Under Scenario S (Fig. 2a), the gradient remanufacturer offers a selling option alone in the EVB secondary use market. In this case, the EVB secondary users (or consumers) have no choice but to purchase or remain inactive. Let (varphi) denote consumers' perceived value of spent EVBs, which is uniformly. Under scenario S, the optimal pricing of the sorter and the gradient remanufacturer is (w_{h}^{(S) * } = frac{{1 + v_{f} - c_{g} }}{2} = frac{{1 - c + varphi rho + c(rho - rho_{0} )^{2} }}{2}),. Under Scenario S, if (m ge c_{s} + p_{u} - 2w_{l} (1 - alpha )beta) or if (m < c_{s} + p_{u} - 2w_{l} (1 - alpha )beta) and (Q_{r} le overline{Q}_{r}), we have (pi_{s}^{(S) * } ge pi_{g}^{(S) *. Under Scenario L (Fig. 2b), the EVB supply chain merely provides a leasing option to the EVB secondary users. We assume that the level of consumers' preference for a lease option is (theta). Additionally, unlike the sell option, the lease option means consumers have no ownership of EVBs, thus leading to the non-existence of residual value in con. Under Scenario L, the optimal pricing of the sorter and the gradient remanufacturer are (w_{h}^{(L) * } = frac{{theta - c_{g} }}{2} = frac{{theta - c + c(rho - rho_{0} )^{2} }}{2}), (p_{fl}^{(L) * } = frac{{3theta + c_{g} }}{4} = frac{{3theta + c - c(rho - rho_{0} )^{2} }}{4}), respectively. By Lemma 2, we can determine the optimal.
