In the dissertation, the author studies two special inventory problems via the technique of optimization. The first problem discusses inventory management in monopoly markets in which utilities are involved. To utility companies, the inventory (materials and supplies) can be treated as an asset and affect the selling price of the utility. The results of the research indicate a potential behavior of utilities operating on an “inefficient” level of inventory and develop an optimal policy for maximizing profits in this scenario. The second problem discusses a basic two-echelon inventory problem – joint replenish problem (JRP). In the JRP, the first echelon contains only one installation serving several other installations in the second echelon. It tries to minimize the total cost related to the inventory. The dissertation focuses on the JRP with constraints of a fixed transportation capacity and dissimilar items. It is studied by two different demand models: continuous time and discrete time. In the continuous time model, a Poisson process of customer demand is considered and a Markov decision model is built to solve the problem. An efficient algorithm developed facilitates heuristic methods to find acceptable solutions out of an exponential solution space. The work for discrete time model considers a more general case and the initial efforts rely on the delayed renew process.