Delivery process is a critical issue from the viewpoint of supply chain management. However, in the delivery process, deterioration would occur because of natural disasters (e.g. earthquake, fire, flood, hurricane and landslide) or man-made factors (e.g. explosion, terrorist attack and vehicular collision). The results in the intact products arriving at the market may not satisfy the demand. This paper thus concentrates on a multi-state delivery network (MSDN) with multiple suppliers, in which a vertex denotes a supplier, a transfer station or a market, while a branch denotes a carrier providing the delivery service for a pair of vertices. The available capacity of the carrier responsible for the delivery on a branch is multi-state because the capacity may be partially reserved by other customers. The addressed problem is to evaluate the network reliability, the probability that the MSDN with the deterioration consideration can satisfy the market demand within the budget and production capacity limitations. An algorithm is developed in terms of minimal paths to evaluate the network reliability along with a numerical example to illustrate the solution procedure. A real case study of the deteriorating auto glass is utilised to demonstrate the utility of the proposed algorithm.