditions that characterize it are established, to later be transformed into a system that can easily be solved by common linear programming methods. A system of equations and matrices resulting from a transport network of few elements is presented as an example. The model is applied in the simulation of the future operation of the Colombian natural gas transport network to project the cost of its operation, section flows, its associated tariffs, and shortage level. Finally, the conclusions derive possible use applications of this model for the analysis of natural gas transport networks and other energy systems.