Coordinated control of Multi-Stage Inventory System
Abstract: This thesis is based on three scientific papers dealing with different models for coordinated control of multi-stage inventory systems. The ability to control multi-echelon inventory systems, is paramount for reducing tied up capital and inventory costs in large distribution systems. It is also one key issue in achieving efficient supply chain management. We focus our attention on a general distribution system, consisting of one central warehouse and N retailers, facing stochastic demand. The retailers replenish their stock from the central warehouse and the transportation times for these deliveries are assumed to be constant. However, due to stockouts at the warehouse the lead-times are still stochastic. The warehouse, on the other hand, replenishes its stock from an outside supplier, which provides constant lead-times. All stockouts, both at the warehouse and at the retailers, are backordered and delivered on a first-come-first-served basis. Inventory holding costs at both echelons, and backorder costs, proportional to the time until delivery at all retailers, are considered. The efficiency of the system is measured in terms of the expected long run holding and backorder costs per time unit. In Paper A, we consider a situation, where all installations in the system use continuous review installation-stock (R,Q) policies for controlling their inventory replenishments. We present a new decentralized model, based on limited information availability, for determining near optimal reorder points at all installations in the system. The restricted information availability is modeled by approximating the stochastic retailer lead-times with correct averages. By introducing a modified cost structure at the warehouse, we manage to decompose this multi-echelon inventory problem into N+1 single-stage problems, one for each installation. These sub-problems are then solved within the framework of a simple coordination procedure. The procedure can be interpreted as a negotiation process or a game where the different installations are the players. In the case of normally distributed customer demand, we can guarantee that the procedure converges to a near optimal solution. To assess the quality of the obtained solutions, a bound for the relative cost increase of using the lead-time approximation is provided. Paper B extends the decentralized modeling approach presented in Paper A to a more general setting, which allows for non-identical order quantities at the retailers. This seemingly minor generalization significantly enhances the practical value of the model. Further, we provide a tighter bound for the excess cost incurred by replacing the stochastic lead-times with correct averages. An alternative optimization procedure with better convergence properties is also presented In Paper C, we consider a slightly different representation of the general system where the customer demand is modeled as independent Poisson processes. To investigate the benefit of centralized inventory control a new replenishment policy is introduced at the warehouse. The retailers, on the other hand, still use continuous review installation-stock (R,Q) policies. The main theoretical contribution is that we provide an exact cost evaluation technique for the case when the new policy is used. A numerical study shows that there exist situations, where significant cost savings can be made by using the new policy instead of traditional echelon-stock and installation stock policies.
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