When designing and operating an order fulfillment system for an on-line retailer, many factors must be taken into account. We begin by discussing these factors and by proposing an architecture for a fulfillment system. The main goals of this dissertation are to construct a planning model and an execution model for managing inventory levels for each item at each stocking location in the fulfillment system. The planning model represents the system's operating architecture, the order response time requirements associated with customer orders and other operational constraints. This type of model is used in the sales and operations planning activities that are undertaken by an on-line retailer. It is not primarily intended to make daily procurement and allocation decisions. Rather, the planning model is designed to assist management when it makes warehousing, transportation, budgeting and collaboration decisions. The execution models are designed to make daily operational decisions. They indicate when inventories should be procured, how these inventories should be allocated throughout the warehousing network structure, and the timing of fulfilling customer orders. Real on-line retail systems contain millions of items. We describe an algorithm for making these execution decisions for each item at every location within seconds. Hence, both the planning and execution models we propose are of practical value. We report computational results for certain of these algorithms as well.