This thesis in the field of inventory management for deteriorating items studies the effects of deterioration on optimal policies in inventory and production-inventory models. Four different models are developed and analysed to address some of the gaps identified in this part of the inventory management literature. The first two models have been studied adopting the classic approach towards inventory modelling, where the holding cost is assumed to be proportional to a known exogenous unit holding cost parameter. Taking this approach, first a two-echelon (single-buyer, single-supplier) model is investigated in which the capacity is considered to be limited. In this model also the exact inventory level over time of the supplier is obtained whereas the literature to date has only considered the average inventory level. As the analysis shows, this results in a complex model, and therefore a heuristic is developed. In the second model, a single supplier, multiple buyers system is developed where there is a (in)finite production rate. It has been identified that the literature fails to calculate accurately the average inventory level of the supplier in situations where the production rate is finite. In this model this issue has been addressed, and further analysis reveals the significance of the more accurate modelling approach developed. The literature evaluates inventory models in different ways in terms of objective function. A body of research is identified in the literature that assumes an equivalence between profit maximisation and cost minimisation, and it often seems logical to discard revenues and minimise the cost function. This equivalence, however, is not always easily established when the objective function is to maximise the Net Present Value (NPV) of the profit function. In the third model of this thesis, this equivalence is analysed in detail, and it is shown that taking a cost minimisation model instead of a profit maximisation objective in some cases should be done cautiously and in the best case only adopted after establishing the relevant equivalence conditions using NPV Equivalence Analysis (NPVEA). Finally, in a fourth model a two-echelon supply chain with capacity constrains is developed using the NPV criterion. In this model a modification in the inventory level is suggested which makes the model more practical compared to the existing models in cases that the customers are serviced from the own warehouse.