Weight stability intervals for multi-criteria decision analysis using the weighted sum model

Multi-criteria decision analysis (MCDA), or multi-criteria decision making (MCDM) encompasses a wide set of mathematical methods to compare alternatives whilst considering multiple criteria and the relative importance (weight) of each criterion or the allowable trade-off between criteria. MCDA/MCDM may be implemented in a decision support system to aid decision makers compare multiple alternatives. A key consideration in any MCDA is the sensitivity of the results obtained to alterations of the criteria weights used. Prior methods to determine the weight stability interval (WSI, the range of values for individual weights for which the ranking of alternatives will not change) include the manual alteration of criteria weights, the use of different sets of criteria weights in a form of scenario analysis, or the process of iteratively searching for the maximum and minimum allowable alterations to individual criteria weights to determine the weight stability interval. The first contribution of this paper is the development of a novel method for determining precise weight stability intervals which does not rely on enumeration or simulation for use with the weighted sum model (WSM, based on the L₁ Minkowski norm), one of the most widely used aggregation methods within MCDA. The second contribution of this work is the use of these WSIs to identify the most sensitive weight(s) based on a Pareto dominance approach whilst considering both the allowable increase and decrease in criteria weights. The above points are demonstrated and applied in an analysis of several alternatives for renewable energy (biogas) production.