Stochastic Models for Inventory Systems and Networks

This dissertation, "Stochastic Models for Inventory Systems and Networks" by Hoi-lun, Allen, Tai, 戴凱倫, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled STOCHASTIC MODELS FOR INVENTORY SYSTEMS AND NETWORKS Submitted by TAI Hoi-Lun Allen for the degree of Master of Philosophy at The University of Hong Kong in July 2006 In managing an inventory system, constructing optimal ordering policy for replenishment is an important issue. In studying a social network, one major concern is the identification of certain prestigious members in it. In this thesis, some stochastic models were proposed for the captured problems in these top- ics. Numerical examples were also given to demonstrate the effectiveness of the proposed models. Renewal theory is a useful tool for system performance analysis. Here a sto- chasticmodelformachinereplacementsystemwasgiventoillustratetheconcept of renewal theory. A comparison between the quantity-based replacement pol- icy and the time-based replacement policy in a single machine system was also studied. These two policies are popular in inventory management. Recyclingofusedproductsisahotissueasthereisarisingconcernabouten- vironmentalprotection. Italsofavorscostreduction. Meanwhile, sincecustomers are usually scattered over a large regional area, a network of local warehouses for inventory of products and handling of returns is necessary to maintain a high service level. To further enhance the customer service level, Lateral Transship- ment(LT)isoftenallowedamongthelocalwarehouses. Bysharingtheinventory at the local warehouses, substantial savings can also be realized. In this thesis, a Markovian model was proposed to model a two-echelon inventory and return system. The system consisted of a supply plant, a central warehouse and several local warehouses. The local warehouses were capable of re-manufacturing used products and LT was also allowed in the system. In a Vendor-managed Inventory (VMI) system, the supplier is authorized to coordinate the inventories at the retailers level. The advantage of VMI is that the bullwhip effect can be minimized and the stock-out situations can also be reduced. Moreover, it provides a framework for synchronizing transportation decisions and hence reduces the transportation cost significantly. Here some sto- chastic models for a VMI system were built to analyze two dispatching policies, namely the quantity-based dispatching policy and the time-based dispatching policy. The long-run average costs for both policies were derived by using re- newal theory. The extension to the model of quantity-time-based dispatching policy was also discussed. The computation of prestige is an important issue in studying a social net- work. Anumberofeigenvector-likemethodshavebeenproposedforthemeasure- ment of prestige of both symmetric and asymmetric networks. The PageRank algorithm has been successfully applied in the computation of ranking of web- pages and data mining in the Internet. In this thesis, it was modified for the computation of the prestige of general social networks when negative relations were introduced. DOI: 10.5353/th_b3768175 Subjects: Stochastic analysis Inventory control - Statistical methods Social networks - Statistical methods