Performance analysis and optimization of supply networks

An important issue in supply chain and/or manufacturing system management is to control inventory costs along the chain while meeting the end-customer system service level requirement. In this thesis, we develop a network of inventory-queues model for the evaluation and optimization of a distributed manufacturing and supply network with inventory control at all sites. An inventory-queue is a queueing model that incorporates an inventory replenishment policy (base-stock, kanban, etc.) for the output store. A network of inventory-queues is a collection of inventory-queues in which materials/jobs flow from one queue to another following prespecified routings. Because of the complexity of this system, the exact analysis is extremely difficult, if not impossible. We evaluate the performance of the system by decomposing this network into multiple single-stage inventory-queues with modified raw material arrival processes. This approximation is simple and accurate. It enables us to carry out system optimization that minimizes the total inventory cost subject to the end-item (end-customer) service level requirement. The optimal solutions are proved to be on the “frontier curves” of the service level requirements which are independent of the cost parameters. For a two-stage problem, the elements on a frontier curve can be sorted by a single parameter and the frontier curve can be easily determined. The optimization procedure can thus be divided into two steps: (1) obtaining the frontier curve for the specific service level requirement; (2) finding the optimal solution on the frontier curve with specific cost parameters. This division allows us to conduct cost parameter sensitivity analysis easily. For multi-stage optimization problems, it is very difficult to obtain the entire frontier curve and a two-step relaxation method is proposed. We construct a relaxed problem of the original one. This relaxation has good analytical properties and its optimal solution can be computed easily. From this optimal solution, we then search for a feasible solution of the original problem on the frontier curve with a searching scheme. An upper bound has been derived for the error due to the relaxation approach.; Our numerical results show that when inventory holding unit costs are different at different production stages, it is desirable to use intermediate inventory control. In other words, in a make-to-stock system, when finished goods (FG) inventory is more costly than work-in-progress (WIP), minimizing WIP may not be a good approach to provide satisfactory service level. It is more cost-effective to actively manage WIP and create “WIP buffers” at appropriate locations. As a result, it may be better to allocate high variable server to some upstream stage other than to the last one, as suggested in the literature for systems where actual inventory costs are not explicitly considered.; As today's manufacturing competition becomes increasingly more focused on operational issues and customer-based service level improvements, there is an emerging need to integrate the traditional queueing analysis and inventory control theory so as to provide tools and solutions for more complicated design and control problems. Here, we contribute to this important field by developing an effective and systematic approach for a large class of systems. We expect our research results to find ample applications in manufacturing logistics and supply chain management, and to stimulate further research along this direction.