The Preference Ranking Organization METHod for Enrichment of Evaluations and its descriptive complement geometrical analysis for interactive aid are better known as the Promethee and Gaia methods. Based on mathematics and sociology, the Promethee and Gaia method was developed at the beginning of the 1980s and has been extensively studied and refined since then. It has particular application in decision making, and is used around the world in a wide variety of decision scenarios, in fields such as business, governmental institutions, transportation, healthcare and education. Rather than pointing out a "right" decision, the Promethee and Gaia method helps decision makers find the alternative that best suits their goal and their understanding of the problem. It provides a comprehensive and rational framework for structuring a decision problem, identifying and quantifying its conflicts and synergies, clusters of actions, and highlight the main alternatives and the structured reasoning behind.
History The basic elements of the Promethee method have been first introduced by Professor Jean-Pierre Brans (CSOO, VUB Vrije Universiteit Brussel) in 1982. It was later developed and implemented by Professor Jean-Pierre Brans and Professor Bertrand Mareschal (Solvay Brussels School of Economics and Management, ULB Université Libre de Bruxelles), including extensions such as GAIA. The descriptive approach, named Gaia, allows the decision maker to visualize the main features of a decision problem: he/she is able to easily identify conflicts or synergies between criteria, to identify clusters of actions and to highlight remarkable performances. The prescriptive approach, named Promethee, provides the decision maker with both complete and partial rankings of the actions. Promethee has successfully been used in many decision making contexts worldwide. A non-exhaustive list of scientific publications about extensions, applications and discussions related to the Promethee methods was published in 2010.
Uses and applications While it can be used by individuals working on straightforward decisions, the Promethee & Gaia is most useful where groups of people are working on complex problems, especially those with several criteria, involving a lot of human perceptions and judgments, whose decisions have long-term impact. It has unique advantages when important elements of the decision are difficult to quantify or compare, or where collaboration among departments or team members are constrained by their different specializations or perspectives. Decision situations to which the Promethee and Gaia can be applied include:
Choice – The selection of one alternative from a given set of alternatives, usually where there are multiple decision criteria involved. Prioritization – Determining the relative merit of members of a set of alternatives, as opposed to selecting a single one or merely ranking them. Resource allocation – Allocating resources among a set of alternatives Ranking – Putting a set of alternatives in order from most to least preferred Conflict resolution – Settling disputes between parties with apparently incompatible objectives
The applications of Promethee and Gaia to complex multi-criteria decision scenarios have numbered in the thousands, and have produced extensive results in problems involving planning, resource allocation, priority setting, and selection among alternatives. Other areas have included forecasting, talent selection, and tender analysis.
Some uses of Promethee and Gaia have become case-studies. Recently these have included:
Deciding which resources are the best with the available budget to meet SPS quality standards (STDF – WTO) [See more in External Links] Selecting new route for train performance (Italferr)[See more in External Links]
The mathematical model
Assumptions Let A = { a 1 , . . , a n } {\displaystyle A=\{a_{1},..,a_{n}\}} be a set of n actions and let F = { f 1 , . . , f q } {\displaystyle F=\{f_{1},..,f_{q}\}} be a consistent family of q criteria. Without loss of generality, we will assume that these criteria have to be maximized. The basic data related to such a problem can be written in a table containing n × q {\displaystyle n\times q} evaluations. Each line corresponds to an action and each column corresponds to a criterion.
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