Evaluation and Management of Sustainable Supply Chain Systems with Carbon Emissions and Transport Damage Based on Multi-state System Reliability Assessment

In this study, the performance and management of sustainable supply chains with certain risks are explored. A multi-state sustainable supply chain (MSSC) is modeled as a network with multi-state arcs (routes) and vertices (suppliers, customers, etc.). “Multi-state†refers to the risks of stochastic capacities (the number of available transportation facilities and vehicles) owing to maintenance and failures. “Sustainable†refers to carbon emissions and transport damage. To monitor and manage MSSCs, multi-state system reliability is calculated, which is the probability of transmitting customer demands within a specific carbon emission limitation with transport damage. Two algorithms are developed to generate minimal and maximal capacity vectors as necessary capacities satisfying the demands and upper bounds satisfying a carbon emission constraint, respectively, to calculate multi-state system reliability. The feasibility of the proposed methods is demonstrated using time complexity analyses. For management purposes, any capacity vector between the minimal and maximal capacity vectors represents a feasible solution. Managers can determine and monitor system states based on minimal and maximal capacity vectors. Finally, a real pineapple supply chain is studied. The best carbon emission limitation and selection for demand decrease are determined using multi-state system reliability evaluated by the proposed algorithms and sensitivity analyses.