Network reliability with deteriorating product and production capacity through a multi-state delivery network

Abstract

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.

Hybrid fuzzy-probabilistic approach to supply chain resilience assessment

“…Xu et al (2014) develop a quantitative model for analysis of predicted SC resilience based on structural evolution against random supply disruptions. The study by Lin et al (2014) concentrates on the reliability assessment for a multi-state SC with multiple suppliers as the probability to satisfy the market demand within the budget and production capacity limitations.…”

Conventional and Improved Inclusion-Exclusion Derivations of Symbolic Expressions for the Reliability of a Multi-State Network

“…Lin et al [22] studied a specific multi-state delivery network (MSDN) with multiple suppliers, one market, multiple transfer centers and eight branches. They derived an expression of system success for specific data of delivery costs, probability distributions of all branches, available capacities, suppliers' production capacities, deterioration rate vector for the minimal paths obtained, demand, and budget.…”

“…This paper deals with a fundamental application of the IE principle to the computation of multistate reliability, specifically the computation of the expectation of the logical expression of a multi-state disjunctive normal form (DNF). Currently, the most computationally efficient method for handling this problem is an automated implementation of the method of the recursive sum of disjoint products (RSDP) [21,22]. We present a tutorial discussion and exposition of the conventional IE method and an improved IE approach for solving this problem.…”

“…The organization of the remainder of this paper is as follows. Section 2 introduces the running example used herein of a multi-state delivery network (MSDN) with multiple suppliers, borrowed from Lin et al [22]. Section 3 introduces the multi-state inclusion-exclusion (MS-IE) principle, and hints at its special cases and improved variants.…”

Supply chain dynamics, control and disruption management

“…Benyoucef, Xie, and Tanonkou (2013) consider supply chain design with unreliable suppliers. The study by Lin, Huang, and Yeh (2014) concentrates on the reliability assessment for a multi-state SC with multiple suppliers as the probability to satisfy the market demand within the budget and production capacity limitations. They develop an algorithm in terms of minimal paths to evaluate the network reliability along with a numerical example regarding auto glass.…”