Product Line Optimization for Car-Sharing Platforms in the Sustainable Transportation

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Introduction
Te sharing economy has developed rapidly in recent years, especially in developing countries.According to the Chinese National Development and Reform Commission, the market transaction volume in the sharing market was about 4,920.5 billion yuan in 2017, an increase of 47.2% over the previous year (https://www.ndrc.gov.cn/xwdt/ztzl/zgzxjjbg/201911/t20191114_1213801.html).Te sharing economy is emerging in many industries, such as transportation, durable goods, and personal service, so it provides great opportunities for customers, manufacturing frms, and online platforms.Especially, in the feld of low-carbon transportation, car-sharing platforms reduce the number of private vehicles on the road and take responsibility for environmental sustainability, which is conducive to decreasing greenhouse gas emissions and relieving trafc pressure in urban areas.Tis green transportation mode improves the allocation efciency of idle vehicles, provides new job opportunities, and creates a resource-saving society.
However, the development of the sharing economy has not been smooth as expected.A lot of debates arise from diferent stakeholders who have been involved in the sharing market, such as the manufacturer's heavy capital cost, the platform's low technical threshold, and the government's insufcient resource allocation.Especially, the biggest challenge in the sharing market comes from the customer's heterogeneous valuation for the diferentiated products in the product line For example, if a manufacturing frm produces two products and sells them to two customers, it should consider that each customer will buy which type of the two products.Similarly, if the e-commerce platform has two products and rents out to two customers, it should consider which type of the two products should be shared with each customer.To solve this problem, the product line design is proposed.
Each consumer in the market has his preference and makes the best choice by evaluating the quality of each product [1][2][3].Tis will further lead the manufacturing frm to launch a variety of products to meet the needs of customers.With the introduction of the e-commerce platform, the sharing market adds a new option for the customers, and fexible online pricing brings extra benefts to the platform transaction [4][5][6].As a prime example of C2C platforms, all the cars on Uber are owned by private sharers, not the platform itself.According to the prices of car models, Uber has launched several ride-hailing services for diferent passengers, like Uber X for ofce workers, Uber XL for leisure travelers, Uber Black for businessmen, and Uber Wav for disabled people.Unlike C2C car sharing, Hertz purchases and owns various self-supported vehicles on its B2C platform, like Economy 2/4 Door for a family of three, Large SUV for group tourists, Large Luxury Sedan for administrative ofcers, and Small Commercial Van/Truck for passengers with lots of luggage.Terefore, how to match the platform's product line with the customer's choice behavior is the most important issue for the supply and demand side in the sharing market.For the seller's proft maximization, when two (or more) products are in the same market, the seller should consider how to set the quality attribute and the pricing strategy to induce two (or more) customers to buy.Otherwise, some designed products will cause dull sales and some unsatisfed customers will be empty-handed when leaving the market.
In this study, we set up a game-theoretic model to study the customer's choice behavior and the platform's product line pricing.Te sequence of events is shown in Figure 1.In Figure 1(a), B2C sharing proceeds as follows.In period 1, when the manufacturing frm sells the products, all customers decide to buy or not (buyer/nonbuyer).In period 2, the buyers decide whether to use it, and if not, they can rent the self-supported products from the sharing platform (user/ lessee).Te nonbuyers decide to rent or not from the platform (lessee/nonlessee).In Figure 1(b), C2C sharing proceeds as follows.In period 1, when the manufacturing frm sells the products, all customers decide to buy or not (buyer/nonbuyer).In period 2, the buyers decide whether to use it, and if not, they can share the purchased products on the sharing platform (user/sharer).Te nonbuyers decide to rent or not from the sharers (lessee/nonlessee).Compared with the benchmark of homogeneous customers and the single product, we introduce two customer segments with the valuation heterogeneity into the product line and solve the equilibrium product quality, selling price, and sharing price in the B2C and C2C sharing.Te numerical experiments show the impact of the valuation heterogeneity and the cost structure on the pricing strategy over the two periods.
Te contribution of our study is summarized as follows: (1) Our study is the frst to introduce the product line design into the sharing economy (2) We establish an analytical model to solve the optimal quality and the optimal price in the B2C and C2C sharing (3) Numerical experiments examine the impact of the quality sensitivity and the cost sensitivity on the manufacturing frm's selling proft and the ecommerce platform's sharing proft Te remaining of this study proceeds as follows.We give a literature review in Section 2. Section 3 sets up the equilibrium pricing model in the B2C and C2C sharing markets.In Section 4, we give a sensitivity analysis of the numerical experiments.Te last section summarizes some managerial insights and future directions.All proofs of the propositions are supplemented in the appendix.

Literature Review
2.1.B2C/C2C Sharing.Recently, the sharing economy has had potential in many industrial felds (e.g., car sharing, home sharing, and crowdfunding), and some related academic studies have been published in leading journals.By using a dynamic game, Yu et al. [7] studied the regulatory policy in C2C sharing.Diferent from our study, they investigated the role of the government in regulating the ondemand services (Uber/DiDi) and concluded that imposing a strict policy towards ride-hailing services was not efective in the transportation system while lowering the taxi fare was a benefcial way for the total social welfare.Jiang and Tian [8] established an analytical framework for C2C sharing in the distribution channel.Tey concluded that when the capacity was relatively costly, C2C sharing was more proftable for the downstream retailer than the upstream manufacturer.Although our study sets up a game-theoretic model, we mainly clarify the interplay between sellers and buyers instead of the relationship between manufacturers and retailers.Pei et al. [9] considered a two-period game by extending the B2C and C2C sharing to internal and external sharing.Tey compared whether an incumbent frm or an entrant frm should join the sharing market.However, they did not consider product diferentiation among competitors as in our study.From the view of ownership, Filippas et al. [10] investigated the short-run equilibrium and the long-run equilibrium in the sharing economy.By studying the exchange of ownership between owners and nonowners, they empirically surveyed the bring-to-market costs and showed some economics of owning, using, and renting to the stakeholders in the sharing market.

Product Leasing.
Another relevant stream is product leasing.Te frst study related to leasing dates from the 1970s [11].Te author drew the classic conclusion that leasing was often a less costly way to obtain durable goods.Desai and Purohit [12] proposed a diferent viewpoint by considering the depreciation rate.When the durable products had a high depreciation rate, selling the products was a better-of decision rather than leasing.Later, Desai and Purohit [13] studied a combination of the selling and leasing market.By developing a game-theoretic model, they proved that a higher fraction of leasing was a disadvantage for the frm in the competition.Bhaskaran and Gilbert [14] flled the gap by giving the decision-making power of leasing to the downstream dealers.When the level of competitive intensity was high among dealers, selling durable goods was the dominant strategy.From the view of the lifecycle environmental impact, Agrawal et al. [15] established an analytical framework of green leasing.Tey proved that disposal fees or remanufacturing could both efciently improve environmental performance.
Diferent from B2C or C2C sharing, which is called short rental, product leasing usually requires the customers to rent on a long-term basis, and the platform's charging method is more fexible.Benjaafar et al. [16] proposed that the leasing product was often supplied to the market without ownership and was charged for a weekly or monthly cost.In contrast, the product on the peer-to-peer sharing platform was charged per use.Similarly, Tian and Jiang [17] concluded that leasing could be regarded as a bundle of sharing, where the consumer's product usage would last over many periods instead of one single period in the sharing.In the context of car sharing, Bellos et al. [18] pointed out that the customer's payment was directly linked to vehicle use.Besides, they demonstrated that the vehicle production volume was much larger in car leasing because there was a pooling efect on the sharing platform.

Product Line Design.
From the academic review, how to design a product line optimally was frst proposed in the 1970s [19].Ten, Moorthy [20] set up mathematical modeling to address this issue.Moorthy and Png [21] discussed the beneft of the product line design and concluded that the monopolist should always sell highquality products to high-valuation customers and sell low-quality products to low-valuation customers.Based on the literature, our study applies the classic theory of product line design to the sharing economy.Te study most close to ours is the study by Bellos et al. [18].Based on the mechanism of incentive compatibility, they considered an original equipment manufacturer shared diferentiated cars in the B2C sharing.By investigating the impact of the corporate average fuel economy, they found that higher fuel efciency led to a higher price in the high-end market.However, our study has two obvious diferences.First, we set up a gametheoretic model in that the participants can choose to buy from the manufacturing frm and then share or rent on the ecommerce platform.Second, we apply the product line pricing to both B2C sharing and C2C sharing.

Research Methods in the Sustainable Transportation.
Tere are three main streams of research methods in sustainable transportation.Te frst stream is mathematical programming.Aydin et al. [22] set up a multiobjective stochastic optimization model to solve the optimal location and demand allocation in car sharing.Te fndings could minimize the total cost and the average unsatisfed demand in the region with sensitive parameters.Johnsen and Meisel [23] built a mixed-integer program model to solve the dial-a-ride problem in rural areas.Tey tested how diferent interrelated trips infuenced the service quality and the total transportation cost.Aydin et al. [24] established a mixed-integer linear programming model for the location and routing problem when the postdisaster damage happened.By developing the new version of the ant colony algorithm, the experiment results manifested that the improved algorithm could be time-saving in very small-scale instances.

Journal of Advanced Transportation
Te second stream is the fuzzy set.Deveci et al. [25] proposed a decision support system based on the q-rung orthopair fuzzy set in the sustainable transportation.With the weighted sum and weighted product models, the system's efectiveness was examined by numerous infuencing factors and input uncertainties.Krishankumar and Ecer [26] adopted a similar approach to select the optimal service provider for the internet-of-things.Te sensitivity analysis investigated the impact of availability, total cost, and security on the evaluation of the service provider.
Te third stream is the simulation experiment.By adopting the data sources of connected autonomous vehicles, Gokasar et al. [27] put forward an algorithm with the modifed standard normal deviation and validated its effectiveness in the trafc simulation software.In the simulation of urban mobility platform, Nguyen and Jung [28] applied swarm intelligence to green transportation and demonstrated that the average fuel consumption and the average trip duration could be both reduced by the framework.Gokasar et al. [29] used the shockwave speed to control the connected autonomous vehicles in sustainable transportation.Te simulation results showed that the trafc density throughout the network was lower than in other trafc management systems.
Recently, the sharing economy is becoming one popular stream.However, how to match the platform's product line with the customer's choice behavior becomes a problem for all the stakeholders in the sharing market.Table 1 compares the contribution between the relevant literature and our study.Our study is the frst to introduce the product line into the sharing economy and establishes an analytical model to solve the optimal quality and price in B2C and C2C sharing.

Modeling
Considering a product line consisting of two diferentiated products, two customer segments choose to buy from the manufacturing frm in period 1 or rent on the e-commerce platform in period 2. Te lessee in the sharing period can rent from the platform directly in the B2C sharing or the sharer indirectly in the C2C sharing.
On the demand side, the customer segment i ∈ H, L { }'s choice behavior of the product j ∈ h, l { } is dependent on the valuation and the expectation.In the traditional utility theory, diferent customers have their preferences for the same product [30].If one customer likes the product very much, the intensity of the customer preference is strong, so the customer is called the high-valuation customer H. Conversely, if the customer dislikes the product, the intensity of the customer preference is weak, so the customer is called the low-valuation customer L. However, in the product line design, the seller often provides more than one product for the customers, so the products in the sharing market are quality-diferentiated [19][20][21].If the product quality in the product line is high, the product is called a high-end product h; otherwise, the product is a low-end product l.Te valuation v ij � θ i q j is linear with the personal preference θ i ∈ (0, 1) and the product quality q j ∈ (0, 1), where θ H > θ L , q h > q l .Due to the owner of the product, the customers have n ≥ 1 times the valuations from buying in period 1 than renting in period 2. Assuming the customers are risk neutral, ξ ∈ [0, 1] denotes the probability that the buyer in period 1 expects to use in period 2 and 1 − ξ denotes the probability that the buyer in period 1 expects sharing in period 2. Te number of each segment is N i , so the demand N fj (i.e., the customers who buy from the frm) in period 1 and the demand N pj (i.e., the customers who rent through the platform) in period 2 are both dependent on N i .
On the supply side, the frm's proft π f and the platform's proft π p is dependent on the price and the cost.Te frm sets the selling price p fj in period 1, and then the owner of the product sets the sharing price p pj in period 2 [16] (in the B2C sharing, the owner of the product is the platform, and in the C2C sharing, the owner of the product is the sharer).Specifcally, in the C2C sharing, the platform charges a commission fee cp pj from the sharer, where the commission rate is c ∈ [0, 1].Te production cost is quadratic with the product quality cq 2 j , where c ∈ [0, 1] is the cost sensitivity.Let t ∈ [0, 1] denote the coefcient of transaction cost for each sharing, and the linear transaction cost is tq j [8].Te discounted rate satisfes δ ∈ [0, 1].

Product Line in the B2C
Sharing.In the traditional product line design, the optimal price and quality are solved by the mechanism of incentive compatibility [20,21], i.e., H buys h and L buys l.However, the introduction of the ecommerce platform changes the market structure, so the frm should consider the impact of product sharing on the product line design.
In the B2C sharing, the frm sells h, l to H, L in period 1 and the platform shares h, l to H, L in period 2. Te proft optimization of the frm in period 1 is as follows: ( Te proft optimization of the platform in period 2 is as follows: ( Te optimal quality and price are solved in Proposition 1. Proposition 1.In the B2C sharing, the frm's optimal product line pricing is p * fh � nθ H q h − (nθ H q l − nθ L q l ) and p * fl � nθ L q l and the platform's optimal product line pricing is Proof.See the appendix.Proposition 1 shows an intuitive result for the product line design in the B2C sharing.Without any capacity constraints, the frm and the platform can supply enough diferentiated products for heterogeneous customers.Although the product sharing in period 2 is later than the product selling in period 1, the platform can rent out the same product (as the frm) to customers, and the discounted value in the product sharing is counterbalanced by the same product line pricing (as in the product selling).Terefore, the frm's product line faces new competition from the platform, where its high-quality product is not only cannibalized by the low-quality product in the product selling but also by the high-quality product in the product sharing.Te high segment's surplus in period 1 will be extracted by the platform that ofers the same high-quality product in period 2. However, the high-quality product from the platform incurs a lower surplus than the low-quality product from the frm, so it implies that the high-quality product in the product sharing will not cannibalize the product line as long as the low-quality product in the product selling does not.Te frm should reduce the price for the high-quality product and optimize the product line by inducing each segment to buy the corresponding product.As a result, the shared product incurs no cannibalization on the product line design because both segments buy from the frm in period 1, and the platform in period 2 becomes useless.□ 3.2.Product Line in the C2C Sharing.In the C2C sharing, the frm sells h, l to H, L in period 1, and the sharer H, L (who buys the product) shares h, l to the lessee H, L (who does not buy the product) in period 2. Te proft optimization of the frm in period 1 is as follows:

Proposition
Proof.See the appendix.
Proposition 2 shows how to use product line pricing in the sharing economy.(a) When H shares only in period 2, if the customer heterogeneity (θ L /θ H ) is higher, the frm's pricing strategy is the same as the traditional product line pricing; otherwise, the pricing strategy in period 1 depends on the quality diferentiation (q h − q l ).If the quality diferentiation in the product line is strong, the high segment's valuation between the two products is quite diferent, so the frm should adopt the traditional product line pricing.However, if the quality diferentiation in the product line is weak, the low segment's valuation between the two products is almost similar, so the frm should adopt the product line pricing by inducing the high-quality product.(b) When L shares only in period 2, if the customer heterogeneity (θ L /θ H ) is lower, the frm's pricing strategy is the same as the traditional product line pricing; otherwise, the pricing strategy in period 1 depends on the quality diferentiation (q h − q l ).However, if the quality diferentiation in the product line is weak, the low segment's valuation between the two products is almost similar, so the frm should adopt the product line pricing by inducing the low-quality product.(c) When H shares and L shares in period 2, no matter whether the customer heterogeneity is lower or higher, the pricing strategy in period 1 depends on the quality diferentiation.If the customer heterogeneity is lower and the quality diferentiation in the product line is strong, the frm should adopt the traditional product line pricing.
Proof.See the appendix.In Proposition 3, the optimal product quality in the product line changes with the economic parameters in the sharing economy, and we make the comparison between the B2C sharing and C2C sharing in Table 2.In two types of sharing platforms, the product quality decreases with the cost sensitivity.Te higher cost sensitivity leads to a higher variable cost of production in period 1, so reducing the product quality is an efcient way for the frm to maintain the proft in the product line.However, the high segment has the intention to buy low-quality products.Te frm should set the product line pricing by considering the cannibalization from the low-quality product, and the positive infuence of the cost sensitivity depends on the number ratio of the two segments.
In the C2C sharing, the low segment would like to buy the product and then share it, so the sharing probability only infuences the low-quality product in the product line.Diferent from the B2C sharing, the higher commission rate is proftable for the platform and has no impact on the frm directly.Te frm should decrease the quality of the shared product or increase the quality of the used product, to reduce the cannibalization efect from the platform in period 2. □

Numerical Experiment
In this section, we compare the impact of some parameters on diferent sharing markets and show the managerial implications for the frm, platform, and customers in the product line.We take Proposition 2(b) as an example in which Proposition 2(b1) is the equivalence of the B2C sharing and the second scenario in Proposition 2(b2) is the simplifcation of the C2C sharing.Te parameter setting is ξ � 0.5, c � 0.5, t � 0.05, δ � 0.95, and n � 1, which guarantees that θ H ≤ 2θ L , so that all variables are nonnegative in the experiments.

Firm's Proft.
In B2C sharing and C2C sharing, the frm's proft is mainly infuenced by the cost sensitivity from the seller side and the quality sensitivity from the buyer side.Given the cost sensitivity, we examine how the quality sensitivity infuences the frm's proft.
In Figures 2 and 3, when the cost is more sensitive to the product quality, the frm's proft decreases because of the higher variable cost in production.In Figure 2, the frm's proft increases with the quality sensitivity.In the B2C sharing, both segments buy from the frm in period 1, and no segments rent from the platform in period 2.
However, in Figure 3(b), the frm's proft decreases with the quality sensitivity.In the C2C sharing, both segments buy from the frm in period 1 and only the low segment shares in period 2. Te frm faces cannibalization from the platform in period 2 and should reduce the price for the lowquality product, to induce the low segment to buy in period 1.

Journal of Advanced Transportation
Table 2: Sensitivity analysis of the product quality in the product line.
Journal of Advanced Transportation In Figures 2 and 3, the quality sensitivity satisfes θ L ≤ θ H ≤ 2θ L or θ H /2 ≤ θ L ≤ θ H (to keep the frm's proft nonnegative).Tere is always a valuation diference between two segments, so we defne the customer heterogeneity as ∆ � θ H − θ L where 0 ≤ ∆ ≤ θ L when θ H changes and 0 ≤ ∆ ≤ θ H /2 when θ L changes.Te impact of the customer heterogeneity is contingent on the intervals with the solid line, while the dashed line implies that the frm's proft varies nonmonotonically in other intervals.If the customer heterogeneity is higher, i.e., lower θ L in Figure 3(a) and higher θ H in Figure 3(b), the frm obtains more proft from the C2C sharing.Because there is a sharing price for the same quality product in period 2, the frm always faces price competition with the platform.To make up for the loss, the frm keeps or lowers the price for both products in the product line, but the price diference should be the same for the two heterogeneous segments.Te participants in C2C sharing are the customers instead of the platform, so customer heterogeneity in C2C sharing plays a more important role than in B2C sharing.

Platform's Proft.
Compared with the frm's proft, Figures 4 and 5 show how the platform's proft varies with the cost sensitivity from the seller side and the quality sensitivity from the buyer side.
As shown in Figure 4, the platform's proft is independent of cost sensitivity and quality sensitivity.In the B2C sharing, both segments buy from the frm in period 1 and give up renting from the platform in period 2, so the platform's proft in the B2C sharing is zero.
In contrast to the frm, the platform's proft in Figure 5(a) decreases with the quality sensitivity but increases with the quality sensitivity in Figure 5(b).Te competition between the frm and the platform implies that the selling proft is positively related to the high segment, while the sharing proft is positively related to the low segment.Furthermore, because of the production cost in period 1 and the transaction cost in period 2, the frm's proft is quadric with the quality sensitivity and the platform's proft is linear with the quality sensitivity, which results that the platform's proft being more sensitive than the frm's proft.

Customer Demand.
In the sharing market, the customer can be a buyer, sharer, lessee, or user (who fails to share/rent in period 2), which depends on the choice behavior in each period and determines the demand for the frm or the platform.
In Figure 6(a), the customers who buy in period 1 cannot be the sharers in period 2, due to the product owned by the platform.Tey also cannot be the lessees in period 2 because the frm adopts the product line pricing to induce each segment to buy the corresponding product.In other words, the customers would not like to rent the same product from the platform and use the product that is bought in period 1.
In Figure 6(b), the customers who buy in period 1 can be the sharers or lessees in period 2. Tere are only three possible cases that make the demand match the supply in the C2C sharing: (i) the high segment shares only, (ii) the low segment shares only, and (iii) two segments share.Only if the on-demand deal is achieved, the lessees can rent the diferentiated product from the sharers in period 2; otherwise, they seek the product on the platform.

Policy Implications.
As the sharing economy develops in many industries, the sellers face the new challenge to satisfy the customers' diverse needs for the various products on the sharing platform.How to use the product line design in the sharing market is potential for all stakeholders.Compared with the prior research in the sharing economy, our study further shows the pricing guidelines for the e-commerce platform to meet the diverse needs of customers.Tis study gives some policy implications in the product line design under the sharing economy, which will be insightful for scholars, practitioners, and policymakers in the sharing market.
First, our study has concluded that within the product line, the platform's sharing proft in the C2C sharing may be positively infuenced by the sharer's valuation.Unlike B2C sharing, the sharer replaces the role of the e-commerce platform to rent out the products, so the sharer's willingness to participate will signifcantly infuence the revenue of the C2C platform.In 2016, Uber announces it to stop the ride-hailing service in China and completely leave the local Journal of Advanced Transportation market.Te poor experience on the driver's side is the main factor that results in Uber's failure.For the drivers who ofer the ride-hailing service (i.e., the sharers), Uber sends the order completed by the background algorithms and prohibits the drivers to choose the order according to their wishes.As a result, a lot of drivers reject the long-distance order and make complaints to the department of transportation.
Second, the C2C sharing platforms should implement a policy that improves product quality.Ofering the highend product can further counterbalance the price competition in the sharing market, thus contributing to the proft maximization of the C2C platform.In the early stage of entering the Chinese market, Uber distributes a large number of coupons in the mobile app, so that ordinary passengers can take Uber X (economic car) with a price close to the taxi fare.
Finally, it is an appropriate strategy for the C2C platform to induce low-valuation users with a higher price.Customers who have a low-valuation are more likely to be induced by price discounts, which will be the primary target for the C2C platform to make profts.Te subsidy policy helps Uber to capture the low-end trafc market in urban cities and cannibalizes the huge market share of taxis in China.On the demand side, the separation of the owning right and possessing right incurs a variety of passenger types, so the passenger's behavior will become more fexible (e.g., varietyseeking or boundedly rational) on Uber's ride-hailing platform.

Limitations and Recommendations.
Although our fndings facilitate the optimization of the product line design in B2C sharing and C2C sharing, three limitations should be further addressed.First, competition between two manufacturing frms or e-commerce platforms is very important for customers.Either the quality decision or the pricing strategy in the context of competition will change the customer's decision in the sharing market.Second, the quantitative modeling of fxed costs will have a potential impact on the manufacturing frm's profts, and thus infuences product sharing on the e-commerce platform.Finally, there are some network externalities or showrooming efects on the e-commerce platform, which will make a diference to the manufacturing frm's production and supply in advance.
Tis study will give some recommendations to scholars who focus on the sharing economy for future studies.On the one hand, future directions should consider how to use marketing strategies to coordinate the relationship between manufacturing frms and e-commerce platforms, such as group buying, coupons, and membership.Price promotion can be an efective tool to reduce the loss of market shares in the competition.On the other hand, the role of the government in the sharing market should be evaluated because the fnancial subsidy or regulatory policy is an important incentive for most e-commerce platforms.As a mediator, government involvement will afect the resource allocation to the manufacturing frm in diferent sharing markets.

Figure 2 :Figure 3 :
Figure 2: Firm's proft in the B2C sharing (a) when θ H changes and (b) when θ L changes.

Figure 4 :Figure 5 :
Figure 4: Platform's proft in the B2C sharing (a) when θ H changes and (b) when θ L changes.

Table 1 :
Comparison between the relevant literature and our study.