An orness based decision support model to aggregate ordered costs

Abstract

In this paper each possible decision in a given economic context is assessed according to a weighted aggregation of its ordered costs, what is known in the literature as an Ordered Weighted Averaging, or OWA, measure. We assume these weights are uncertain and belong to a given set through which different decision attitudes toward risk are modeled. A compromise (minmax regret) solution is proposed in order to conciliate these admissible decision scenarios. In particular, the choice of a set of weights with bounded orness, a measure of the aversion to the risk, is analyzed. A Linear Programming problem is proposed in order to find a consensus solution under such a set of bounded orness OWA operators. Later, this model is generalized by adding bounds on the difference of consecutive individual weights for the ordered costs and a Benders decomposition scheme is analyzed in order to solve the corresponding optimization problem. It is shown how this model can support decisions about the location of a new facility under a set of different OWA operators and its relation with the efficiency (Pareto optimality) from a multicriteria decision making viewpoint.