The Vehicle Routing Problem (VRP) is a classical problem in logistics that has been well studied by the operations research and transportation science communities. VRPs are defined as follows. Given a transportation network with a depot, a set of pickup or delivery locations, and a set of vehicles to service these locations: find a collection of routes starting and ending at the depot, such that (i) the customer's demand at a node is satisfied by exactly one vehicle, (ii) the total demand satisfied by a vehicle does not exceed its capacity, and (iii) the total distance traveled by the vehicles is minimized. This problem is especially hard to solve because of the presence of sub--tours, which can be exponential in number. In this dissertation, a special case of the VRP is considered -- where the underlying network has a tree structure (TVRP). Such tree structures are found in rural areas, river networks, assembly lines of manufacturing systems, and in networks where the customer service locations are all located off a main highway. Solution techniques for TVRPs that explicitly consider their tree structure are discussed in this dissertation. For example, TVRPs do not contain any sub-tours, thereby making it possible to develop faster solution methods. The variants that are studied in this dissertation include TVRPs with Backhauls, TVRPs with Heterogeneous Fleets, TVRPs with Duration Constraints, and TVRPs with Time Windows. Various properties and observations that hold true at optimality for these problems are discussed. Integer programming formulations and solution techniques are proposed. Additionally, heuristic methods and conditions for lower bounds are also detailed. Based on the proposed methodology, extensive computational analysis are conducted on networks of different sizes and demand distributions. / text

Path planning that considers accurate vehicle dynamics and obstacle avoidance is an important problem in the area of autonomous driving. This paper describes a method of implementing trajectory planning for autonomous parking in conditions where the starting point and the position of fixed obstacles are uncertain. The narrow spaces and complicated manoeuvres required for parking demands a lot from the trajectory planning algorithm. It needs to have the ability to accurately model vehicle dynamics and find an efficient way around obstacles. Having obstacles in the way of the parking vehicle makes this a nonconvex problem the goal can usually not be reached by travelling in a straight line and finding a perfect trajectory around them is generally not computationally tractable. This paper reviews a two tiered approach to solving this problem. First a rough path is found using a modified Rapidly-exploring Random Tree (RRT) algorithm called Forward-Backward RRT, which runs two treebuilding processes in parallel and constructs a feasible path from where they intersect. Using optimisation this is then improved into a trajectory that is at least a local optimum. These methods will be demonstrated to produce efficient and feasible trajectories that respects the dynamic constraints of the vehicle and avoids collisions.

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Master thesis is dealing with the issue of condensate creation and removal from the Nesher Ramle steam turbine during start-up and steady state. At the beginning a preliminary calculation of heat balance and the turbine itself is done. It is followed by description and design of drainage system supplemented by calculation of the steam flow through the orifices. Steam flow calculation was done via S. D. Morris, Pavelek with Kalčík and Ambrož, all three methods were compared. The main goal is the theoretical calculation of the amount of condensate created during start-up which is influenced by its initial state from which it is started. Three default states are considered, cold, warm and hot. In the last chapter the comparison of theoretical calculation with the measured data on real turbine is done and it is supported by the evaluation of the data from the measurement of the steam turbine at steady state on maximum power and half power. From the steady state analysis, percentage of water flow to expander from the total amount of condensate formed in the turbine were obtained.