POTENTIAL PITFALLS IN RENEWABLE RESOURCE DECISION MAKING THAT UTILIZES CONVEX COMBINATIONS OF DISCRETE ALTERNATIVES

Decision makers in renewable resource planning are often unable to specify their objective function a priori, and are presented with a discrete set of alternatives reflecting a range of options that are actually much more continuous. It is common for the decision maker to be interested in some other alternative than those originally developed. An iterative process thus often takes place between decision maker an analyst as they search for a satisfactory alternative. This paper analyzes the economic tenability of simply interpolating (taking convex combinations of) initial alternatives to generate new alternatives in this process. It is shown that convex combinations of outputs will be producible (feasible) with the interpolated input levels, under very common conditions. In fact, the cost estimate resulting from interpolating the cost of two (or more) alternatives will generally be an overestimate. The magnitude of this overestimate is investigated in a test case. It is concluded that this cost overestimate can be rather large, and is not systematically predictable. Only when the output sets in the original alternatives are very similar are the interpolated cost estimates fairly accurate.