Resolution of an Uncertain Closed-loop Logistics Model with Risk Analysis

Due to global warming, green supply chain management, in particular, logistics, has drawn the attention of researchers. Although there were closed-loop logistics models appeared in the literatures, most of them did not consider the uncertain environment in general terms. In this study, a generalized model was proposed when the uncertainty was expressed by fuzzy numbers. An interval programming model was proposed by the defined means and variances obtained from the integrated information of all level cuts of fuzzy numbers. Resolution for interval programming was based on the decision maker (DM)'s preference. The resultant solution provides useful information of the expected solutions under a confidence level with a risk degree. The results suggested that the more is the optimistic DM, the better is the resultant solution, yet with the higher risk of violating the resource constraints. By defining this risk with a probability, a solution procedure was developed with numerical illustration, which provides a DM a trade-off mechanism between logistic cost and the risk.