Refine
Document Type
- Working paper (4)
- Bachelor thesis (1)
- Report (1)
Has Fulltext
- yes (6)
Is part of the Bibliography
- no (6)
Keywords
- Mixed-integer programming (6) (remove)
Institute
In wire-arc additive manufacturing, a wire is molten by an electrical or laser arc and deposited droplet-by-droplet to construct the desired workpiece, given as a set of two-dimensional layers. The weld source can move freely over a substrate plate, processing each layer, but there is also the possibility of moving without welding. A primary reason for stress inside the material is the large thermal gradient caused by the weld source, resulting in lower product quality. Thus, it is desirable to control the temperature of the workpiece during the process. One way of its optimization is the trajectory of the weld source. We consider the problem of finding a trajectory of the moving weld source for a single layer of an arbitrary workpiece that maximizes the quality of the part and derive a novel mixed-integer PDE-constrained model, including the calculation of a detailed temperature distribution measuring the overall quality. The resulting optimization problem is linearized and solved using the state-of-the-art numerical solver IBM CPLEX. Its performance is examined by several computational studies.
Since the beginning of its development in the 1950s, mixed integer programming (MIP) has been used for a variety of practical application problems, such as sequence optimization. Exact solution techniques for MIPs, most prominently branch-and-cut techniques, have the advantage (compared to heuristics such as genetic algorithms) that they can generate solutions with optimality certificates. The novel process of additive manufacturing opens up a further perspective for their use. With the two common techniques, Wire Arc Additive Manufacturing (WAAM) and Laser Powder Bed Fusion (LPBD), the sequence in which a given component geometry must be manufactured can be planned. In particular, the heat transfer within the component must be taken into account here, since excessive temperature gradients can lead to internal stresses and warpage after cooling. In order to integrate the temperature, heat transfer models (heat conduction, heat radiation) are integrated into a sequencing model. This leads to the problem class of MIPDECO: MIPs with partial differential equations (PDEs) as further constraints. We present these model approaches for both manufacturing techniques and carry out test calculations for sample geometries in order to demonstrate the feasibility of the approach.
We address the single container packing problem of a company that has to serve its customers by first placing the products in boxes and then loading the boxes into a container. We approach the problem by developing and solving mixed-integer linear models. Our models consider geometric constraints that feature non-overlapping constraints, box orientation constraints, dimensionality constraints, relative packing position constraints, and linearity constraints. We also develop an extension of the models by integrating load balance and the deviation of the center of gravity. We tested the models on a broad set of real instances involving up to 41 boxes and obtained optimal solutions in most cases and very small gaps when optimality could not be proven.
The German Armed Forces provide an operation contingent to support the North Atlantic Treaty Organization (NATO) Response Force (NRF). For this purpose, a „warehouse” containing accommodations, food supplies, medical supplies, and spare parts for the systems has to be available. Such a warehouse is restricted in weight, in order to be quickly movable in an upcoming deployment situation. It should be able to supply the NRF troops for a certain amount of time (e.g., one month) without re-supply from the outside. To ensure optimal use of such a restricted warehouse, we developed the computer program „The OPtimization of a Spare Parts Inventory” (TOPSPIN) to find an optimal mix of spare parts to restore a set of systems to functionality. Each system is composed of several parts, and it can only be used again in the mission if all broken parts are replaced. The failure rate of the individual parts follows a given random distribution, and during deployment it is expected to be higher than in the homeland. Due to the stochastic nature of the problem, we generate scenarios that simulate the actual failure of the parts. The backbone of TOPSPIN is a mixed-integer linear program that determines an optimal, scenario-robust mix of spare parts and is solved using standard state-of-the-art numerical solvers. Using input data provided by the Logistikzentrum, we analyze how many scenarios need to be generated in order to determine reliable solutions. Moreover, we analyze the composition of the warehouse over a variety of different weight restrictions, and we calculate the number of repairable systems as a function of this bound.
We deal with a very complex and hard scheduling problem. Several types of products are processed by a heterogeneous resource set, where resources have different operating capabilities and setup times are considered. The processing of the products follows different workflows, allowing also assembly lines. The goal is to process all products in minimum time, i.e., the makespan is to be minimized. Because of the complexity of the problem an exact solver would require too much running time. We propose a compound method where a heuristic is combined with an exact solver. Our proposed heuristic is composed of several phases applying different smart strategies. In order to reduce the computational complexity of the exact approach, we exploit the makespan determined by the heuristic as an upper bound for the time horizon, which has a direct in uence on the instance size used in the exact approach. We demonstrate the efficiency of our combined method on multiple problem classes. With the help of the heuristic the exact solver is able to obtain an optimal solution in a much shorter amount of time.
Die Bachelorarbeit beschäftigt sich mit der Erstellung eines möglichst guten, zulässigen Stundenplans für eine Unteroffiziersschule der Bundeswehr. Die Bildungseinrichtung kann vorhandene Optimierungsprogramme für Stundenpläne nur teilweise zu Rate ziehen, da hier im Vergleich zu normalen Schulen und Universitäten die Veranstaltungen nicht in einem Wochenzyklus stattfinden. Des Weiteren gibt es Spezialveranstaltungen, die nur an bestimmten Tagen besucht werden können. Zusätzlich haben die zu absolvierenden Kurse eine fest vorgegebene Reihenfolge, die beachtet werden muss.