This paper focuses on the formulation and solution of the problem of planning vehicle routes for material delivery within the premises of a plant working under a just-in-time production system. The unique characteristic of this problem is that the quantity to be delivered at each of the demand nodes is a function of the route taken by the vehicle assigned to serve that node. The problem is modeled by adding a non-linear capacity constraint to the standard vehicle routing model, such that vehicle idle times and inventories at the customer locations are minimized. A heuristic solution procedure is outlined, and the formulation of a lower-bound relaxation is suggested. The performance of the heuristic solution procedure is evaluated in comparison to the lower-bound relaxation, and the heuristic procedure is shown to provide generally good results.