This thesis investigates several kinds of models of describing multi-commodity dynamical flow. Three models have been developed for a spatial logistic network, on which packages are delivered by vehicles and another
model was developed to describe interactions between the customers, the stores and the deliverers, which does not explicitly take delivery time into account like before. The former three models consist of an agent-based model (ABM), and two different (differential) equation-based models (EBMs). One of the EBMs is built from the bottom up, and was created by averaging the randomness in the ABM. The other EBM was built top-down and involved optimizing a general model with respect to some parameters, such that its solution resembles the
ABM solution as closely as possible. These three models were tested and compared in the first half of the thesis.

In the second part of the thesis, the focus shifted to a generalized model (GM) approach of underlying interactions on multi-commodity dynamical
flow networks; especially the dynamics describing order placement,
scheduling and delivery. Such a network is cyclic and contains a feedback loop, where customers are less likely to order more products if they were recently delivered. This can range from someone not needing to purchase a
car if they just bought a brand new one to one not needing to order dinner when they just did so. Such networks are in general described by four kinds of elasticities in this thesis, namely the elasticities to stock, inventory level,
saturation, and co-production. These influence different parts in the network. For example, the negative elasticities to inventory level model that high inventory levels inhibit more inventory production, to prevent build-up,
and low inventory levels allow for larger inventory production, to prevent drainage. The other elasticities fulfil similar roles. This model was tested using a bifurcation analysis, a statistical ensemble method and by computing influences and sensitivities of parts and nodes in the network.

In this thesis I take a look at various aspects of the brachistochrone problem. In the first half I consider the classical brachistochrone problem, without friction, after which I generalize to also consider drag; friction proportional to the squared speed. I do this numerically, with the shooting method, and following some papers, which Euler wrote. Then I will look at how Euler's results compare to modern results and discuss how they are different. In the second half I consider the quantum brachistochrone problem, following a paper by A. Carlini, and afterwards I look at a related problem, where there is not enough time to change an electron spin between two predetermined states. This problem has been numerically solved in an example.