A framework for sensitivity analysis in discrete multi-objective decision-making

A framework for sensitivity analysis in multi-objective decision-making within a Bayesian context, allowing for simultaneous variation in all the data, benefiting from the recent advances in optimisation theory and the advent of cheap computer power is introduced.

Abstract

This paper introduces a framework for sensitivity analysis in multi-objective decision-making within a Bayesian context. In designing decision aids, it is essential to check the sensitivity of the conclusions to the data. Data input is constantly revised as decision makers come to understand the implications - and the possible inconsistencies - of their judgements. Sensitivity analysis can focus on those judgemental inputs which are most important in determining choice and, therefore, need to be revised most carefully. After introducing the basic problem, we review some of the previous approaches to sensitivity analysis, which are, by and large, ad hoc specific 'rules of thumb', tailored to the particular decision aid being used. Moreover, with few exceptions, they consider sensitivity to one or, at most, two data inputs at a time, the remaining data being taken as fixed. Our aim is to provide a general approach to sensitivity analysis, allowing for simultaneous variation in all the data, benefiting from the recent advances in optimisation theory and the advent of cheap computer power. We introduce several solution concepts, and analytic ways of determining them, which allow us to identify the possible competitors of a current best solution. We analyse, then, distance-based tools for sensitivity analysis, according to some general lines. Finally, we describe some computational experience with two examples and suggest some ways of displaying the information to the decision-maker.