This dissertation addresses a few fundamental questions on the interface between supplier financing schemes and inventory management. Traditionally, retailers finance their inventories through an independent financing institution or by drawing from their own cash reserves, without any supplier involvement ( Independent Financing ). However, suppliers may reduce their buyers' costs and stimulate sales and associated revenues and profits, by either (i) adopting the financing function themselves (Trade Credit ), or (ii) subsidizing the inventory costs (Inventory Subsidies ). In the first part (Chapter 2) we analyze and compare the equilibrium performance of supply chains under these three basic financing schemes. The objective is to compare the equilibrium profits of the individual chain members, the aggregate supply chain profits, the equilibrium wholesale price, the expected sales volumes and the average inventory levels under the three financing options, and thus provide important insights for the selection and implementation of supply chain financing mechanisms. Several of the financing schemes introduce a new type of inventory control problem for the retailers in response to terms specified by their suppliers. In Chapter 3 we therefore consider the inventory management problem of a firm which incurs inventory carrying costs with a generalshelf age dependent structure and, even more generally, that of a firm with shelf age and delay dependent inventory and backlogging costs. Beyond identifying the structure of optimal replenishment strategies and corresponding algorithms to compute them, it is often important to understand how changes in various primitives of the inventory model impact on the optimal policy parameters and performance measures. In spite of a voluminous literature over more than fifty years, very little is known about this area. In Chapter 4, we therefore study monotonicity properties of stochastic inventory systems governed by an ( r,q ) or ( r,nq ) policy and apply the results in our general theorems both to standard inventory models and to those with general shelf age and delay dependent inventory costs.