In this paper, we propose a generic model based on linear programming that allows building an optimal production plan for a work shift in an open-pit mine. The linear program takes into account different groups of constraints such as the characteristics of the blending at the crusher, the equipment capacity, the amount of material available at the sources, the capacity of the fleet of trucks, etc. The paper puts emphasis on the approximation and the linearization of a set of constraints that computes the waiting time of the trucks at the service points.