  Let an oil and gas field consists of clusters in each of which an investor
can launch at most one project. During the implementation of a particular
project, all characteristics are known, including annual production volumes,
necessary investment volumes, and profit. The total amount of investments that
the investor spends on developing the field during the entire planning period
we know. It is required to determine which projects to implement in each
cluster so that, within the total amount of investments, the profit for the
entire planning period is maximum.
  The problem under consideration is NP-hard. However, it is solved by dynamic
programming with pseudopolynomial time complexity. Nevertheless, in practice,
there are additional constraints that do not allow solving the problem with
acceptable accuracy at a reasonable time. Such restrictions, in particular, are
annual production volumes. In this paper, we considered only the upper
constraints that are dictated by the pipeline capacity. For the investment
optimization problem with such additional restrictions, we obtain qualitative
results, propose an approximate algorithm, and investigate its properties.
Based on the results of a numerical experiment, we conclude that the developed
algorithm builds a solution close (in terms of the objective function) to the
optimal one.
