This thesis is focused on the topic of assignment problems. The theoretical part presents a summary of the most important previously published findings on linear and quadratic assignment problem. The basic formulations of both problems are introduced, as well as the outline of some methods developed for their solution. Finally both problems are illustrated by practical applications that have appeared in the literature. The practical part gives insight into the issue of assignment of transport orders to drivers in a company and proposes a suitable model that speeds up the process of distributing the orders. The transfers conducted by the company start at the airport and terminate in a hotel in the city centre of Prague or vice versa. When proposing order schedules for the drivers, it is necessary to take into account not only the time of the transfers, but additionally the capacity and the category of the vehicle.

<div> <p><br></p> </div> Individuals with disabilities and persons operating in inaccessible environments can greatly benefit from the aid of robotic manipulators in performing activities of daily living (ADLs) and other remote tasks. Users relying on robotic manipulators to interact with their environment are restricted by the lack of sensory information available through traditional operator interfaces. These interfaces only allow visual task access and deprive users of somatosensory feedback that would be available through direct contact. Multimodal sensory feedback can bridge these perceptual gaps effectively. Given a set of object properties (e.g. temperature, weight) to be conveyed and sensory modalities (e.g. visual, haptic) available, it is necessary to determine which modality should be assigned to each property for an effective interface design. However, the effectiveness of assigning properties to modalities has varied with application and context. The goal of this study was to develop an effective multisensory interface for robot-assisted pouring tasks, which delivers nuanced sensory feedback while permitting high visual demand necessary for precise teleoperation. To that end, an optimization approach is employed to generate a combination of feedback properties to modality assignments that maximizes effective feedback perception and minimizes cognitive load. A set of screening experiments tested twelve possible individual assignments to form the combination. Resulting perceptual accuracy, load, and user preference measures were input into a cost function. Formulating and solving as a linear assignment problem, a minimum cost combination was generated. Results from experiments evaluating efficacy in practical use cases for pouring tasks indicate that the solution is significantly more effective than no feedback and has considerable advantage over an arbitrary design. <br>