We introduce, formulate, and solve the Generalized Median Tour Problem, which is motivated in the health supplies distribution for urban and rural areas. A region comprises districts that must be served by a specialized vehicle visiting its health facilities. We propose a distribution strategy to serve these health facilities efficiently. A single tour is determined that visits a set of health facilities (nodes) composed of disjoint clusters. The tour must visit at least one facility within each cluster, and the unvisited facilities are assigned to the closest facility on the tour. We minimize the sum of the total tour distance and the access distance traveled by the unvisited facilities. Efficient formulations are proposed and several solution strategies are developed to avoid subtours based on branch & cut. We solve a set of test instances and a real-world instance to show the efficiency of our solution approaches.

The hierarchical network design problem consists of finding a minimum cost bilevel network that connects all the nodes in a set, created by a loopless main path and a forest. The main path is formed by primary (higher cost) arcs, providing a path between an origin node and a destination node. The forest, built using secondary (lower cost) arcs, connects all the nodes not on the main path, to the path itself. We state and prove some properties of the problem, which allow finding good upper bounds to the solution in polynomial time when the primary costs are proportional to secondary costs. We also propose an O(n ⁴) procedure to improve on these bounds. In turn, these bounds are used to significantly reduce the number of nodes and arcs of the problem. Once the problem is reduced, large instances can be solved to optimality. At this stage, we use one of two linear integer optimization formulations. The first and preferred one is based on multicommodity flows, which avoids the formation of subtours. The second formulation avoids subtours by iteratively adding ad hoc constraints. We show some examples and provide computational experiments performed on networks with sizes up to 600 nodes and 14 000 arcs.

We introduce the p-Cable Trench Problem with Covering. Secondary servers are located to provide service within a coverage radius (e.g., Wi-Fi antennas). Each secondary server must be connected to a primary server (a router), through a dedicated cable (wire pair). Trenches need to be dug to bury ducts that contain all the cables. The service must be provided to a whole region, at the minimum cost, consisting of the trench and duct cost and the total cable length cost. The number of primary servers is preset, and they are located on nodes belonging to a set of candidate locations (nodes of an existing telephone network). We propose a linear integer optimization model based on multicommodity flow, which we solve using branch and bound, a linear relaxation and two different Lagrangian relaxation-based heuristics, for which we design ad-hoc procedures to improve the upper bounds. We solve instances of up to 200 nodes, and also an application consisting in locating Wi-Fi antennas in Viña del Mar, Chile.

This study presents a novel approach that integrates Discrete Event Simulation (DES) with Design of Experiments (DOE) techniques, framed within a stochastic optimization context and guided by a multi-objective goal programming methodology. The focus is on enhancing the operational efficiency of an emergency department (ED), illustrated through a real-world case study conducted in a Chilean hospital. The methodology employs Response Surface Methodology (RSM) to explore and optimize the impact of four critical resources: physicians, nurses, rooms, and radiologists. The response variable, formulated as a goal programming function, captures the aggregated patient flow time across four representative care tracks. The optimization process proceeded iteratively: early stages relied on linear approximations to identify promising improvement directions, while later phases applied a central composite design to model nonlinear interactions through a quadratic response surface. This progression revealed complex interdependencies among resources, ultimately leading to a local optimum. The proposed approach achieved a 50% reduction in the aggregated objective function and improved individual patient flow times by 7% to 26%. Compared to traditional metaheuristic methods, this simulation–optimization framework offers a computationally efficient alternative, particularly valuable when the simulation model is complex and resource-intensive. These findings underscore the value of combining simulation, RSM, and multi-objective optimization to support data-driven decision-making in complex healthcare settings. The methodology not only improves ED performance but also offers a flexible and scalable framework adaptable to other clinical environments seeking resource optimization and operational improvement.