This thesis addresses the open questions of providing a cosmological model describing an accelerated expanding Universe without violating the energy conditions or a model that contributes to the physical interpretation of the dark energy. The former case is analyzed considering a closed model based on a regular lattice of black holes using the Einstein equation in vacuum. In the latter case I will connect the dark energy to the Shan-Chen equation of state. A comparison between these two proposals is then discussed. As a complementary topic I will discuss the motion of test particles in a general relativistic spacetime undergoing friction effects. This is modeled following the formalism of Poynting-Robertson whose link with the Stokes’ formula is presented. The cases of geodesic and non-geodesic motion are compared and contrasted for Schwarzschild, Tolman, Pant-Sah and Friedman metrics respectively.

In this study, we focus on a real life problem that involves a single item which is used in military operations. The items in use fail according to a Poisson process and lead times are deterministic. Four alternative inventory control models are developed. Among these models, a two-echelon system consisting of a depot in the upper and several bases in the lower echelon is operated currently. This system is compared to a single-echelon system that consists of several bases. The comparison reveals the importance of the holding cost incurred for the items intransit between the depot and the base which is ignored in most of the studies in literature. Both the two and single-echelon models are also extended to have repair ability. A continuous-review base-stock policy is used for all models. Exact models are formulated. The results are obtained under various lead time, unit costs and demand parameters. Results of four different settings are compared and the findings are reported.