Noninferior set scenario analysis

Although many Mathematical Programming techniques have been developed for application to decision making under uncertainty, these techniques are based on three implicit assumptions. The first is that probabilities can be determined for the outcomes of the uncertain parameters, the second is that the decision maker is risk neutral, and the third is that all of the decision maker's concerns can be included in the formulation. While there are many decision making situations for which these assumptions are appropriate, there are many other situations for which they are not. In particular, these assumptions are seldom supportable for strategic decision making problems. Strategic decision making must consider possible future events that have seldom, if ever, occurred before, and for which probabilities cannot be determined. Because the situation will occur only once, and the decision will have a large impact, the decision ma.ker is unlikely to be risk neutral. Finally, the decision makers will often have concerns that cannot be represented in a mathematical programming formulation. In this work we present an approach to decision making under uncertainty that relaxes the three assumptions listed above. We assume that the uncertain future can be described as a small set of scenarios. These scenarios can be considered to have separate, competing objectives, because decisions that prepare well for one scenario generally prepare poorly for the others. The problem is formulated as a multi-objective optimisation problem, and a set of non-dominated decisions is found. The decision maker can choose a decision from this set according to his/her attitudes to risk, and to account for other requirements that cannot be represented in a mathematical programming formulation. This approach is developed for problems with continuous variables, and then extended to problems that include binary variables