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.
We study a nonlinear exact penalization for optimization problems with a single constraint. The penalty function is constructed as a convolution of the objective function and the constraint by means of increasing positively homogeneous (IPH) functions. The main results are obtained for penalization by strictly IPH functions. We show that some restrictive assumptions, which have been made in earlier researches on this topic, can be removed. We also compare the least exact penalty parameters for penalization by different convolution functions. These results are based on some properties of strictly IPH functions that are established in the article.
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