ABSTRACT
The Lexicographic and ε-constraint methods are two of the most known methods in Multi-Objective Linear Programming (MOLP). Both methods fit in the category of Reduced Feasible Region Methods. In short, they transform the MOLP problem into a single objective problem by optimizing one objective function and taking the remaining objectives (all at once, or step by step) as constraints. The Lexicographic method asks for the Decision Maker (DM) to sort all objective functions from the most important to least important one. Then, it takes one objective function at a time and finds its optimal solution within a reduced feasible region. The ε-constraint method asks the DM for the most important objective and solves the single objective problem considering only this function, while all the remaining are tackled as constraints. Given its popularity an improved version of this method, AUGMECON, is also presented. For each method, several examples are solved enhancing each method features. Their major limitations are highlighted, and strategies are proposed to overcome them. A set of exercises covering all topics are proposed at the end of the chapter.
