Oil exploration: A property of Beale’s model

This paper assumes that an oil company has k areas in which to drill and occurrences of undiscovered oilfields are represented by the model of Beale. The company is seeking a strategy for drilling that maximizes its expected return under the constraint that the total amount spent on drilling in all areas must not exceed R. This leads to an integer programming problem. It establishes that the expected return functions for the separate areas are concave and that this property can be used to reduce the computational effort required to find an optimal solution.