AbstractGoal Programming within a pre-emptive priority structure has been one of the most widely used multi-objective mathematical model formulations. By considering its dual problem, Ignizio has shown that a very efficient computational procedure for solving linear goal-programming problems can be problems can be implemented with any conventional large-scale simplex system. This note gives an overview of Ignizio's dual formulation, and identifies when a certain dual variable must be incorporated in the model to preserve the pre-emptive priority structure.