Abstract: To encourage commercial banks behavioral changes that help lower the overall societal costs of cash processing and distribution by curtailing overuse of a free governmental service, the coordination mechanism of recirculation fee is proposed to motivate commercial banks (CBs) to reduce the cross-shipping and fulfill their fit-sorting obligations in a socially optimal manner. The influence of two types coordination mechanisms on the cross-shipping is studied. A nonlinear coordination mechanism is first proposed (NLRF) based on the recirculation fee with the linear characteristic (LRF) which is the current practice of foreign central bank, and the differences between them are analyzed in three aspects: the measurement standard, minimum quota and calculation method. To examine the efficacy of two mechanisms, the social optimum is then characterized using the Cash Closed-Loop Supply Chain (C-CLSP) framework, and the responses of commercial banks under LRF, NLRF and without mechanism are analyzed respectively by three decentralized optimization models of commercial banks. Numerical examples demonstrate that the CBs’ complex decision-making behaviors face the coordination mechanisms from various different aspects and the influence of different circulation parameters on the coordination effect. The results show that the LRF mechanism cannot guarantee a socially optimal response from CBs. NLRF mechanism, as a fundamentally different mechanism characterized non-linear, helps induce CBs to self-select the social optimum. Our mechanism incorporates a fairness adjustment that avoids penalizing CBs that recirculate their fair share of cash and rewards CBs that recirculate more than this amount.

Key words: cash closed-loop supply chain; cross-shipping; coordination mechanism