Stochastic preemptive goal programming to balance goal achievements under uncertainty

Structured decision-making in the presence of conflicting goals is difficult, and even more so when accounting for uncertainties in the goals or constraints. In this article, we propose a new approach to multi-criteria decision-making that extends the deterministic preemptive goal programming approach to account for such uncertainties. The uncertainties may be characterized in various ways including a Bayesian network or extensive Monte Carlo multi-variate output. We contend the proposed stochastic preemptive goal programming approach is particularly applicable when better goal achievement increases uncertainty or induces risk to other goals. Resulting solutions tend to be a balance of the goals' achievements and robust to minor changes to the goals or constraints. We demonstrate the approach using three illustrative examples: a univariate example, a bivariate example, and a stock portfolio optimization example along with an application to determine military requests for absence. Our preliminary results suggest that a stochastic preemptive goal programming approach represents an effective means of analysing multi-criteria decision-making problems under uncertainty.