Globalization, product proliferation, and fast product innovation have significantly increased the complexities of supply chains in many industries. One of the most important advancements of supply chain management in recent years is the development of models and methodologies for controlling inventory in general supply networks under uncertainty and their widefspread applications to industry. These developments are based on three generic methods: the queueing-inventory method, the lead-time demand method and the flow-unit method. In this paper, we compare and contrast these methods by discussing their strengths and weaknesses, their differences and connections, and showing how to apply them systematically to characterize and evaluate various supply networks with different supply processes, inventory policies, and demand processes. Our objective is to forge links among research strands on different methods and various network topologies so as to develop unified methodologies. 1. Introduction Many real-world supply chains, such as those found in automotive, electronics, and consumer packaged goods industries, consist of large-scale assembly and distribution operations with geographically dispersed facilities. Clearly, many of these supply chains support the production and distribution of multiple end-products which are assembled from hundreds or thousands of subsystems and components with widely varying lead times and costs. One challenge in all these supply chains is the efficient management of inventory in a complex network of facilities and products with stochastic demand, random supply and high inventory and transportation costs. This requires one to specify the inventory policy for each product at each facility so as to minimize the system-wide inventory cost subject to customer service requirements. For many years, both practitioners and academicians have recognized the potential benefit of effective inventory control in such networks. In fact, the literature on multi-echelon inventory control can be dated back to the 1950s. However, it is only in the last few years that some of these benefits have been realized, see, for example, Lee and Billington [1], Graves and Willems [2], and Lin et al. [3]. Three reasons have contributed to this trend:(1) the availability of data, not only on network structure and bill of materials (BOMs), but also on demand processes, transportation lead times and manufacturing cycle times, and so forth;(2)industry that is searching for scientific methods for inventory management that help to cope with long lead times and
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