||An important issue in a distributed supply network is how to allocate the stocks to competing downstream nodes so as to minimize the total inventory holding cost while satisfying the end-customer service level requirements. In this thesis, an alternative allocation policy, Longest-Queue- First-Served (LQFS), is proposed and studied in a two-stage distributed supply network. Such an allocation policy represents one type of management mode, centralized information control structure, of collecting and utilizing information in production-inventory systems. The distributed supply system studied in this thesis is an inventory-queue network with inventory control at all nodes. An inventory-queue is a queueing model that incorporates an inventory replenishment policy for the output store. Following the specific allocation policy, all jobs (material and information) flow from one node to another in such a supply network. First, we investigate characteristics of the splitting departure processes under the LQFS allocation policy. We also provide the explicit solutions of the distribution and squared coefficient of variation of the in-terdeparture times in M/G/1 inventory queues. Because of the complexity of system and the LQFS policy, the exact analysis and calculation of the performance are utmostly difficult. Therefore, a simple and effective approximated approach, the decomposition method, is developed to evaluate the performance of the supply network under the LQFS policy. Lastly, the optimization problem is solved by using frontier curve method to minimize the total inventory holding capital meeting the end-customer service level under the LQFS policy. The optimal procedure can be split into two steps: (1) constructing the frontier curve for the specific service level; (2) searching the optimal base stock level on the frontier curve. The sensitivity analysis of the optimization under both LQFS and FCFS policies is addressed. The analytic and numerical results illustrate that approximated splitting and composite SCVs of inter-departure times in inventory queues are close to the simulation results. By comparing the effects of two allocation policies, the LQFS and FCFS policies, it can be seen from our numerical results of the optimization that the LQFS allocation policy performs better than the FCFS policy when the service times at the center node are exponential and hyperexponential distribution. In other words, when the density function of service times at the center node is monotonicity, the LQFS policy can optimize the total holding cost under the same conditions as the FCFS policy. This important founding of our research provide guidelines for managers in practical application of the LQFS policy. With the rapid development of information management technology, the centralized information management mode increasingly becomes preferred choice. The LQFS allocation policy will be integrated in the supply network to increase efficiency and coordination. This thesis contributes to this important trend and we expect our research results to unearth practical applications in supply chain management and electronic commerce and to stimulate further research in this direction.