Maximum Principle in a Problem of Maximization of the Income for Model of a Gas Deposit (Continued)

This article is devoted to the study of the maximization of the accumulated income for the model of the gas deposit on a finite horizon, a detailed analysis of the obtained results and their comparison with the results of the previously posted this same problem on an infinite horizon. So far the same tasks, based on a model with interacting wells, were solved at a constant price for gas. In reality, however, the price for the goods quite often has a nonlinear dependence and depends on the volume of purchases. Therefore, the statement of the problem is modified by the inclusion in its description of the procurement function. A major tool in the search for the solution to the maximization of income on a finite horizon is the Pontryagin’s maximum principle under the condition of its existence. There are two areas, separated from each other parametric dependence. On each of the selected areas with the use of the method of “phase diagram” the optimal solution is being found. The optimal solution of the problem of maximization on a finite horizon is explicitly described. Joint analysis of the obtained solutions in the problems of maximization on finite and infinite horizon revealed that under certain conditions a part of wells is used inefficiently. Several ways to solve this problem are recommended.

maximum principle, model of gas deposits, finite horizon, infinite horizon, procurement function, maximum accumulated income, phase diagram