Rail-road terminals are the chain links in intermodal rail-road transportation where standardized load units (containers, swap bodies and trailers) are transfered from trucks to trains and vice versa. We consider three subproblems of the operational planning process at rail-road terminals that terminal operators are facing in their daily operations. These are the optimization problems storage planning, load planning and crane planning. The aim of storage planning is to determine load unit storage positions for a set of load units in a partially filled storage area. Here, different restrictions like non-overlapping of stored load units have to be respected. The objective of storage planning is to minimize the total transportation costs and the number of load units that are not stored at the ground level. For the load planning we assume a scenario of overbooked trains. So, the aim of load planning is to assign a subset of the load units that are booked on a train to feasible positions on the wagons such that the utilization of the train is maximized and the costs for the handling in the terminal are minimized. For the feasible positioning of load units length and weight restrictions for the wagons and the train have to be respected. For the load planning of trains we consider a deterministic version and a robust approach motivated by uncertainty in the input data. The last considered optimization problem is the crane planning. The crane planning determines the transfer of the load units by crane between the different transportation modes. For each crane a working plan is computed which contains a subset of the load units that have to be handled together with individual start times for the transfer operations. For the load units which have to be transfered in the terminal, storage and load planning compute destination positions (inside the terminal). These destination positions are part of the input for the crane planning. The main objective of crane planning is to minimize the total length of the empty crane moves that have to be performed between successive transports of load units by the cranes. We provide MIP-models for all three subproblems of the operational planning process at rail-road terminals. For the storage and crane planning we also propose fast heuristics. Furthermore, we present and compare computational results based on real world data for all subproblems. The main contributions of this thesis concern load and storage planning. For the deterministic load planning we provide the first model that represents all practical constraints including physical weight restrictions. For the load planning we furthermore present robustness approaches for different practical uncertainties. For the storage planning we provide complexity results for different variants. For the practical setting we developed a heuristic which is able to compute solutions of high quality in a small amount of runtime.

Diplomová práce je zaměřena na problematiku nelineárních diferenciálních rovnic. Obsahuje věty důležité k určení chování nelineárního systému pouze za pomoci zlinearizovaného systému, což je následně ukázáno na rovnici matematického kyvadla. Dále se práce zabývá problematikou diferenciálních rovnic se zpoždéním. Pomocí těchto rovnic je možné přesněji popsat některé reálné systémy, především systémy, ve kterých se vyskytují časové prodlevy. Zpoždění ale komplikuje řešitelnost těchto rovnic, což je ukázáno na zjednodušené rovnici portálového jeřábu. Následně je zkoumána oscilace lineární rovnice s nekonstantním zpožděním a nalezení podmínek pro koeficienty rovnice zaručující oscilačnost každého řešení.