This master thesis deals with various mathematical models, which can be used for designing the location of collection points for various fractions of municipal waste with consideration of walking distance, economic demands and utilization of allocated capacities. Scripts for generating input datasets for applied models from basic input data, which are address points with population and GPS coordinates, is also included in the thesis. The model was implemented in GAMS and the script was written in VBA in Microsoft Excel. Model was used in case study. Results of single and multi-criteria approaches are analyzed and compared.

The aim of my thesis is to find the shortest total route to export trash at the bus stops for several variants and also determine the suitability of approximate algorithms. The tasks are solved by insertion heuristic, closest neighbor heuristic and optimization. The optimal solution is gained by using the system LINGO and by using optimization solver CPLEX. In my thesis I first describe the problem of maintenance of bus stops. Following chapter is devoted to the role of routing problems, its classifications, problems to solve, possibilities of solution. The used methods are Traveling Salesman Problem with one or multiple vehicles available in a unique depot and Vehicle Routing Problem with one or multiple vehicles available in a unique depot or multiple depots. The last chapter describes and compare the results of the solution of insertion heuristic, closest neighbor heuristic and optimization for problem of replacement of bus schedules and of maintenance of bus stops.

We present robust explicit construction of 3D configuration spaces using controlled linear perturbation. The input is two planar parts: a fixed set and a moving set, where each set is bounded by circle segments. The configuration space is the three-dimensional space of Euclidean transformation (translations plus rotations) of the moving set relative to the fixed set. The goal of constructing the 3D configuration space is to determine the boundary representation of the free space where the intersection of the moving set and fixed set is empty. To construct the configuration space, we use the controlled linear perturbation algorithm. The controlled linear perturbation algorithm assigns function signs that are correct for a nearly minimal input perturbation. The output of the algorithm is a consistent set of function signs. This approach is algorithm-independent, and the overhead over traditional floating point methods is reasonable. If the fixed and moving sets are computer representations of physical objects, then computing the configuration space greatly aids in many computational geometry problems. The main focus of computing the configuration space is for the path planning problem. We must find if a path exists from the start to the goal, where the fixed set is the obstacle, and the moving set is the object trying to reach the goal.