# Pricing of Complementary Products in Online Purchasing under Return Policy

^{1}

^{2}

^{3}

^{4}

^{*}

*J. Theor. Appl. Electron. Commer. Res.*

**2021**,

*16*(5), 1718-1739; https://doi.org/10.3390/jtaer16050097

## Abstract

**:**

## 1. Introduction

- How do online distributors determine the optimal selling price, optimal quality level, and optimal refund amount for two complementary products?
- How can online distributors maximize the total profits of the system when the conditions of the selling price, refund amount, and quality of products are all assumed to be at the optimum values?
- When customer’s demands are highly sensitive to the selling price, how should online distributors determine the optimal product quality and the refund amount?
- How should online distributors indicate the refund amount and product quality when the sensitivity of customers to product quality is high?
- When customers are more sensitive to refund amounts, how should online distributors set the optimal price and product quality?

## 2. Relevant Works

#### 2.1. Return Policy

#### 2.2. Pricing of Complementary Products

## 3. Problem Definition and Modeling

- The two complementary products are considered;
- The product quality level refers to the consistency between the purchased product and its online description;
- The online distributor’s total profit is obtained by the summation of each product’s profit function;
- The demand for each product is sensitive to its price and the price of the other product;
- The refund amount for both products influences the demand;
- A low quality of product causes customer dissatisfaction and leads to an increase in the number of returns.

#### 3.1. Demand Function

#### 3.2. Return Function

#### 3.3. The Online Distributor’s Profit

^{th}product is defined as the difference between revenue and cost (producing and quality costs). By considering Equations (1)–(4), the firm’s model can be formulated as follows:

## 4. A Special Case of the Proposed Model

## 5. Solution Method

**Proposition 1.**

**Proof.**

_{1}, q

_{1,}and r

_{1}(p

_{2}, q

_{2,}and r

_{2}) that maximize the profit of selling the first product (and the second product).

**Proposition 2.**

**Proof.**

**Proposition 3.**

- (1)
- The optimal pricing for the first product is as follows:

- (2)
- The optimal refund amount for the first product is as follows:

- (3)
- The optimal quality policy for the first product is as follows:

- (4)
- The optimal pricing for the second product is as follows:

- (5)
- The optimal refund amount for the second product is as follows:

- (6)
- The optimal quality policy for the second product is as follows:$${q}_{2}^{*}=\frac{{\psi}_{2}{r}_{2}^{*}}{2{\lambda}_{2}}$$

## 6. Solution Algorithm

## 7. Illustrative Example

**Example 1.**

**Example 2.**In this example, we changed the parameters as follows:

#### 7.1. Sensitivity Analysis

- For the first product, optimal values of the decision variables are highly sensitive to an increase in α
_{1}; - ${q}_{1}^{*}$ is highly sensitive to a decrease in ${\lambda}_{1}$, and ${q}_{2}^{*}$ is highly sensitive to a decrease in ${\lambda}_{2}$;
- Optimal values for decision variables are moderately sensitive to decreases in ${\gamma}_{1}$ and ${\gamma}_{2}$;
- ${q}_{1}^{*}$ is sensitive to an increase in ${\psi}_{1}$, and ${q}_{2}^{*}$ is sensitive to an increase in ${\psi}_{2}$;
- Optimal values for decision variables are slightly sensitive to changes in ${\varphi}_{1}$ and ${\varphi}_{2}$;
- ${q}_{1}^{*}$ and ${r}_{1}^{*}$ are highly sensitive to a 40% decrease in parameter ${\phi}_{1}$;
- ${q}_{2}^{*}$ and ${r}_{2}^{*}$ are highly sensitive to a 40% decrease in parameter ${\phi}_{2}$;
- For the first product, optimal values of the decision variables are highly sensitive to a 40% decrease in parameter ${\beta}_{1}$;
- For the second product, optimal values of the decision variables are highly sensitive to a 40% decrease in parameter ${\beta}_{2}$;
- ${q}_{1}^{*}$ and ${r}_{1}^{*}$ are sensitive to a 40% increase in parameter ${\upsilon}_{11}$;
- ${q}_{2}^{*}$ and ${r}_{2}^{*}$ are sensitive to a 40% increase in parameter ${\upsilon}_{22}$;
- ${q}_{2}^{*}$ and ${r}_{2}^{*}$ are moderately sensitive to a 40 and 20% increase, respectively, parameter ${\upsilon}_{12}$;
- Change in the values of ${\omega}_{1}$ and ${\omega}_{2}$ does not have a significant effect on the optimal value of decision variables.

#### 7.2. Managerial Insight

- This study filled an important research gap in presenting a comprehensive model for two complementary products in online selling where a return policy exists, by deciding on the selling price, quality level, and refund amount for returned products.
- As the potential market demand has a positive effect on the online distributor’s profit, the managers should try to expand the target market of their products by applying appropriate marketing policies.
- Managers of two complementary products should spend more on the refund of returned products when the sensitivity of demand to refund amount is high. By applying this strategy, the demand will increase, and the online distributor can increase the selling price and quality.
- With an increasing sensitivity of returned quantity with respect to product quality, the online distributor should provide products with a higher quality and, correspondingly, retain the price and the refund amount.
- Managers should decrease the price of the first (or second) product by increasing the sensitivity of its demand to price. In contrast, they are advised to increase the price of the second (or first) product.
- The negative effect of the quality cost parameter on profit implies that managers should reduce the quality and keep the refund on returned products unchanged. In other words, they should take the position of “low quality and low price”.
- When customers are less sensitive to a return policy, they will pay more attention to quality. Thus, managers should seek a lenient return policy, such as increasing the quality and refund on returned products.
- The proposed model is a proper starting point to present a new model that considers other marketing variables, such as advertising.

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Appendix A. A Proof of the Concavity of the Profit Functions for the Both Products

## Appendix B. A Proof of the Concavity of the Total Profit Functions with Respect to Hessian Matrix

## Appendix C. Deriving the Optimal Decision Variables

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Symbol | Definition |
---|---|

i | Set of products (for i = 1,2) |

D_{i} | The demand function of the i^{th} product (units) |

α_{i} | The potential market demand for the i^{th} product (units) |

${\gamma}_{i}$ | The sensitivity of the i^{th} product demand with respect to the selling price of the (3-i)^{th} product |

${\upsilon}_{ii}$ | The sensitivity of the i^{th} product demand with respect to the return rate of the i^{th} product |

${\upsilon}_{ij}$ | The sensitivity of the i^{th} product demand with respect to the return rate of the (3-i)^{th} product |

${\beta}_{i}$ | $\mathrm{The}\mathrm{sensitivity}\mathrm{of}\mathrm{the}\mathrm{demand}\mathrm{of}\mathrm{the}{i}^{\mathrm{th}}\mathrm{product}\mathrm{with}\mathrm{respect}\mathrm{to}\mathrm{its}\mathrm{selling}\mathrm{price},{\beta}_{i}{\upsilon}_{ii},{\psi}_{i}$ |

${\varphi}_{i}$ | The return quantity factor of the i^{th} product that is not dependent on quality and return policy |

${\phi}_{i}$ | $\mathrm{The}\mathrm{sensitivity}\mathrm{of}\mathrm{the}{i}^{\mathrm{th}}\mathrm{product}\mathrm{returns}\mathrm{quantity}\mathrm{with}\mathrm{respect}\mathrm{to}\mathrm{its}\mathrm{return}\mathrm{policy},{\phi}_{i}{\upsilon}_{ii},{\psi}_{i}$ |

${\psi}_{i}$ | The sensitivity of the i^{th} product returns quantity with respect to its quality level |

${C}_{i}$ | The total quality improvement cost of the i^{th} product (USD) |

${\lambda}_{i}$ | $\mathrm{The}\mathrm{constant}\mathrm{parameters}\mathrm{of}\mathrm{the}\mathrm{quality}\mathrm{cos}\mathrm{t}\mathrm{function}\mathrm{of}\mathrm{the}{i}^{\mathrm{th}}\mathrm{product},{\lambda}_{i}1$ |

${R}_{i}$ | The returned quantity of the i^{th} product (unit) |

${w}_{i}$ | The unit producing cost of the i^{th} product (USD/unit) |

${\omega}_{i}$ | The return quantity of the i^{th} product affected by the return quantity of the (3-i)^{th} product |

TPF | The total profit function (USD) |

Symbol | Definition |
---|---|

${p}_{i}$ | The selling price of the i^{th} product (USD/unit) |

${r}_{i}$ | The refund amount on the return of the i^{t}^{h} product (USD/unit) |

${q}_{i}$ | $\mathrm{The}\mathrm{quality}\mathrm{level}\mathrm{of}\mathrm{the}{i}^{\mathrm{th}}\mathrm{product}(0\le {q}_{i}\le 1$) |

Percentage | New Value of Decision Variable | Change Percentage of Decision Variable | TPF | ||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

${\mathit{p}}_{1}^{*}$ | ${\mathit{p}}_{2}^{*}$ | ${\mathit{q}}_{1}^{*}$ | ${\mathit{q}}_{2}^{*}$ | ${\mathit{r}}_{1}^{*}$ | ${\mathit{r}}_{2}^{*}$ | ${\mathit{p}}_{1}^{*}$ | ${\mathit{p}}_{2}^{*}$ | ${\mathit{q}}_{1}^{*}$ | ${\mathit{q}}_{2}^{*}$ | ${\mathit{r}}_{1}^{*}$ | ${\mathit{r}}_{2}^{*}$ | ${\mathit{\pi}}^{*}$ | |||

${\alpha}_{1}$ = 1400 | −40% | 840 | 93.9 | 920.3 | 0.17 | 0.51 | 60.7 | 155 | −84% | 36% | −69% | 4% | −69% | 3% | 709.140 |

−20% | 1120 | 342.9 | 797.6 | 0.36 | 0.50 | 129.2 | 152.4 | −42% | 18% | −35% | 2% | −34% | 1% | 766.960 | |

20% | 1680 | 840.9 | 552.2 | 0.76 | 0.49 | 266.1 | 147.3 | 42% | −18% | 35% | 0% | 34% | −1% | 1091.800 | |

40% | 1960 | 1090 | 429.5 | 0.95 | 0.48 | 334.5 | 144.7 | 84% | −36% | 69% | −2% | 69% | −3% | 1358.700 | |

${\alpha}_{2}$ = 1500 | −40% | 900 | 855 | 161.9 | 0.72 | 0.28 | 254.7 | 84.2 | 44% | −76% | 28% | −42% | 28% | −43% | 651.170 |

−20% | 1200 | 723.5 | 418.4 | 0.64 | 0.39 | 226.1 | 117 | 22% | −38% | 14% | −20% | 14% | −21% | 734.310 | |

20% | 1800 | 460.4 | 931.4 | 0.48 | 0.60 | 169.1 | 182.7 | −22% | 38% | −14% | 22% | −14% | 21% | 1131.700 | |

40% | 2100 | 328.9 | 1187.9 | 0.40 | 0.71 | 140.6 | 215.6 | −44% | 76% | −28% | 44% | −28% | 43% | 1446 | |

${\lambda}_{1}$ = 70 | −40% | 42 | 592 | 674.9 | 0.94 | 0.49 | 197.8 | 149.9 | 0.01% | 0% | 67% | 0% | 0.55% | 0% | 894.510 |

−20% | 56 | 591.9 | 674.9 | 0.70 | 0.49 | 197.7 | 149.9 | 0% | 0% | 25% | 0% | 0.50% | 0% | 894.500 | |

20% | 84 | 591.9 | 674.9 | 0.47 | 0.49 | 197.6 | 149.9 | 0% | 0% | −16% | 0% | 0% | 0% | 894.490 | |

40% | 98 | 591.9 | 674.9 | 0.40 | 0.49 | 197.6 | 149.9 | 0% | 0% | −28% | 0% | 0% | 0% | 894.490 | |

${\lambda}_{2}$ = 60 | −40% | 36 | 591.9 | 674.9 | 0.56 | 0.83 | 197.6 | 150 | 0% | 0% | 0% | 69% | 0% | 0.06% | 894.510 |

−20% | 48 | 591.9 | 674.9 | 0.56 | 0.62 | 197.6 | 149.9 | 0% | 0% | 0% | 26% | 0% | 0% | 894.500 | |

20% | 72 | 591.6 | 674.9 | 0.56 | 0.41 | 197.6 | 149.8 | −0.05% | 0% | 0% | −16% | 0% | −0.06% | 894.490 | |

40% | 84 | 591.6 | 674.9 | 0.56 | 0.35 | 197.6 | 149.8 | −0.05% | 0% | 0% | −28% | 0% | −0.06% | 894.490 | |

${\gamma}_{1}$ = 0.4 | −40% | 0.24 | 648.5 | 712.3 | 0.61 | 0.53 | 215.8 | 160 | 9% | 5% | 8% | 8% | 9% | 6% | 961.840 |

−20% | 0.32 | 619.8 | 692.3 | 0.59 | 0.51 | 206.5 | 154.7 | 4% | 2% | 5% | 4% | 4% | 3% | 926.940 | |

20% | 0.48 | 564.4 | 660.1 | 0.53 | 0.48 | 188.9 | 145.5 | −4% | −2% | −5% | −2% | −4% | −2% | 864.290 | |

40% | 0.56 | 536.6 | 648.3 | 0.51 | 0.47 | 180.3 | 141.6 | −9% | −3% | −8% | −4% | −8% | −5% | 836.120 | |

${\gamma}_{2}$ = 0.4 | −40% | 0.24 | 646.5 | 714.1 | 0.61 | 0.53 | 215.3 | 160.2 | 9% | 5% | 8% | 8% | 8% | 6% | 961.740 |

−20% | 0.32 | 618.7 | 693.3 | 0.58 | 0.51 | 206.3 | 154.8 | 4% | 2% | 3% | 4% | 4% | 3% | 926.900 | |

20% | 0.48 | 565.7 | 658.9 | 0.54 | 0.48 | 189.3 | 145.4 | −4% | −2% | −3% | −2% | −4% | −3% | 864.300 | |

40% | 0.56 | 539.6 | 645.5 | 0.51 | 0.47 | 181.1 | 141.3 | −8% | −4% | −8% | −4% | −8% | −5% | 836.120 | |

${\psi}_{1}$ = 0.4 | −40% | 0.24 | 591.9 | 674.9 | 0.33 | 0.49 | 197.5 | 149.9 | 0% | 0% | −41% | 0% | −0.05% | 0% | 894.488 |

−20% | 0.32 | 591.9 | 674.9 | 0.45 | 0.49 | 197.5 | 149.9 | 0% | 0% | −19% | 0% | −0.05% | 0% | 894.490 | |

20% | 0.48 | 591.9 | 674.9 | 0.67 | 0.49 | 197.7 | 149.9 | 0% | 0% | 19% | 0% | 0.05% | 0% | 894.510 | |

40% | 0.56 | 591.9 | 674.9 | 0.79 | 0.49 | 197.9 | 149.9 | 0.01% | 0% | 41% | 0% | 0.15% | 0% | 894.520 | |

${\psi}_{2}$ = 0.4 | −40% | 0.24 | 591.9 | 674.9 | 0.56 | 0.29 | 197.6 | 149.8 | 0% | 0% | 0% | −40% | 0% | −0.06% | 894.480 |

−20% | 0.32 | 591.9 | 674.9 | 0.56 | 0.39 | 197.6 | 149.8 | 0% | 0% | 0% | −20% | 0% | −0.06% | 894.490 | |

20% | 0.48 | 591.9 | 674.9 | 0.56 | 0.59 | 197.6 | 149.9 | 0% | 0% | 0% | 20% | 0% | 0% | 894.500 | |

40% | 0.56 | 591.9 | 674.9 | 0.56 | 0.70 | 197.6 | 150 | 0% | 0% | 0% | 42% | 0% | 0.06% | 894.510 | |

${\varphi}_{1}$ = 0.1 | −40% | 0.06 | 592 | 674.9 | 0.56 | 0.49 | 197.8 | 149.9 | 0% | 0% | 0% | 0% | 0.05% | 0% | 894.525 |

−20% | 0.08 | 591.9 | 674.9 | 0.56 | 0.49 | 197.8 | 149.9 | 0% | 0% | 0% | 0% | 0.05% | 0% | 894.521 | |

20% | 0.12 | 591.9 | 674.9 | 0.56 | 0.49 | 197.7 | 149.9 | 0% | 0% | 0% | 0% | 0% | 0% | 894.513 | |

40% | 0.14 | 591.9 | 674.9 | 0.56 | 0.49 | 197.7 | 149.9 | 0% | 0% | 0% | 0% | 0% | 0% | 894.509 | |

${\varphi}_{2}$ = 0.1 | −40% | 0.06 | 591.9 | 674.9 | 0.56 | 0.50 | 197.8 | 150 | 0% | 0% | 0% | 0% | 0% | 0% | 894.538 |

−20% | 0.08 | 591.9 | 674.9 | 0.56 | 0.50 | 197.8 | 150 | 0% | 0% | 0% | 0% | 0% | 0% | 894.536 | |

20% | 0.12 | 591.9 | 674.9 | 0.56 | 0.49 | 197.7 | 149.9 | 0% | 0% | 0% | −2% | −0.05% | −0.06% | 894.530 | |

40% | 0.14 | 591.9 | 674.9 | 0.56 | 0.49 | 197.7 | 149.9 | 0% | 0% | 0% | −2% | −0.05% | −0.06% | 894.526 | |

${\phi}_{1}$ = 0.5 | −40% | 0.3 | 625.8 | 662.6 | 0.98 | 0.50 | 345.5 | 150.2 | 5% | −1% | 75% | 2% | 74% | 0.2% | 908.070 |

−20% | 0.4 | 604.2 | 670.4 | 0.71 | 0.50 | 251.4 | 150 | 2% | −0.66% | 26% | 2% | 27% | 0.06% | 899.440 | |

20% | 0.6 | 583.9 | 677.8 | 0.46 | 0.49 | 162.8 | 149.8 | −1% | 0.42% | −17% | 0% | −17% | −0.06% | 891.300 | |

40% | 0.7 | 578.3 | 679.8 | 0.39 | 0.49 | 138.4 | 149.7 | −2% | 0.72% | −30% | 0% | −29% | −0.13% | 889.060 | |

${\phi}_{2}$ = 0.6 | −40% | 0.36 | 592 | 687.8 | 0.56 | 0.84 | 198.2 | 253.5 | 0.01% | 1% | 0% | 71% | 0.3% | 69% | 903.590 |

−20% | 0.48 | 592 | 679.7 | 0.56 | 0.62 | 197.8 | 188.4 | 0.01% | 0.71% | 0% | 26% | 0.1% | 25% | 897.870 | |

20% | 0.72 | 591.9 | 671.7 | 0.56 | 0.41 | 197.5 | 124.4 | 0% | −0.47% | 0% | −16% | −0.05% | −17% | 892.270 | |

40% | 0.84 | 591.9 | 669.5 | 0.56 | 0.35 | 197.4 | 106.4 | 0% | −0.8%1% | 0% | −28% | 0.1% | −29% | 890.680 | |

${\beta}_{1}$ = 0.8 | −40% | 0.48 | 1367.5 | 292.8 | 1 | 0.47 | 410.8 | 141.9 | 100% | −56% | 78% | −4% | 100% | −5% | 1148.700 |

−20% | 0.64 | 825.4 | 559.8 | 0.74 | 0.49 | 261.8 | 147.5 | 39% | −17% | 32% | 0% | 32% | −1% | 971.030 | |

20% | 0.96 | 461.9 | 739 | 0.46 | 0.50 | 161.9 | 151.2 | −21% | 9% | −17% | 2% | −18% | 0.86% | 851.880 | |

40% | 1.12 | 379 | 779.8 | 0.39 | 0.50 | 139.1 | 152.1 | −35% | 15% | −30% | 2% | −29% | 1% | 824.720 | |

${\beta}_{2}$ = 0.8 | −40% | 0.48 | 177.4 | 1483.2 | 0.30 | 0.84 | 107.8 | 253.4 | −70% | 100% | −46% | 71% | −45% | 69% | 1210.600 |

−20% | 0.64 | 462.7 | 926.8 | 0.48 | 0.60 | 169.6 | 182.1 | −21% | 37% | −14% | 22% | −14% | 21% | 992.920 | |

20% | 0.96 | 665.6 | 531.2 | 0.61 | 0.43 | 213.6 | 131.5 | 12% | −21% | 8% | −12% | 8% | −12% | 838.400 | |

40% | 1.12 | 713.2 | 438.3 | 0.63 | 0.39 | 223.9 | 119.6 | 20% | −35% | 12% | −20% | 13% | −20% | 802.160 | |

${\upsilon}_{11}$ = 0.3 | −40% | 0.18 | 562.5 | 687.6 | 0.35 | 0.50 | 123.3 | 152.6 | −4% | 1% | −37% | 2% | −37% | 1% | 884.230 |

−20% | 0.24 | 575.1 | 682.3 | 0.45 | 0.50 | 159.1 | 151.3 | −2% | 1% | −19% | 2% | −19% | 0.93% | 888.680 | |

20% | 0.36 | 613.6 | 665.2 | 0.68 | 0.49 | 239.8 | 148.3 | 3% | −1% | 21% | 0% | 21% | −1% | 901.920 | |

40% | 0.42 | 641.1 | 652.7 | 0.81 | 0.48 | 286.8 | 146.5 | 8% | −3% | 44% | −2% | 45% | −2% | 911.280 | |

${\upsilon}_{22}$ = 0.2 | −40% | 0.12 | 596.2 | 662 | 0.57 | 0.32 | 201 | 104.8 | 0.72% | −1% | 1% | −30% | 1% | −30% | 888.370 |

−20% | 0.16 | 594.4 | 667.6 | 0.56 | 0.42 | 199.4 | 127 | 0.42% | −1% | 0% | −14% | 0.91% | −15% | 891.130 | |

20% | 0.24 | 588.6 | 683.8 | 0.55 | 0.57 | 195.7 | 173.4 | −0.55% | 1% | −1% | 16% | −0.96% | 15% | 898.530 | |

40% | 0.28 | 584.4 | 694.4 | 0.55 | 0.66 | 193.4 | 198 | −1% | 2% | −1% | 34% | −2% | 32% | 903.260 | |

${\upsilon}_{12}$ = 0.1 | −40% | 0.06 | 587.5 | 674.6 | 0.56 | 0.43 | 197.5 | 130.3 | −0.74% | −0.04% | 0% | −12% | −0.05% | −13% | 891.500 |

−20% | 0.08 | 589.6 | 674.8 | 0.56 | 0.46 | 197.5 | 140 | −0.38% | −0.01% | 0% | −6% | −0.05% | −6% | 892.940 | |

20% | 0.12 | 594.6 | 674.8 | 0.56 | 0.53 | 197.8 | 159.8 | 0.45% | −0.01% | 0% | 8% | 0.05% | 6% | 896.170 | |

40% | 0.14 | 597.7 | 674.5 | 0.56 | 0.56 | 198.1 | 169.8 | 0.97% | −0.05% | 0% | 14% | 0.25% | 13% | 897.970 | |

${\upsilon}_{21}$ = 0.05 | −40% | 0.03 | 590.3 | 673 | 0.52 | 0.50 | 183.9 | 150 | −0.27% | −0.28% | −7% | 2% | −6% | 0.06% | 892.090 |

−20% | 0.04 | 591.1 | 673.9 | 0.54 | 0.49 | 190.7 | 149.9 | −0.13% | −0.14% | −3% | 0% | −3% | 0% | 893.270 | |

20% | 0.06 | 592.6 | 676 | 0.58 | 0.49 | 204.5 | 149.8 | 0.11% | 0.16% | 3% | 0% | 3% | −0.06% | 895.770 | |

40% | 0.07 | 593.3 | 677.2 | 0.60 | 0.49 | 211.4 | 149.8 | 0.23% | 0.34% | 7% | 0% | 6% | −0.06% | 897.100 | |

${\omega}_{1}$ = 0.1 | −40% | 0.06 | 592.9 | 674.5 | 0.57 | 0.50 | 202 | 150 | 0.16% | −0.05% | 1% | 2% | 2% | 0.06% | 895.330 |

−20% | 0.08 | 592.4 | 674.7 | 0.57 | 0.50 | 199.8 | 150 | 0.08% | −0.02% | 1% | 2% | 1% | 0.06% | 894.910 | |

20% | 0.12 | 591.4 | 675.1 | 0.55 | 0.49 | 195.5 | 149.8 | −0.08% | 0.02% | −1% | 0% | −1% | −0.06% | 894.090 | |

40% | 0.14 | 590.9 | 675.2 | 0.55 | 0.49 | 193.3 | 149.7 | −0.16% | 0.04% | −1% | 0% | −2% | −0.13% | 893.680 | |

${\omega}_{2}$ = 0.1 | −40% | 0.06 | 592 | 675.3 | 0.56 | 0.51 | 197.9 | 153.6 | 0.01% | 0.05% | 0% | 4% | 0.15% | 2% | 895.200 |

−20% | 0.08 | 591.9 | 675.1 | 0.56 | 0.50 | 197.8 | 151.7 | 0% | 0.02% | 0% | 2% | 0.10% | 1% | 894.850 | |

20% | 0.12 | 591.9 | 674.7 | 0.56 | 0.49 | 197.5 | 148 | 0% | −0.02% | 0% | 0% | −0.05% | −1% | 894.150 | |

40% | 0.14 | 591.9 | 674.4 | 0.56 | 0.48 | 197.4 | 146.1 | 0% | −0.07% | 0% | −2% | −0.10% | −2% | 893.810 |

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## Share and Cite

**MDPI and ACS Style**

Taleizadeh, A.A.; Beydokhti, S.R.; Cárdenas-Barrón, L.E.; Najafi-Ghobadi, S.
Pricing of Complementary Products in Online Purchasing under Return Policy. *J. Theor. Appl. Electron. Commer. Res.* **2021**, *16*, 1718-1739.
https://doi.org/10.3390/jtaer16050097

**AMA Style**

Taleizadeh AA, Beydokhti SR, Cárdenas-Barrón LE, Najafi-Ghobadi S.
Pricing of Complementary Products in Online Purchasing under Return Policy. *Journal of Theoretical and Applied Electronic Commerce Research*. 2021; 16(5):1718-1739.
https://doi.org/10.3390/jtaer16050097

**Chicago/Turabian Style**

Taleizadeh, Ata Allah, Shima Rezvan Beydokhti, Leopoldo Eduardo Cárdenas-Barrón, and Somayeh Najafi-Ghobadi.
2021. "Pricing of Complementary Products in Online Purchasing under Return Policy" *Journal of Theoretical and Applied Electronic Commerce Research* 16, no. 5: 1718-1739.
https://doi.org/10.3390/jtaer16050097