Mujgan Sagir

An essay on rank preservation and reversal

Rank preservation and reversal, so fundamental in decision making, have been an unresolved issue in the field of economics and utility theory and came into focus when the Analytic Hierarchy Process was developed because it uses paired comparisons that inevitably make the priorities of the alternatives interdependent. This paper summarizes the important issues that can play a role in rank preservation and reversal with counterexamples to show that preserving rank in all situations is wrong.

Extending the Measurement of Tangibles to Intangibles

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.

Exam scheduling: Mathematical modeling and parameter estimation with the Analytic Network Process approach

An invigilator is a person who supervises students during examinations in educational systems. Assigning invigilators to exams is an important phase in the exam scheduling process. The problem has its own constraints and a multi-objective structure. Hardly any mathematical models have been used in the past. Mostly, heuristic approaches are used to assign invigilators to exams. The Analytic Network Process (ANP) with dependence and feedback is a general framework for a detailed analysis of societal, governmental and corporate decisions that is available today to the decision maker. Within the ANP networks of influence one includes all the factors and criteria, tangible and intangible, which have bearing on making a best decision. In this paper, an ANP model is used to prioritize the objectives of the invigilator-exam assignment problem. The model has ten clusters. All the participants and the criteria with their interrelations are defined. Different objectives of the problem are treated as alternatives in this model. Relative weights are obtained for the elements in the ANP model by using the Super Decisions software. Then we solve a previously developed nonlinear optimization model with several constraints using these weights.

AN AUTOMATED MULTI-OBJECTIVE INVIGILATOR-EXAM ASSIGNMENT SYSTEM ∗

This paper is concerned with the invigilator-exam assignment problem. A web-based Automated Invigilator Assignment System (AIAS), consists of a mathematical model; a database storing the information and web-based user interfaces is constructed to solve the problem by providing an environment for a practical usage. The core of the system is the mathematical model developed for obtaining the exact solution. We conclude the paper by presenting a real-life problem solved by the proposed approach.