Distributionally robust design for bicycle-sharing closed-loop supply chain network under risk-averse criterion

Abstract The requirement of environmental improvement has led to the innovative emergence of shared bicycles. The production and recycling of shared bicycles are a closed logistics network, which can be considered a typical closed-loop supply chain (CLSC) problem. In practice, the CLSC network is influenced by social, economic and environmental factors, which impose high degrees of uncertainty and usually trigger various unanticipated risks, so controlling uncertain parameters becomes a key issue in supply chain decisions. The purpose of this research is to construct a new distributionally robust optimization model for a multi-product, multi-echelon CLSC network, in which the distributions of uncertain transportation cost, demand and the returned product are only partially known in advance. In the proposed model, robust mean-CVaR optimization formulation is employed as the objective function for a trade-off between the expected cost and the risk in the CLSC network. Further, to overcome the obstacle of model solvability resulting from imprecise probability distributions, two kinds of ambiguity sets are used to transform the robust counterpart into its computationally tractable forms. Finally, a case study on a Chinese bicycle-sharing company is addressed to validate the proposed robust optimization model. A comparison study is conducted on the performance between our robust optimization method and the traditional optimization method. In addition, a sensitivity analysis is performed with respect to the risk aversion parameter and the confidence level.