In logistic applications that require the pickup and delivery of items, route optimization problems can be modeled as precedence constrained traveling salesperson problems. The combinatorial nature of this problem restricts the application of exact algorithms to small instances, and heuristics are largely preferred for tractability. However, due to precedence constraints that restrict the order in which locations can be visited, heuristics outside of the nearest neighbor algorithm have been neglected in literature. While the convex hull cheapest insertion heuristic is known to produce good solutions in the absence of precedence constraints, i.e., when locations can be visited in any order, it has not been adapted for pick-up and delivery considerations. This paper presents an adapted convex hull cheapest insertion heuristic that accounts for precedence constraints and compares its solutions with the nearest neighbor heuristic using the TSPLIB benchmark data set. The proposed algorithm is particularly suited to cases where pickups are located in the periphery and deliveries are centrally located, outperforming the Nearest Neighbor algorithm in every examined instance.