The Pareto frontier indicates an improvement potential of ∼50 $/m3 ethanol when keeping emissions fixed, or ∼250 kg CO2-eq/m3 ethanol when keeping costs fixed.
The optimal solution obtained from Pareto frontier indicates that unequal triple-cell tube with appropriate thickness distribution and arrangement of internal ribs is superior in energy absorption to initial design.
Thus, the efficiency frontier indicates a lower bound for input reduction.
Thus, the efficiency frontier indicates an upper bound for the input increase.
By doing so, it defines productive efficiency in the context of that production set: a point on the frontier indicates efficient use of the available inputs, while a point beneath the curve indicates inefficiency.
However, this result is rejected by the LR test, which favors separate frontiers indicating the two groups have different production function.
The estimated value of sigma are significant at less than 1% probability level for all frontier functions indicating the conventional average production function is not an adequate representation of the data.
An analysis of the frontier orbitals indicates that the growth of the nanotube is likely to start at one side only.
Efficiency change is change in a unit's production relative to the frontier with >1 meaning it is operating closer to the frontier than previously, and <1 indicating it is further from the frontier.
