Lexicographic, Ꜫ-constrained, Weighted Sum, & Minimax Methods with Graphical Presentations

This 18-page document demonstrates four mathematical modelling approaches for multiobjective optimization, namely lexicographic method, Ꜫ-constrained method, weighted sum method, and modified weighted sum method with minimax objective. It uses a simple example of two decision variables and two functional constraints to explain the concepts. The graphical representations for the problem and the solutions obtained from the four methods are intended to enhance the ease of understanding the concepts.

The document can be useful to someone who wants to learn or understand the process of solving multiobjective optimization problems using mathematical programming. The four different methods provide four different approaches for formulating and solving such problems, highligting the conditions where the methods are best suited.