Inadequate staffing and long waiting times in hospital emergency rooms are key concerns that can have a negative impact on patient safety and health, as well as the hospital’s overall performance. The purpose of this paper is to investigate the scope of combining the DMAIC (define, measure, analyze, improve, and control) methodology with discrete event simulation and to explore its successful deployment in the Jordanian healthcare sector. The study discussed in this paper is based on a case study conducted utilizing the DMAIC and simulation technique and its application in reducing waiting time and enhancing overall system efficiency in Jordan’s Princess Rahma hospital’s pediatric emergency department. The study shows improvements in the performance of the process and thus productivity in the emergency department through adapting the combined Six Sigma DES methodology. The cycle time of the process was reduced by 73% of the present value, while simultaneously enhancing the total performance of the emergency department by 83%.

This paper introduces the Drone-Truck Rural Postman Problem (DT-RPP), a novel arc routing problem that coordinates a single truck and a single drone to service a set of required edges in a network. The truck travels along network edges to designated launch-and-recovery nodes, where it deploys the drone to service nearby required edges. The drone can fly directly between any two points in Euclidean space but must return to the truck before exceeding its endurance limit. Building upon the classical Rural Postman Problem and the Drone RPP, the DT-RPP leverages the drone's ability to fly directly between points and access areas unreachable by ground vehicles, while using the truck as a mobile hub to overcome the drone's limited flying range. This coordination is particularly valuable for applications such as power line inspection, pipeline monitoring, and border surveillance, where ground vehicle access is limited. A decomposition-based heuristic method is proposed, consisting of four phases: partitioning required edges; identifying candidate launch-and-recovery nodes; determining the truck route; and computing optimal drone routes. Extensive computational experiments and analyses are conducted on ten synthetic instances with 20 to 100 nodes. Sensitivity analysis reveals that moderate parameter settings provide a favorable balance between solution quality and computational efficiency.