# Measuring Efficiency and Effectiveness of Highway Management in Sustainability
## 2 Theoretical Considerations
### Concept of Efficiency  
In the field of sustainability management, the definition of efficiency is well known and measured by the ratio of output to input. Similarly, the International Transport Forum [16] defines efficiency as \"some combination of reduced costs and/or increased benefits to society (p. 89).\" From this view, three specific definitions are explained: \"reducing inputs for the same outputs; obtaining more outputs or improved quality for the same inputs; obtaining proportionally more outputs or improved quality in return for an increase in resources.\"  
However, the meaning of efficiency encompasses several concepts according to various perspectives, such as technical efficiency, allocative efficiency, and overall efficiency. Technical efficiency focuses on lower spending. It implies the maximum possible output at a given cost for a set of inputs in terms of output or, in cost terms, a certain level of output at the minimum possible cost [17; 18]. Allocative efficiency is explained as \"the right things are being done\"; that is, the resources of a community should be allocated and used to maximize its welfare. More specifically, allocative efficiency is very close to Pareto efficiency, which means it is impossible to make a person better off without another person becoming worse off. \"Another formal version of the same idea is to define an allocatively efficient level of production of a commodity as that level for which the difference between the 'total social benefits' from the consumption of the commodity and the 'total social costs' of its production is as large as possible' [17] (p. 425).  
Economists define allocative efficiency, technical efficiency, and overall efficiency by using geometrical and mathematical terms [19; 20; 21; 22]. In Figure 1, the isoquants \(Ya\) and \(Yb\) indicate the same levels of output at different levels of input (A-D). First, the input mix for achieving allocative efficiency (AE) is defined as a set that minimizes production costs or a set that maximizes the level of output under \"a fixed money outlay\" (D. 74). To compute the allocative efficiency (AE), the relative price of the input factor is required. In Figure 1, AE is measured as OD/OB and allocative inefficiency is \(1-\text{OD/OB}\). Second, technical efficiency (TE) is defined as when an authority produces the same level of output with a lower level of input compared with others. Since the ability to create the difference in efficiency is regarded as a technique that can reduce the level of input, this efficiency is called technical efficiency. For example, in Figure 1, authority A uses a lower level of input than authority B; thus, authority A is appraised as technically more efficient than authority B, given the same levels of output (_Ya_ and _Yb_). TE is OB/OA and inefficiency is measured as \(1-\text{OB/OA}\). Third, overall efficiency is the product of AE and TE, which is defined as OD/OA (p. 75). In sum, allocative efficiency (AE) = OD/OB, technical efficiency (TE) = OB/OA, overall efficiency (OE) = AE * TE = OD/OA.