Tangibles have measurements generally on ratio scales with arbitrary units that are always interpreted by using judgments as to what particular purpose the measurements serve. How two measurements on a ratio scale are related with respect to dominance leads to forming their ratio which is a dimensionless number. The judgment of an expert can be used to estimate this ratio when the objects are homogeneous. The process of using judgments to make comparisons is then extended by clustering and using pivots to measure inhomogeneous objects or criteria. The paper shows the generality of the analytic network process (AHP) as a method of measurement comparing it with direct measurement and with the utility approach through an example. It is also shown with an application from economics that the judgment process can be sufficiently accurate to produce numerical outcomes that are close to what one obtains by conventional methods, thus serving to validate its use in the measurement of intangibles when informed people are involved.
A faculty-course-time slot assignment problem is studied. The multiobjective 0-1 linear programming model considering both the administration's and instructors' preferences is developed and a demonstrative example is included. Both modeling and solving such problems are difficult tasks due to the size, the varied nature, and conflicting objectives of the problems. The difficulty increases because the individuals involved in the problem may have different preferences related to the instructors, courses and time slots. The Analytic Hierarchy Process (AHP) and Analytic Network Process (ANP) are used to weight different and conflicting objectives. These weights are used in different scalarization approaches. The scalarized problems are solved using a standard optimization package, and solutions corresponding to AHP and ANP weights are compared.
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