The following analysis is based on the data in existing references36, 38, 39. The parameters are (C = 1000), (phi { = }100), (beta { = }0.3), (c_{m} = 20), and (Delta { = }15).Comparison of different modesIn this section, the optimal decisions of the three dual-channel collection modes are compared, and the reverse channel choice is explored from the perspectives of the collection rate and the total profit. In addition, the effects of third-party economies of scale are investigated.The retail price
Corollary 1
The retail prices in the three dual-channel collection modes are ordered as follows:
$$left{ begin{aligned} & p^{M& R*} > p^{M& TP*} > p^{R& TP*} quad if ;; 0 < delta < frac{{1 – alpha^{2} }}{{4 – alpha^{2} (5 – alpha^{2}…