This research aims to optimize a VRPTW that incorporates the driver satisfaction factors ‘region consistency’ and ‘workload preference’ while not increasing routing costs too much. The developed measures were optimized for using the ‘Random Allocation’, ‘Driver Assignment’ and ‘Integrated Approach’ methods for various weightings in a multi-objective setting. Driver satisfaction was explicitly optimized in the state-of-the-art VRPTW solver called PyVRP developed by ORTEC. The integrated approach outperformed both the driver assignment and random allocation methods on small and medium sized instances, whereas Driver Assignment performed best on large instances.

Representation theory is a branch in mathematics that studies group homomorphisms between a group and the automorphism group of a vector space. A special representation that every group has is the regular representation. This representation permutes all elements of the group in a vector space which dimension is equal to the order of the group.
Within this vector space there are group invariant subspaces. There are several methods to finding representation invariant subspaces of this vector space.

This thesis aims to do two things: First of all, this thesis aims to give the reader an introduction to representation theory, presenting various key concepts, definitions and theorems. Moreover, ways to construct character tables are presented along with multiple worked out examples. Second, the regular representations of D4 and Q8 are decomposed into representation invariant subspaces of C8. To this end, two methods were used.

The first method (A), proposed by dr. Jeroen Spandaw, works out all the possible decompositions of the vector space a regular representation acts on. This is quite a laborious process in which change of basis matrices, expressed in several parameters, will have to be made for all generators of the considered group. The second methods (B), proposed by dr. Paul Visser, is known as the grand orthogonalization method and makes use of an extended version of the character table of the considered group.

Both methods are perfectly fine to make a desired decomposition. However, method A
takes a lot more computational effort than method B to come up with the desired result. The benefit of using method A over method B is that method A considers all possible decompositions, whereas method B only considers one of the infinitely many that are possible.