@article{GnegelSchaudtClausenetal.2024, author = {Gnegel, Fabian and Schaudt, Stefan and Clausen, Uwe and F{\"u}genschuh, Armin}, title = {A graph-refinement algorithm to minimize squared delivery delays using parcel robots}, series = {Mathematics}, volume = {12}, journal = {Mathematics}, publisher = {MDPI}, address = {Basel}, issn = {2227-7390}, doi = {10.3390/math12203201}, year = {2024}, abstract = {In recent years, parcel volumes have reached record highs, prompting the logistics industry to explore innovative solutions to meet growing demand. In densely populated areas, delivery robots offer a promising alternative to traditional truck-based delivery systems. These autonomous electric robots operate on sidewalks and deliver time-sensitive goods, such as express parcels, medicine and meals. However, their limited cargo capacity and battery life require a return to a depot after each delivery. This challenge can be modeled as an electric vehicle-routing problem with soft time windows and single-unit capacity constraints. The objective is to serve all customers while minimizing the quadratic sum of delivery delays and ensuring each vehicle operates within its battery limitations. To address this problem, we propose a mixed-integer quadratic programming model and introduce an enhanced formulation using a layered graph structure. For this layered graph, we present two solution approaches based on relaxations that reduce the number of nodes and arcs compared to the expanded formulation. The first approach, Iterative Refinement, solves the current relaxation to optimality and refines the graph when the solution is infeasible for the expanded formulation. This process continues until a proven optimal solution is obtained. The second approach, Branch and Refine, integrates graph refinement into a branch-and-bound framework, eliminating the need for restarts. Computational experiments on modified Solomon instances demonstrate the effectiveness of our solution approaches, with Branch and Refine consistently outperforming Iterative Refinement across all tested parameter configurations.}, subject = {Integer programming; Layered graph refinement; Delivery robots; Electric vehicle-routing problem; Partial recharging}, language = {en} } @techreport{ZellFuegenschuh2025, type = {Working Paper}, author = {Zell, Sascha and F{\"u}genschuh, Armin}, title = {Optimizing autonomous unmanned aircraft system deployment locations for enhanced wildfire detection and monitoring}, doi = {10.26127/BTUOpen-6942}, url = {http://nbn-resolving.de/urn:nbn:de:kobv:co1-opus4-69422}, year = {2025}, abstract = {The increase in the frequency and severity of wildfires as a symptom of climate change requires innovative methods of wildfire fighting. For this reason, we propose a framework for an autonomous Unmanned Aircraft System (UAS), consisting of a fleet of Micro Air Vehicles (MAVs) stored in purpose-built hangars. The intention is to deploy the UAS as the first responder to an alarm and have the sensor-equipped MAVs monitor the target area even before other standard firefighting vehicles have arrived. The focus of this paper is primarily on the development and application of a location-allocation optimization Mixed-Integer Linear Programming (MILP) model that selects different MAV and hangar types and locates them, with the objective of approaching the target area as quickly as possible while guaranteeing a certain monitoring time at the scene. The model is applied to a large, sparsely populated, rural operational area, around a third of which consists of forest in the South of Brandenburg, Germany. The spatial demand is measured through an easily reproducible and transferable open data approach. Finally, several instances with different fixed numbers of hangars and MAVs to be set up are solved by the commercial state-of-the-art solver CPLEX and analyzed for their computation time.}, subject = {Mixed-lnteger linear programming; Unmanned aircraft systems; Micro air vehicles; Autonomous wildfire monitoring; Location-allocation optimization; Gemischt-ganzzahlige Programmierung; Drohnen; Drohnenhangar; Standortproblem; Autonome Waldbrandbek{\"a}mpfung; Waldbrand; {\"U}berwachung; Drohne (Flugk{\"o}rper); Autonomes System; Standortproblem; Lineare Optimierung}, language = {en} }