Benefit-cost problems: A bi-criteria approach

In environmental systems planning, benefit-cost ratio and net benefit maximization are widely used as project evaluation criteria. The linear benefit-cost functions lead to a linear fractional program in the case of benefit-cost ratio maximization, and to a linear program in the case of net benefit maximization. In general, the optimal solutions of these problems are different. Usually two different problems need be solved for the optima. This paper presents a bi-criteria maximization approach wherein both the optima can be found by solving a single parametric linear program. An extension for nonlinear benefit-cost functions over a convex set is also provided. The procedure provides the decision maker with additional insights in terms of efficient solutions. Also, a condition for the optimal solutions of the benefit-cost ratio and net benefit problems to be the same is derived. The methodology is illustrated by an example of agricultural decision making.