Planning in an uncertain environment: Stochastic goal programming using the versatility criterion

This article presents a planning model that applies the versatility criterion to goal programming problems with uncertainty about the constraints which define the set of feasible decisions. Some of the constraint parameters are assumed to be stochastic variables with a joint normal distribution. The solution sought maximizes the probability of satisfying all the constraints. A nonlinear programming model is set out which can be solved by using numerical integration at every step. An illustrative example is provided which shows the possible application of the versatility model to land-use planning.