QUEUEING OPTIMIZATION AND MULTI-ECHELON AND MULTI-INDENTURE LOGISTICS SYSTEM WITH LIMITED CAPACITY (DIFFUSION, DYNAMIC PROGRAMMING, OPTIMAL CONTROL, APPROXIMATION, DEFENSE, INVENTORY)

The objectives of this study are: (1) to survey the current state of methodologies available (a) for the optimal control and numerical aspects of queueing systems, and (b) for analyzing a multi-echelon and multi-indenture logistics system, (2) to develop a new approach for determining the optimal number of servers in a time-dependent M/M/s queueing system using dynamic programming, and (3) to study a dynamic multi-echelon and multi-indenture logistics system with limited capacity during the initial surge period of an emergecy using the deterministic fluid approximation and the diffusion approximation.; Literature on methods available for the optimal control and for the numerical aspects of queueing system is reviewed briefly. For the multi-echelon and multi-indenture logistics system, studies based on the METRIC model are reviewed. This survey provides readers with a brief introduction to the existing methods.; A new approach to the optimal control of a time-dependent M/M/s queueing system is presented. Two models are used. The first is an M/M/s queueing system with time-dependent arrival rate that is solved numerically by using the fourth-order Runge-Kutta method. The second is a dynamic programming program in which an optimal number of servers is determined to be kept open during each shift (8-hour period) of a 24-hour day. The optimality criterion used is the total cost over a finite horizon.; In order to apply the diffusion approximation to the logistics system, an appropriate diffusion equation is derived. Invariant imbedding is introduced as a new approach to solve the diffusion equation. Formulation of the invariant imbedding approach is presented.; A simplified dynamic single-echelon and single-indenture logistics system is first investigated. The differences among unlimited, limited, and variable capacity is demonstrated by using the deterministic fluid approximation. The diffusion approximation is also applied to the system with limited capacity. Then the multi-indenture characteristics is added to investigate the relationship between an item (e.g., aircraft engine) and its sub-components (e.g., modules). The diffusion approximation is used to estimate the desired stock level of an item. Finally, multi-echelon part is added to examine the behavior of the Air Force logistics system. . . . (Author's abstract exceeds stipulated maximum length. Discontinued here with permission of author.) UMI...