MCDM (Multi-Criteria Decision Making)

MCDM is the operations-research sub-discipline addressing problems in which a decision maker must rank or select among a finite number of alternatives evaluated on two or more conflicting criteria (cost, quality, risk, environmental impact, etc.). Roy (1968) founded the European school via ELECTRE, Saaty (1980) launched the American school via AHP, and Zeleny (1973) opened the multi-objective generalization. The method family splits into three branches: (1) value/utility-function methods — Weighted Sum Method (WSM), Weighted Product Method (WPM), AHP (Saaty 1980), MAUT (Keeney and Raiffa 1976); (2) reference-point / distance-based methods — TOPSIS (Hwang and Yoon 1981, Euclidean distance to ideal and anti-ideal solutions), VIKOR (Opricovic 1998), Grey Relational Analysis; (3) outranking methods — ELECTRE I-IV (Roy 1968), PROMETHEE I-II (Brans and Vincke 1985), which build preference relations via concordance and discordance indices. Criterion weights are either subjective (AHP pairwise comparison, direct assignment) or objective (Entropy, CRITIC). The output is a total or partial ranking; the distinction from multi-objective optimization (an infinite Pareto frontier) is that MCDM operates on a finite alternative set. Complexity: most methods run in polynomial time. Practical applications dominate supplier selection, facility location, personnel evaluation, project portfolios, and sustainability decisions.