Erratum to: Research on closed loop supply chain with reference price effect

Erratum to: J Intell Manuf DOI 10.1007/s10845-014-0961-0

There are some calculation errors in the original publication of the paper, and Figs. 1–4, 9–14, 16 and 17 were published incorrectly. Therefore, the authors would like to make the following rectification:

• 1. The inaccurate Figs. 1–4 should be replaced with a table (Table 1). The reason is that the optimal performance for the M-, R-, and 3P-managed models is so close to each other numerically, and the subtle difference was not illustrated in the figures. However, Table 1 in this erratum shows the actual difference and is more helpful in understanding Corollaries 1–3.

• 2. Secondly, the more accurate Figs. 9, 10, 11, 12, 13, 14, 16 and 17 are displayed with this erratum ($r=30$, $c_m =20$, $c_r =10$, $A=5$, B = 1,000, $\phi =100$, $\beta =0.5$).

Table 1 The effect of reference price coefficient on the optimal performance in $M$-, $R$- and 3P-managed channels, respectively

Fig. 9

The retail price ($R$) with reference price effect versus ($R^{\prime }$) without reference price effect in $R$-managed channel

Fig. 10

The manufacturer’s profit ($R$) with reference price effect versus ($R^{\prime })$ without reference price effect in $R$-managed channel

Fig. 11

The retailer’s profit ($R)$ with reference price effect versus ($R^{\prime }$) without reference price effect in $R$-managed channel

Fig. 12

The collection rate ($R)$ with reference price effect versus ($R^{\prime }$) without reference price effect in $R$-managed channel

Fig. 13

The manufacturer’s profit (3P) with reference price effect versus (3P $^{\prime }$) without reference price effect in 3P-managed channel

Fig. 14

The retailer’s profit (3P) with reference price effect versus (3P $^{\prime }$) without reference price effect in 3P-managed channel

Fig. 16

The retail price (3P) with reference price effect versus (3$P^{\prime }$) without reference price effect in 3P-managed channel

Fig. 17

The collection rate (3P) with reference price effect versus (3P $^{\prime }$) without reference price effect in 3P-managed channel