System reliability for a multi-state distribution network with multiple terminals under stocks

To achieve the most efficiency in supply chain management, the capability of distribution networks is a key point for the entire supply chain. Stocks are critical for enhancing the efficiency of satisfying the demand of retailers in the distribution network. A configuration of a distribution network is consisted of routes and nodes. Each route connects a pair of nodes and each node is denoted as a supplier, a distribution center, or a retailer. For each route, it has a carrier whose available capacity for demand transmission is multi state. Hence, a distribution network is also regarded as a multi state network and such a network is named as a multi state distribution network (MDN) in here. The propose of this paper is to evaluate the system reliability which is defined as the probability that the MDN can meet all retailers' demand under stocks. In practical, all retailers' demand should be satisfied by stocks in the distribution centers (DCs) firstly. Therefore flow assignment in MDN model is mainly clarified by the relationship between the demand of retailers, stocks on DCs, and suppliers. The concept of minimal capacity vectors (MCVs) is then proposed and an algorithm is developed to obtaining MCVs for evaluating system reliability.