Sensitivity Analysis

In this section, we describe the numerical studies that examine the return rates and profits of manufacturer of the proposed recycling models. We examine return rates and profits of the manufacturer in each recycling model by adjusting parameters, C , _L A, r, and b. The difference between the two proposed models is that the retailer collects those used products in the retailer collection model but those used products are collected by the third-party player in the current practice model. Then we are interested in the effect of different collection efforts on the return rate and the profits of manufacturer between the retailer and the third-party player. We also examine the performance measures in the two proposed models by taking into account some parameters such as C , _L A, r and b.

In the retailer collection model, those obsolete products are collected by the retailer instead of the third-party player who collects used products in the current recycling system.

Then we conduct sensitivity analysis to examine the performance of each recycling model when the collection effort parameters, C , are different between the retailer and the _L third-party player. Other parameters are given in Table 4 where C_L^C denotes the collection effort parameter in the current practice model.

Table 4: Parameters in Sensitivity Analysis of CL

CLC φ c b A r

200 40 10 15 5 15 We vary the values for collection effort parameter, C , in the retailer collection model _L from 180 to 580 which are 0.9 to 2.9 times of C_L^C when the collection effort parameter in

the current practice model, C_L^C, remains the same level. The results of the return rates and the profits of the manufacturer are depicted in Figure 8.

Figure 8: Return Rate and Profits of Manufacturer as Functions of CL

The ratio above one indicates that the performance measure in the retailer collection model is higher than that in the current practice model. The collection effort, I =C_L⋅τ², is the cost paid by the associated party who engages in collecting those returned products. An increase in C means that it is more costly to increase the return rate. As the collection _L

cost of the retailer, C , increases, the return rate and the profits of manufacturer in the _L retailer collection model decrease, even lower than the return rate and the profits of manufacturer in the current practice model. In this parameter setting, the return rate in the retailer collection model would be lower than that in the current practice model when the collection effort of the retailer is more than the third-party player’s collection effort about 2.5

0 1 2 3 4 5

0.9 1.3 1.7 2.1 2.5 2.9

Return Rate

Profits of Manufacturer Ratio of Performances

Ratio of C_L

times and the ratio of manufacturer’s profit would be lower than one when the ratio of C is _L over 2.9.

We also conduct sensitivity analysis to examine the performance measures affected by the collection effort parameter, C , and the collection service fee, A . Parameters are given _L in Table 5.

Table 5: Parameters in Sensitivity Analysis of CL and A

CLC φ c b ^r

200 40 10 15 15

We consider the values for collection service fee, A, from five to zero and the collection effort of the retailer, C_L, from 200 to 1000. Then the relationship of the return rate and the profits of manufacturer between the retailer collection model and the current practice model are depicted in Figure 9.

(a) (b)

Figure 9: Effect of Return Rate and Profits of Manufacturer by C and _L A

The return rate in the retailer collection model is better than that in the current practice model when the ratio of C and _L A are in the lower region of Figure 9(a). The manufacturer earns more profits in the retailer collection model than in the current practice model with any value of the collection service fee, A, when the ratio of C is less than _L

C_L Profits of Manufacturer

Retailer Collection Current Practice

Then we examine the interaction effect of the collection service fee, A, and the unit payment from the third-party player to the retailer in the retailer collection model, r, on the return rate and the profits of manufacturer. Other parameters are given in Table 6.

Table 6: Parameters in Sensitivity Analysis of r and A

CL φ c b

500 40 10 15

We vary the values for collection service fee, A, from five to zero and the payment from the third-party player to the retailer , r, from -5 to 50. Then the comparison results of the return rate and the profits of manufacturer between the retailer collection model and the current practice model are depicted in Figure 10.

Figure 10: Effect of Return Rate and Profits of Manufacturer by r and A

The retailer collection model acts better performances than the current practice model as r and A both increase. In the retailer collection model, the retailer has more incentive to collect obsolete products with a higher service fee or a higher unit payment from the third-party player. If r and A are in low levels, the retailer may not pay much attention on the collection work.

We also conduct sensitivity analysis for both, b and r, which are the unit revenue and cost from handling those returned products, to examine the return rate and the profits of manufacturer. Other parameters are given in Table 7.

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Table 7: Parameters in Sensitivity Analysis of r and b

CL φ c A

500 40 10 5

We vary the values of b from 10 to 15 and the values of r from -5 to 50. Then we depict the comparison results of the return rate and the profits of manufacturer between the retailer collection model and the current practice model in Figure 11.

Figure 11: Effect of Return Rate and Profits of Manufacturer by r and b

As the unit revenue from handling those returned products, b, increases, the return rate and the profits of manufacturer would increase in both proposed recycling models. From Figure 11, as b increases, we find that the current practice model acts better performances in a large range of r compared to the retailer collection model. Therefore, the effect of the parameter, b, in the current practice model is larger than in the retailer collection model.

We summarize some conclusions and future research in the next section.

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