Multi-objective problems often arise in practice. It consists of optimizing several objectives
\(f(1), f(2), ..., f(n)\) that are generally in conflict (e.g., increase quality, reduce cost, save time). A common way to tackle such problems is to give the same importance to each objective, and to optimize their values. This approach is referred to as Pareto optimization. Such a way of simultaneously optimizing all objectives ultimately leaves the involved decision makers with a set of tradeoff solutions, and they have then to select the most appropriate one for the company. Unfortunately, from a practical standpoint, this selection process among the possible tradeoff solutions could be complicated and finally abandoned.
With lexicographic optimization, the managerial sensitive discussion occurs before the optimization is performed (i.e., without being in front of solutions). More precisely, the decision makers have to initially formulate preferences in order to rank the competing objectives (formally,
\(f(1) > f(2) > ... > f(n)\)). Such an approach has many advantages: it reduces the conflicts within the company; it allows using more appropriate optimization tools; it has more chance to be finally used.
In this presentation, we highlight the legitimacy of adopting a lexicographic optimization framework for multi-objective problems arising in various industrial contexts (e.g., production, transportation, supply chain management). The talk will be either in English or in French, depending on the audience. Moreover, this seminar is tailored for mathematicians and non-mathematicians alike, with a view to help 1) future decision makers; 2) graduate students; and 3) faculty working on framing and solving issues that involve managerial problems in various fields and industries.
Bienvenue à tous!