Tank and Hopfield have shown that networks of analog neurons can be used to solve linear programming (LP) problems. We have re-examined their approach and found that their network model frequently computes solutions that are only suboptimal or that violate the LP problem's constraints. As their approach has proven unreliable, we have developed a new network model: the goal programming network. To this end, a network model was first developed for goal programming problems, a particular type of LP problems. From the manner the network operates on such problems, it was concluded that overconstrainedness, which is possibly present in an LP formulation, should be removed, and we have provided a simple procedure to accomplish this.