Multi-Criteria Decision Support Systems (MCDM)

Multi-criteria methods take a table and return an order. The order is always sharp: supplier C beats D by 0.0031.

That 0.0031 is not a finding. It is one decimal place of a number built on weights someone estimated in a meeting. The method never says so; an order is all a method can say.

Four methods (SAW, WASPAS, TOPSIS, VIKOR) are implemented properly, with weights elicited from qualitative judgements through MACBETH, and then what the methods cannot say about themselves is measured.

Two things are measured. First rank reversal: removing a losing alternative should not change the winner. Second robustness: how much error in the weights the recommendation survives.

19,200 decision problems across 48 conditions. Over 153,600 removals per method, rank reversal runs at WASPAS 0.70% · SAW 1.19% · TOPSIS 2.75% · VIKOR 3.76%.

In the worked case (seven suppliers, six criteria) MACBETH finds the buyer's twelve judgements inconsistent and narrows the fault to a single one. Four of the six weights cannot change the answer at any value in (0, 1); the recommendation holds up to ±30% measurement error.

The hypothesis written before the run was refuted and reported as such: disagreement was expected to track criterion correlation. It does not. What drives it is the weight distribution and the size of the problem. 139 tests.