Retailer–supplier coordination of pricing and delivery ratings availability decisions in online marketplaces

2.1. Setting and data

We next describe the institutional context and the respective data that inform and support our analyses. Specifically, we consider a supplier–retailer supply chain in which the retailer sells the supplier’s product through a digital retailing platform. The supply chain thus implements the drop-shipping business model, in which the retailer sets the retail price and the supplier determines both the wholesale price and the promised delivery time. For the actual delivery time to reflect the promised delivery time, the supplier sets the delivery speed and incurs a cost proportional to the speed. This general setup describes the operations of the Tmall platform, a major marketplace operated by Alibaba Group—the world’s largest e-commerce company. At Tmall, when a retailer sells a product to a consumer, the supplier can directly ship the product to the consumer using the services of logistics companies in the Cainiao Network. The Cainiao Network is a consortium formed by the Alibaba Group and several leading logistics firms that, altogether, handle approximately 70% of all the online orders in China (Deagon, 2018). These logistics service providers offer several standardized shipping options, including Cainiao Super Economy, Cainiao Expedited Standard, and Cainiao Heavy Parcel Line, ¹ each of which involves a different delivery speed and fee. ² Cainiao helps suppliers choose among these logistics service providers by collecting and sharing information from all affiliated logistics firms. ³ These firms report order details, delivery status, and user feedback to Cainiao with an aim to provide high-quality service to both suppliers and consumers.

Our dataset includes information regarding almost 160 million orders handled by a sample of 527 supplier–retailer pairs operating on Tmall’s platform. The data include dates, prices, quantities, promised delivery speed, and consumer ratings for individual transactions occurring between January 1st and July 31st, 2017 (see Appendix A and online Appendix I for details). We use this dataset for two purposes. First, we use the data to inform modeling decisions and to ensure that our theoretical model is realistic and sound. Second, we use the data to empirically test the predictions made by the theoretical model. We note that the data reflects the effects of factors that fall outside of the scope of our problem of interest, such as the unobserved physical distances between suppliers and consumers and unobserved differences across products. The effects of these extraneous factors could be confounded with the effects of our interest and hence we need to take them into consideration. We do so in two different ways.

First, we condition out the extraneous factors by selecting a subsample within which the extraneous factors are constant or absent. This approach allows us to analyze the data without having to rely on restrictive distributional assumptions. To control for unobserved distances between suppliers and consumers, we drop observations in which the shipments originate at a city different from the city of the final destination. Likewise, we only consider the orders that were fulfilled by the logistic firms affiliated with the Cainiao Network to control for unobserved characteristics of different fulfillment services. We note that, at Tmall, orders are shipped by suppliers rather than by retailers. Hence, each order contains items from one supplier only and the supplier can set the promised delivery time independently. Even if the Cainiao Network pools some orders, it does so after all orders have been placed and promised delivery times have been set (Chen et al., 2024). Nonetheless, a supplier could source different products from different origins and thus the delivery time of one item may depend on the delivery time of another item. Because this could induce noise in the measurement of promised delivery time, we drop a small percentage of orders with multiple items and analyze orders that involve a single product only. In addition, we drop observations with missing promised delivery time and ratings. We verify that our final sample is representative by confirming that these filtering steps preserve the average values of product prices, promised delivery time, actual delivery time, and delivery-time ratings, as reported in Table 3 of Appendix A. The final sample thus consists of 4,741,544 observations (about 55% of all complete observations) that correspond to 277 supplier–retailer pairs and 14,459 distinct items. Descriptive statistics appear in Table 4 of Appendix A.

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Table 2.

Empirical tests of implications of theoretical model.

	Dependent variables
	log(Unit sales)		Avg. promised wait
	(1)	(2)	(3)	(4)
Avg. promised wait	− 0.043 * * *	− 0.039 * * *
	(0.001)	(0.001)
Avg. price	− 0.0004 * * *	− 0.0003 * * *	− 0.003 * * *	− 0.003 * * *
	(0.0001)	(0.0001)	(0.001)	(0.001)
Rating availability indicator		2.282 * * *		− 3.912 * * *
		(0.057)		(0.544)
Subcategory fixed effects	Yes	Yes	Yes	Yes
Supplier fixed effects	Yes	Yes	Yes	Yes
Observations	7,798	7,798	7,798	7,798
Adjusted R 2	0.707	0.759	0.981	0.981

Note. * p < 0.1 ; * * p < 0.05 ; * * * p < 0.01 .

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Table 3.

Effect of sample filtering on sample means of main empirical variables.

	Sample
	Initial	Same city	Single items	Valid
Promised wait (h)	54.486	52.569	52.948	52.948
Delivery time (h)	−18.135	−16.972	−17.161	−17.161
Price (CNY)	387.546	495.869	510.469	512.602
Delivery time rating	4.867	4.868	4.865	4.867
Rating availability indicator	0.939	0.935	0.932	0.932
Same city indicator	0.591	1.000	1.000	1.000
Single-item indicator	0.933	0.941	1.000	1.000
Valid delivery time indicator	0.992	0.987	0.987	1.000
Sample size	8,640,159	5,107,615	4,804,499	4,741,544

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Table 4.

Descriptive statistics of final sample ( n = 4 , 741 , 544 ).

Variable	Mean	Std. dev.	Median	Min.	Max.	25 Pctl.	75 Pctl.
Promised wait (h)	52.95	24.56	38.60	0.37	95.98	32.80	78.68
Delivery time (h)	35.79	21.39	30.87	0.25	740.13	23.48	45.08
Price (CNY)	512.60	893.15	158.82	0.01	39,161.47	65.41	509.81
Quantity	1.04	0.59	1.00	1.00	288.00	1.00	1.00
Delivery time rating	4.82	0.08	4.82	0.50	5.00	4.78	4.86
Product quality rating	4.85	0.08	4.86	0.00	5.00	4.82	4.89
Service quality rating	4.81	0.08	4.81	0.50	5.00	4.78	4.86
Rating availability indicator	0.93	0.25	1.00	0.00	1.00	1.00	1.00

Second, we estimate econometric models that explicitly control for extraneous factors using statistical controls. This approach allows us to account for unobserved heterogeneity and other unobserved factors. To control for unobserved supplier–retailer characteristics, such as their ratings at alternative platforms, we use supplier–retailer-specific fixed effects. To control for unobserved product characteristics, such as perishability, we use product-specific fixed effects.

We next define our model primitives and use the data to support them. Before placing an order, each consumer can learn about the products and delivery services offered by suppliers to infer the utility associated with the offerings. We use v , t , and t c to denote the expected product quality, the promised delivery time, and the delivery-time conformance, respectively. We then follow Shang and Liu (2011) to specify the consumer expected utility of buying one unit of an offering at price p as

U ≡ v − p − γ t + α t c ,

(1)

To model the expected product quality v , we follow Chen and Xie (2008) and Kwark et al. (2014) in defining it as a convex combination of the consumer’s own quality assessment q and the average rating on product quality q r , where the subscript r stands for “rating.” That is, v = ϕ q + ( 1 − ϕ ) q r , where ϕ ∈ ( 0 , 1 ) and ( 1 − ϕ ) denote the weights on the two information components. The parameter ϕ weighs the relative precision of these two information sources and could depend on, for example, how familiar consumers are with the product or on how likely consumers are to search for additional information outside of the retailer’s website. When product-quality ratings are available, consumers can observe the average product-quality rating q r before they make their purchase decisions. This means that the value of q r is given. In contrast, q is the realization of a random variable Q that may differ across consumers because the degree of fit between the product attributes and consumer needs is heterogeneous (Kwark et al., 2014).

As in previous work (see, e.g., Chen et al., 2022, Kwark et al., 2014, Ma et al., 2024), the consumer-specific, product quality assessment Q is uniformly distributed over [ 0 , q ¯ ] , where the single upper bar denotes an upper bound. That is, the probability density function (p.d.f.) g ( Q ) is g ( Q ) = 1 / q ¯ , for Q ∈ [ 0 , q ¯ ] . If product-quality ratings are available, then a consumer’s maximum expected product utility is v ¯ ≡ ϕ q ¯ + ( 1 − ϕ ) q r . Otherwise, if the product-quality rating is not available, then the consumer’s expected product utility v depends only on her own assessment q , that is, v = q , and her maximum expected product quality is q ¯ . No assumption on how v ¯ , q ¯ , and q r compare to each other is required in either case. Hence, our results do not depend on any particular specification of v .

We define p as the retail price set by the retailer excluding shipping fees. The consumer utility specification in (1) does not include a shipping fee, because Tmall shoppers seldom pay shipping fees. Most of the Tmall suppliers provide free shipping within China. ⁴ More generally, domestic shoppers almost always enjoy the free shipping service from Cainiao-affiliated retailers. For example, during the “Double 11” promotional period of year 2021, approximately 98% of all parcels from all retailers in China were delivered under the free shipping service policy, as reported by the Global Times. ⁵ In Tmall’s case, almost all suppliers offer free shipping service as the default and the only shipping option. In these cases, the shipping cost is absorbed by suppliers.

We treat the promised delivery time t as a supplier’s decision that determines the actual time a customer has to wait for the order to be delivered, hereafter referred to as the delivery wait or the actual delivery time T a , where the subscript a stands for “actual.” As mentioned above, in Tmall’s case, the logistics companies members of the Cainiao Network offer standardized shipping options for suppliers to choose from. Regardless of whether a supplier intends a short or long delivery time, the supplier can choose a logistics service provider with a proper shipping option and pay the corresponding shipping fee. Thus, because each supplier is able to choose among all the given logistics service options in the Cainiao Network, we consider the promised delivery time as a supplier’s decision variable.

We expect the actual delivery time T a to increase with the promised delivery time t , and the average actual time to be shorter than the average promised time. In our institutional context, suppliers promise same-day, next-day, and two-day delivery before 9:00 pm for orders that were placed before 11:00 am. Analogous delivery times are offered for orders placed before midnight (see online Appendix I for details). The promised delivery deadlines are reflected in the distribution of T a , which, as depicted in the left-most plot in Figure 2, exhibits modes right below 8, 20, and 44 h. We accordingly let T a = β t + ε , where 0 < β < 1 and ε is a uniformly distributed random variable in the range [ 0 , ε ¯ ] with upper bound ε ¯ and p.d.f. f ( ε ) = 1 / ε ¯ . This definition of T a holds for different combinations of values for β and ε ¯ . For example, we can let β ^ = median ( T a − t ) , where the median is taken across transactions, and define ε ^ = T a − β ^ t . If F ^ ε ^ ( ⋅ ) represents the empirical distribution of ε ^ , then ε = F ^ ε ^ ( T a − β ^ t ) is uniformly distributed on [ 0 , 1 ] . The middle plot in Figure 2 depicts the distribution of ε ^ , which may deviate from normality because of the factors such as differences over days of the week, across products, and across the technologies of different regional operators (Yao et al., 2019). The right-most plot depicts the nearly uniform distribution of F ^ ε ^ ( T a − β ^ t ) for β ^ = median ( T a − t ) = 0.95 and ε ¯ = 1 .

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Figure 2.

Distributions of delivery times for ε ¯ = 1 and β ^ = 0.95 .

Although the exact value ε ¯ may be unknown to consumers, they implicitly estimate it when forming expectations of actual delivery times and delivery time conformance. Making information about expected waiting times available to consumers can significantly reduce an overestimation of actual waiting times and their variance (Esper et al., 2003; Kumar et al., 1997). Hence, making delivery-time ratings available can reduce the expected delivery times as well as their expected variance, both of which are proportional to ε ¯ . That is, the maximum expected delivery time when delivery-time ratings are available, ε ¯ A , is smaller than its counterpart when delivery-time ratings are not available, ε ¯ N ; that is, ε ¯ A ≤ ε ¯ N .

Consumer sensitivity to the delivery time, represented by the parameter γ , satisfies α ( 1 − β ) < ε ¯ γ and thus, the expected delivery utility is decreasing in t . This implication cannot be tested directly because consumer utility is not observable. However, we can support it by showing that prices paid, and thus willingness to pay, decline with t . Noting that prices depend on both unobserved product features (such as quality and size) and unobserved supplier features (such as economies of scale), we estimate the relationship between promised delivery time t and prices conditional on item and supplier fixed effects. To allow for nonlinearity, we consider cubic truncated power function (TPF) splines but we note that delivery delay exhibits a skewed distribution with the vast majority of the observations lumped near zero. This imbalance across the support of the data often leads cubic TPF splines to exhibit bad tail behavior and therefore we instead rely on natural cubic splines (Wood, 2017). We then use the estimated regression equation to predict and plot prices for the observed values of t . Here, we set the values of the fixed effects to 0 so that the prices predicted are centered at 0 and represent the deviation of prices from their item and supplier averages. The results, given in Figure 3, indicate that prices paid, and thus utility, decline with promised delivery time.

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Figure 3.

Mean deviation of prices from their item and supplier averages as a function of promised delivery time. The gray envelope represents the 95% confidence interval of the mean.

Finally, we model delivery-time conformance t c . We start by noting that the supplier promises t ≤ t ¯ a ≡ max T a = β t + ε ¯ , where t ¯ a is the longest actual delivery time. This implies that ( 1 − β ) t ≤ ε ¯ and the actual delivery-time conformance is given by the actual probability of timely delivery:

t c = Pr ( T a ≤ t ) = Pr ( ε ≤ ( 1 − β ) t ) = ( 1 − β ) t / ε ¯ .

(2)

3.1. Consumer expectations when delivery-time ratings are available

When average delivery-time ratings t r are allowed, consumers rate products and delivery times (e.g., on a scale of 1 to 5) after transactions are completed. The retailer aggregates consumer ratings for each product as an average over a rolling 12-month window and updates the average rating displayed on the product’s page. Consumers may then use these posted averages to infer the longest possible delivery delay ε ¯ and the delivery-time conformance t c of the supplier. These variables are related through consumer satisfaction as follows.

Published delivery-time ratings reflect the satisfaction of individual consumers and therefore depend on the conformance of individual deliveries. Industry studies indicate that ratings measure both the actual delivery time and the delivery time conformance. For example, Bringg.com (2021) reports that 57% of customers will not return to a retailer after three late deliveries and, in today’s digital era, those customer complaints may quickly turn into negative reviews online. Therefore, Bringg concludes that measuring on-time delivery rates reveals the effectiveness of a delivery service and can thus help online firms improve rates of customer satisfaction. This implies that ratings measure the conformance of delivery time. MetricHQ (2025) and OptimoRoute.com (2025) report similar insights.

Accordingly, we let the difference T a − t represent consumer satisfaction, which determines the delivery-time rating T r (here, the subscript r again stands for “rating”). Naturally, if T a ≤ t , then the consumer should be satisfied with the actual delivery time and thus grant a high rating. Otherwise, if T a > t , then the consumer is very likely to be displeased and provide a low rating.

The effect of conformance on satisfaction is, however, not linear. Consumer satisfaction is subject to a negativity bias and a ceiling effect (Eisenbeiss et al., 2014), such that the benefits of exceeding consumer expectations are very limited and even negligible compared to the effects of not meeting them (Dixon et al., 2010). We show that this holds in our institutional context by plotting the delivery ratings in the Cainiao dataset as a regression function of the delivery delay T a − t . To control for unobserved items and supplier factors, we include item and supplier fixed effects. To allow the relationship to be nonlinear, we use a natural spline regression model. Altogether, the fixed effects and spline terms explain R 2 = 0.987 of the total variation of ratings. The regression line, plotted in Figure 4, shows that the ratings decline when T a > t but are nearly constant when T a ≤ t . We therefore model both negativity and ceiling effects of satisfaction by defining consumer dissatisfaction with delivery-time conformance at the individual level as min { 0 , T a − t } . Consumer satisfaction is thus given by the negative of dissatisfaction, or μ ≡ − min { 0 , T a − t } = max { 0 , t − T a } = max { 0 , ( 1 − β ) t − ε } . We then construct the rating function as T r = t _ r + k μ , where t _ r ≥ 0 denotes the minimum rating and k represents the unit impact of consumer satisfaction on the delivery-time ratings. This rating function indicates that a consumer with a higher satisfaction level would provide a higher rating score above the minimum rating t _ r (i.e., the lowest delivery-time rating for the logistics service).

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Figure 4.

Average delivery-time rating as a function of delivery delay. The gray envelope represents the 95% confidence interval of the mean.

Next, we express the average delivery-time rating as

t r = E ( T r ) = t _ r + k E ( μ ) = t _ r + k ∫ 0 ( 1 − β ) t [ ( 1 − β ) t − ε ] f ( ε ) d ε = t _ r + k [ ( 1 − β ) t ] 2 2 ε ¯ ,

(3)

Given the useful information contained in the published average delivery-time ratings t r , consumers may use them to derive a rough estimate of the longest possible delay ε ¯ . According to (3), such a consumer estimate should approximate

ε ¯ A ≡ k [ ( 1 − β ) t ] 2 2 ( t r − t _ r ) ,

(4)

t c A ≡ Pr ( ε ≤ ( 1 − β ) t | t r is available ) = ( 1 − β ) t ε ¯ A = 2 ( t r − t _ r ) k ( 1 − β ) t .

(5)

When average delivery-time ratings are not available, consumers can only use promised delivery times and their experience to infer the longest possible delay ε ¯ and the expected delivery-time conformance t c . The lack of additional delivery information leads consumers to expect a lower delivery-time conformance and longer delivery times than when the delivery information is available (Esper et al., 2003). This occurs because (i) trust is less likely without ratings (Rice, 2012) and trust is associated with higher expectations, or (ii) the lack of information leads consumers to consider all (including the worst) possible outcomes. The worst possible expected outcome is associated with the longest possible delay, ε ¯ N , which consumers can infer from their experiences. As a result, consumers assign the largest possible value of ε ¯ to ε ¯ N .

It follows from (2) that consumers may infer the delivery-time conformance of a retailer or supplier to be close to the expected value given by

t c N ≡ Pr ( ε ≤ ( 1 − β ) t | t r is not available ) = ( 1 − β ) t ε ¯ N ,

(6)

We use our individual-level utility specification to derive aggregate demand functions. Without loss of generality, we let the utility of the outside good be zero. A consumer decides to buy a product if U ≥ 0 , which implies that the consumer’s assessment of product quality must satisfy

q ≥ { q _ A ≡ p ϕ − 2 α ( t r − t _ r ) ϕ k ( 1 − β ) t − ( 1 − ϕ ) q r − γ t ϕ , if t r is available, q _ N ≡ p ϕ − α ( 1 − β ) t ϕ ε ¯ N − ( 1 − ϕ ) q r − γ t ϕ , if t r is not available,

(7)

Using (7), we calculate the aggregate demand as

D = { D A ≡ M ∫ q _ A q ¯ g ( q ) d q = M q ¯ − q _ A q ¯ , if t r is available, D N ≡ M ∫ q _ N q ¯ g ( q ) d q = M q ¯ − q _ N q ¯ , if t r is not available,

(8)

Substituting (7) into (8) and using v ¯ ≡ ϕ q ¯ + ( 1 − ϕ ) q r , we obtain the aggregate demand as

D = { D A = M ϕ q ¯ [ v ¯ − p − γ t + 2 α ( t r − t _ r ) k ( 1 − β ) t ] , if t r is available, D N = M ϕ q ¯ [ v ¯ − p − γ t + α ( 1 − β ) t ε ¯ N ] , if t r is not available.

(9)

Using (9), we can find ∂ D A / ∂ p < 0 and ∂ D N / ∂ p < 0 , which implies that an increase in the retail price can invariably reduce consumer demand regardless of whether the ratings information is available or not.

The equations in (9) complete our model specification. For ease of reference, we provide a list of symbols used in Table 1. As defined previously, superscripts A and N label variables for the scenarios with and without available ratings, respectively. We also use the superscript F to qualify variables of scenarios in which prices are “fixed” or exogenous. The superscripts A N and N B identify variables in the setting of two different retailers and the setting of Nash bargaining, respectively. In addition, the tilde “ ∼ ” denotes the retailer-fulfillment scenario, the single overbar “ ⋅ ¯ ” denotes the upper bound of its argument ⋅ , and the single underbar “ ⋅ _ ” denotes the lower bound of ⋅ . These mathematical expressions apply to all symbols in Table 1.

4.1. Main scenario: Available delivery-time ratings and endogenous pricing

We construct the supplier’s expected profit function as π S A ( w , t ) = [ w − c − s ( t ) ] D A , where c denotes the supplier’s unit acquisition cost, s ( t ) is the per unit delivery cost dependent on promised delivery time, and D A is the expected demand in the presence of delivery-time ratings as given in (9). Because the supplier incurs a higher cost when promising shorter delivery times to consumers, s ( t ) is decreasing in t , that is, s ′ ( t ) ≤ 0 . Moreover, s ″ ( t ) ≥ 0 , because the marginal cost decrease is usually larger for the short promised times than for long promised times. The retailer’s expected profit function is π R A ( p ) = ( p − w ) D A . As ∂ D A / ∂ p < 0 according to (9), we find that ∂ π S A / ∂ p < 0 .

Lemma 1

Given a wholesale price w and a promised delivery time t , the optimal retail price is uniquely obtained as

p A * ( w , t ) = k ( 1 − β ) ( v ¯ + w − γ t ) t + 2 α ( t r − t _ r ) 2 k ( 1 − β ) t

when delivery-time ratings are available and pricing is endogenous.

Next, we substitute p A * ( w , t ) into the supplier’s profit function and have

π S A ( w , t ) = M [ w − c − s ( t ) ] q ¯ ϕ [ v ¯ − w − γ t 2 + α ( t r − t _ r ) ( 1 − β ) k t ] .

Proposition 1

Letting t A * be the solution to the following equation:

k t 2 ( 1 − β ) [ s ′ ( t ) + γ ] + 2 α ( t r − t _ r ) = 0 ,

(10)

we find that, if

2 [ s ′ ( t A * ) + γ ] + t A * s ″ ( t A * ) ≥ 0 ,

(11)

then the optimal promised delivery time t A * is unique. The unique optimal wholesale price is

w A * = v ¯ + c + s ( t A * ) − γ t A * 2 + α ( t r − t _ r ) k t A * ( 1 − β ) ,

(12)

and the unique optimal retail price is

p A * = 3 ( v ¯ − γ t A * ) + c + s ( t A * ) 4 + 3 α ( t r − t _ r ) 2 k t A * ( 1 − β ) .

(13)

Proposition 1 indicates that the inequality in (11) is a sufficient condition for the uniqueness of the optimal solutions. If condition (11) in Proposition 1 is not satisfied, that is, 2 [ s ′ ( t A * ) + γ ] + t A * s ″ ( t A * ) < 0 , then ∂ 2 π S A ( w A * ( t ) , t ) / ∂ ( t ) 2 ∣ t = t A * > 0 and thus, t A * , which uniquely satisfies equation (10), is not the optimal solution that maximizes the supplier’s expected profit π S A ( w A * ( t ) , t ) . That is, π S A ( w A * ( t ) , t ) is convex at t A * , which implies that t A * is the unique solution minimizing the supplier’s profit π S A ( w A * ( t ) , t ) . Therefore, the supplier does not have any interior optimal solution but instead has a boundary optimal solution. To ensure that both marginal profit and demand are greater than 0, we should impose the condition ( v ¯ − c − s ( t ) − γ t ) / 2 + [ α ( t r − t _ r ) ] / [ k t ( 1 − β ) ] > 0 to find two realistic boundary points denoted by t 0 (which approaches 0) and t 1 (which makes the condition equal to 0). As the supplier’s profit is 0 at t 1 , the optimal solution maximizing π S A ( w A * ( t ) , t ) is not t 1 but the lower-bound point t 0 . This indicates that the delivery time promised by the supplier might be relatively short if condition (11) is not satisfied.

Since s ′ ( t ) + γ = − [ 2 α ( t r − t _ r ) ] / [ k t 2 ( 1 − β ) ] < 0 as indicated by (10), we can rewrite the inequality in (11) as [ t s ″ ( t ) ] / [ s ′ ( t ) + γ ] ≤ − 2 . Moreover, we have

t s ″ ( t ) s ′ ( t ) + γ < t s ″ ( t ) s ′ ( t ) ≤ − 2 .

Thus, the inequality in (11) is satisfied if the elasticity of the marginal shipping cost reduction with respect to promised delivery time, λ , satisfies the condition

λ ≡ ∂ s ′ ( t ) / ∂ t s ′ ( t ) / t ≤ − 2 .

(14)

The above inequality indicates that, ceteris paribus, a 1% increase in the supplier’s promised delivery time can lead the marginal shipping cost reduction to decrease by more than 2%. The condition then implies that, if the time elasticity of the marginal shipping cost reduction is more than 2 (i.e., the marginal shipping cost reduction is elastic to the supplier’s promised delivery time), then the optimal solutions are unique. How plausible is this elasticity value in practice? To address this question, we rely on previous research. García-Menendéz et al. (2004) examined a total of 157 exporting firms in four Spanish exporting sectors and found that the shipping-cost elasticity of delivery time lies within the range [ − 0.88 , − 0.13 ] . Similarly, Rich et al. (2009, 2011) used relevant freight data from Denmark to show that the shipping-cost elasticity of delivery time lies within [ − 0.53 , − 0.04 ] . Consistently with these extant empirical results, the value of 1 / λ is likely to be in the range [ − 0.5 , − 0.04 ] , or, λ ∈ [ − 1 / 0.13 , − 1 / 0.5 ] = [ − 7.69 , − 2 ] . Hence, we reasonably assume that λ ≤ − 2 , so that the sufficient condition in Proposition 1 is satisfied and the optimal decisions are unique.

It follows that, when the supplier and the retailer implement the optimal decisions as defined in Proposition 1, the realized demand is

D A = M d A 2 q ¯ ϕ , where d A ≡ [ v ¯ − γ t A * − c − s ( t A * ) 2 + α ( t r − t _ r ) k t A * ( 1 − β ) ] ,

(15)

and the two firms’ profits are π S A ( w A * , t A * ) = M ( d A ) 2 / ( 2 q ¯ ϕ ) and π R A ( p A * ) = M ( d A ) 2 / ( 4 q ¯ ϕ ) .

Next, we conduct a sensitivity analysis of the optimal delivery and pricing decisions to investigate how the supply chain reacts to the changes in market conditions.

Corollary 1

When delivery-time ratings are available and pricing is endogenous, the optimal promised delivery time decreases with consumer sensitivity to delivery time and with consumer sensitivity to delivery-time conformance.

This corollary is consistent with the findings of Shang and Liu (2011) and Leng et al. (2024), who show that the optimal promised delivery time should decrease with consumer sensitivity to the promised delivery time. Nonetheless, Shang and Liu (2011) predict that the optimal delivery time increases when consumers care more about delivery-time conformance, whereas we, like Leng et al. (2024), find that the optimal delivery time decreases when consumers care more about delivery-time conformance. To understand this discrepancy, we relax our modeling assumptions one by one.

First, we consider a setting in which the retailer rather than the supplier fulfills the orders (for details, see Appendix B). We find that Corollary 1 holds in this scenario as well and therefore rule out our choice of the drop-shipping context as a potential explanation.

Second, we examine the possibility that consumers may use alternative sources of information to infer the actual delivery time. In particular, we investigate a setting in which two retailers compete, with one providing product-quality and delivery-time ratings and the other one not publishing any ratings (for details, see Appendix C). Our analysis shows that Corollary 1 still holds in this two-retailer scenario as well. We can thus conclude that our results do not depend on our model of consumer inferences or the presence of competition.

Third, we consider a setting in which the retailer negotiates the wholesale price and delivery efforts with the supplier (for details, see Appendix D). There is anecdotal evidence of such bargaining. For example, the retailers Myer, David Jones, and JB Hi-Fi, and also online cosmetics retailer Adore Beauty secure competitive wholesale prices through negotiations with their suppliers. ⁶ We analyze this scenario as a case of Nash bargaining and find that the result in Corollary 1 continues to hold. Hence, we rule out the potential explanation that our result is contingent upon our choice of competition model.

Finally, we note that the model of Shang and Liu (2011) regards pricing as exogenous, whereas Leng et al. (2024) allow firms to jointly determine prices and the promised delivery time. We follow the latter and accordingly proceed to explore the role of pricing as a potential explanation for the differences between our results and those of Shang and Liu (2011).

4.2. Explanatory analyses: Alternative scenarios

If the ability to recoup shipping expenses via higher prices is what explains the difference between the results in Shang and Liu (2011) and the results in Corollary 1, then the difference should not arise if we consider exogenous pricing. We accordingly solve our model for t with fixed w and p .

4.2.1. The scenario with delivery-time ratings and with exogenous pricing

Given that the wholesale price w and the retail price p are fixed, the supplier’s profit when delivery-time ratings are available is π S A F ( w , t ) = [ w − c − s ( t ) ] D A . Using D A in (9), we have

π S A F ( t ) = M [ w − c − s ( t ) ] q ¯ ϕ [ v ¯ − γ t − p + 2 α ( t r − t _ r ) ( 1 − β ) k t ] ,

where the superscript A F means that ratings are “available” and that prices are “fixed.”

Proposition 2

When delivery-time ratings are available and pricing is exogenous, the supplier’s optimal promised delivery time, t A F * , is the solution to the following equation:

s ′ ( t ) [ v ¯ − γ t − p + 2 α ( t r − t _ r ) ( 1 − β ) k t ] + [ w − c − s ( t ) ] × [ γ + 2 α ( t r − t _ r ) ( 1 − β ) k t 2 ] = 0 ,

(16)

and is unique if

2 { s ′ ( t A F * ) [ v ¯ − 2 γ t A F * − p ] + γ [ w − c − s ( t A F * ) ] } + t A F * s ″ ( t A F * ) [ v ¯ − γ t A F * − p + 2 α ( t r − t _ r ) ( 1 − β ) k t A F * ] ≥ 0 .

(17)

The scenario under which delivery-time ratings are available, and pricing is exogenous, possibly has a unique solution. Moreover, the realized demand is obtained as

D A F = M d A F ϕ q ¯ , where d A F ≡ v ¯ − γ t A F * − p + 2 α ( t r − t _ r ) ( 1 − β ) k t A F * ,

and the supplier’s profit is

π S A F ( t A F * ) = M [ − s ′ ( t A F * ) ] ϕ q ¯ ( 1 − β ) k ( t A F * ) 2 ( 1 − β ) k ( t A F * ) 2 γ + 2 α ( t r − t _ r ) × ( d A F ) 2 .

Corollary 2

When delivery-time ratings are available and pricing is exogenous, the supplier’s optimal demand and profit decrease with the retail price.

The finding in Corollary 2 is consistent with results from the main scenario in which pricing is endogenous.

Corollary 3

When delivery-time ratings are available and pricing is exogenous, the optimal promised delivery time decreases with consumer sensitivity to delivery time but increases with consumer sensitivity to delivery conformance.

Corollary 3 is consistent with the findings of Shang and Liu (2011) regarding both consumer sensitivities. This indicates that the ability of the supply chain to increase prices is a necessary condition for the shortening of promised delivery times to be the optimal response to increases in consumer sensitivity to delivery conformance.

4.2.2. The scenario without delivery-time rating and with endogenous pricing

When delivery-time ratings are unavailable, consumers cannot use the ratings to predict their delivery utility. As discussed in Section 3, with no ratings information, consumers assume that the actual delivery time is ε ¯ N > ε ¯ A and construe the expected conformance of delivery time as t c N = ( 1 − β ) t / ε ¯ N . The aggregate demand is D N as given in (9). The supplier’s and the retailer’s expected profits are π S N ( w , t ) = [ w − c − s ( t ) ] D N and π R N ( p ) = ( p − w ) D N , respectively.

When wholesale price w and retail price p are endogenous, the supplier’s profits are given by

π S N ( t ) = M [ w − c − s ( t ) ] q ¯ ϕ [ v ¯ − γ t − p + α ( 1 − β ) t ε ¯ N ] .

It is easy to derive from (9) that ∂ D N / ∂ p < 0 and ∂ π S N / ∂ p < 0 .

Proposition 3

When delivery-time ratings are not available and pricing is endogenous, the supplier’s optimal promised delivery time t N * is uniquely determined as the solution to the following equation:

ε ¯ N [ s ′ ( t ) + γ ] = α ( 1 − β ) .

(18)

The supplier’s optimal wholesale price is

w N * = [ v ¯ − γ t N * + c + s ( t N * ) ] ε ¯ N + α ( 1 − β ) t N * 2 ε ¯ N .

(19)

The retailer’s optimal retail price is

p N * = [ 3 ( v ¯ − γ t N * ) + c + s ( t N * ) ] ε ¯ N + 3 α ( 1 − β ) t N * 4 ε ¯ N .

(20)

Proposition 3 implies that, in contrast to the case with information disclosure, the case without information disclosure always has a unique optimal solution. Thus, the demand is given by

D N = M d N 4 ϕ q ¯ , where d N ≡ ε ¯ N [ v ¯ − c − s ( t N * ) − γ t N * ] + α ( 1 − β ) t N * ε ¯ N ,

(21)

and the profits of the supplier and the retailer are π S N ( w N * , t N * ) = M ( d N ) 2 / ( 8 q ¯ ϕ ) and π R N ( p N * ) = M ( d N ) 2 / ( 16 q ¯ ϕ ) , respectively.

We again conduct a sensitivity analysis to identify a sufficient condition for the trade-off between delivery time and delivery-time conformance to arise.

Corollary 4

When delivery-time ratings are not available and pricing is endogenous, the optimal promised delivery time decreases with consumer sensitivity to delivery time but increases with consumer sensitivity to delivery conformance.

Corollary 4 suggests that endogenous pricing is not sufficient for the trade-off between delivery time and delivery-time conformance to arise.

4.2.3. The scenario without delivery-time rating and with exogenous pricing

Given that the wholesale price w and the retail price p are fixed, the supplier’s profit is π S N F ( w , t ) = [ w − c − s ( t ) ] D N . Using D N from (9), we rewrite the supplier’s profit as

π S N F ( w , t ) = M [ w − c − s ( t ) ] q ¯ ϕ [ v ¯ − γ t − p + α ( 1 − β ) t ε ¯ N ] ,

where the superscript N F denotes “non available” delivery-time ratings and “fixed” prices.

Proposition 4

When delivery-time ratings are not available and prices are exogenous, the supplier’s optimal promised delivery time t N F * is uniquely given by the solution to the following equation:

− s ′ ( t ) [ v ¯ − γ t − p + α ( 1 − β ) t ε ¯ N ] + [ w − c − s ( t ) ] × [ α ( 1 − β ) ε ¯ N − γ ] = 0 .

This scenario with no information disclosure has a unique solution, in which the demand is

D N F = M d N F ϕ q ¯ , where d N F ≡ ε ¯ N [ v ¯ − γ t N F * − p ] + α ( 1 − β ) t N F * ε ¯ N ,

and the profits are π S N F = M ε ¯ N s ′ ( t N F * ) ( d N F ) 2 / [ ϕ q ¯ ( α ( 1 − β ) − γ ε ¯ N ) ] for the supplier.

Corollary 5

When delivery-time ratings are not available and pricing is exogenous, the demand and supplier’s profit decrease with the retail price.

Corollary 6

When delivery-time ratings are not available and pricing is exogenous, the optimal promised delivery time decreases with consumer sensitivity to delivery time but increases with consumer sensitivity to delivery conformance.

Together, Corollaries 3, 4, and 6 imply that the trade-off between promised delivery time and delivery-time conformance can only be precluded by simultaneously making delivery-time ratings available and jointly determining prices and promised delivery times. This important result does not depend on the assumption of a drop-shipping fulfillment model; it also holds for the retailer-fulfillment model (see Appendix B). In addition, our model does not assume that product-quality rating availability must increase consumer utility because it allows for the case q ¯ ≥ q r . Hence, the result does not rest upon the premise that the availability of delivery-time ratings increases consumer utility (see Section 2). Furthermore, the value of ε ¯ N does not play a role in the main scenario in Section 4.1 and thus, increasing the sensitivity to delivery-time conformance does not have a positive effect on the optimal promised delivery time. Conversely, this effect is negative in each of the other three scenarios regardless of how ε ¯ A compares to ε ¯ N .

These results suggest that the availability of delivery-time rating allows the supply chain to generate value for consumers by reducing the uncertainty in the expected delivery time conformance. However, the supply chain may not have incentives to create such value unless it can capture some of it by adjusting prices.

4.3. The profitability of delivery-time rating availability

We compare our results from the scenario with available ratings against those under the scenario with unavailable ratings to characterize the impact of delivery-time rating availability on the supply chain. We focus on the cases with endogenous pricing, as they are more consistent with the dataset and its institutional context.

Corollary 7

The optimal promised delivery time when delivery-time ratings are available is shorter than that when the ratings are unavailable.

Corollary 7 reveals that information disclosure leads the supplier to promise shorter delivery times. This happens mainly because, when delivery-time ratings are not available, consumers have no information on whether the supplier honors the promised delivery time and thus the expected conformance of delivery time does not increase with shorter promised delivery times. On the contrary, consumers may infer that suppliers are more likely to honor longer promised delivery times (i.e., ∂ t c N / ∂ t > 0 ). Therefore, shortening the promised delivery times does not necessarily increase demand and the supplier has no incentive to incur the additional costs associated with shorter delivery times. However, when delivery-time ratings are available, shorter promised delivery times can increase consumers’ expected conformance of delivery time (i.e., ∂ t c A / ∂ t < 0 ) and increase demand. The gains from an increase in demand outweigh the costs of speedy delivery and the supply chain profits from reducing the promised delivery times.

To assess the effects of delivery-time rating availability on the wholesale and retail prices, we first define the supplier’s unit shipping-cost change associated with the information disclosure as Δ s = s ( t N * ) − s ( t A * ) and note that Δ s ≤ 0 . Likewise, we define the delivery utility as u ( t c ) = α t c − γ t and the change in delivery utility that a consumer experiences because of information disclosure as Δ u . We then note that, if Δ u ≥ 0 , then information disclosure increases consumer delivery utility by Δ u . Otherwise, if Δ u < 0 , then consumer delivery utility decreases by | Δ u | .

Corollary 8

Let u ( t c A ) = α t A * ( 1 − β ) / ε ¯ A − γ t A * and u ( t c N ) = α t N * ( 1 − β ) / ε ¯ N − γ t N * . If and only if

Δ u ≡ u ( t c A ) − u ( t c N ) ≥ Δ s ≡ s ( t N * ) − s ( t A * ) ,

(22)

then the wholesale price when delivery-time ratings are available (i.e., w A * ) is no smaller than the wholesale price when the ratings are not available (i.e., w N * ). If and only if Δ u < Δ s , w A * is smaller than w N * . Moreover, if and only if

Δ u ≥ Δ s / 3 ,

(23)

then the retail price when the delivery-time ratings are available (i.e., p A * ) is no smaller than the retail price when the same ratings are not available (i.e., p N * ). If and only if Δ u < Δ s / 3 , retail prices satisfy p A * < p N * .

Corollary 8 reveals that, even if the optimal promised delivery time under no information disclosure is greater than its counterpart under information disclosure, the optimal wholesale and retail prices may not be smaller when the delivery-time ratings are available to consumers. The corollary identifies three possible scenarios that are interpreted as follows.

Scenario 1: Δ u ≥ Δ s / 3 . Condition (23) is satisfied (i.e., Δ u ≥ Δ s / 3 and Δ s ≤ 0 ) and therefore the condition in (22) is also satisfied (i.e., Δ u ≥ Δ s and Δ s ≤ 0 ). As a result, both the wholesale and retail prices under information disclosure are greater than those under no information disclosure, that is, w A * ≥ w N * and p A * ≥ p N * . The underlying intuition is that, if consumers benefit more than the supplier from the disclosure of delivery-time ratings, then, when disclosing the ratings information, the supplier and the retailer should raise their prices to offset the increase in shipping costs.

Scenario 2: Δ s ≤ Δ u < Δ s / 3 ≤ 0 . Under this scenario, w A * ≥ w N * and p A * < p N * . Because Δ u < 0 , information disclosure reduces total consumer utility by a moderate extent. The supplier raises the wholesale price whereas the retailer decreases the retail price. As a result, the retailer’s profit margin (i.e., p A * − w A * ) is larger when information is disclosed.

Scenario 3: Δ u < Δ s ≤ 0 . Under this scenario, w A * < w N * and p A * < p N * . The information disclosure significantly reduces total consumer utility below a certain threshold Δ s ≤ 0 . Both the supplier and the retailer have to decrease their prices to compensate for consumers’ losses.

Corollary 9

The expected demand as well as the supplier’s and the retailer’s expected profits are higher when delivery-time ratings are available than when ratings are unavailable, if

Δ u + Δ s ≥ 0 .

(24)

We learn from Corollary 9 that the valence of the effects of information disclosure on expected demand and the profitability of the supply chain depends on the condition in (24), where Δ u + Δ s is regarded as the “system-wide value” resulting from the availability of delivery-time ratings. If the condition in (24) holds, then the conditions in (22) and (23) are satisfied as well. That is, a positive system-wide value leads to higher wholesale and retail prices. A non-negative system-wide value benefits the supply chain and provides incentives for the retailer and the supplier to disclose the information of delivery-time ratings.

As per the discussion that follows Proposition 1, if condition (11) in Proposition 1 is not satisfied, the optimal solution maximizing the supplier’s expected profit is a realistic lower-bound point. In such a case, we find that Corollary 1 does not hold but Corollaries 7 and 8 may hold.

5. Empirical support

We present empirical support for the theoretical results in Corollaries 7 and 9, which are the results that can be tested with Cainiao’s dataset. The dataset reports delivery-time ratings only when product-quality ratings are available and vice versa. Accordingly, we solve our game-theoretic models with endogenous prices once again but without both quality and delivery-time ratings. We find that the new results are qualitatively equivalent to the results for the case with product quality ratings but no delivery-time ratings. For details, see Appendix E where we obtain Corollaries F, G, and H by comparing the optimal promised delivery time, optimal prices, expected demand as well as profits when both quality ratings and delivery-time ratings are available and those when the two ratings are unavailable.

We then use the implications of these theoretical models to formulate hypotheses that match the features of the data-generating process. First, we rely on Corollary H to posit the following.

Hypothesis 1

Product sales are higher when ratings are available than when ratings are unavailable.

A test of this hypothesis with secondary data faces the challenge of reverse causation. It is possible that the sales of new products are naturally not large enough to generate sufficient ratings and therefore delivery-time ratings may be absent as a consequence of low sales. To eliminate this reverse effect of sales on rating availability, we order the transactions of each seller according to their dates and identify the first transaction that was rated. We then discard all prior transactions. Hence, in the filtered sample, we exclude transactions in which published ratings were absent due to the lack of sales. We thus rule out the possibility of simultaneity bias.

Next, we construct reliable measures of unit sales and promised delivery times by aggregating the data so that the unit of observation is the combination of supplier, item, and rating availability level (available or unavailable). We only keep supplier and item combinations for which we observe both levels of rating availability. This filtering step, together with aggregation, reduces the sample to 7,798 observations. In this sample, we observe that the supplier sales are on average 1,018.98 units when ratings are not available ( n = 3,668 ) and 9,610.93 when ratings are available ( n = 4,130 ). We use the data to estimate regressions of the logarithm of sales on a dummy variable that equals one when delivery-time ratings are available and zero otherwise. We use supplier and subcategory fixed effects to control for unobserved heterogeneity and mitigate omitted-variable biases. The results, as given in Table 2, confirm that sales are higher when ratings are available (also see robustness tests in Table I in online Appendix III). In particular, the sales are exp ( 2.282 ) = 9.796 times higher ( p - value ≤ 0.01 ) when ratings are available. These results are consistent with Corollary H and therefore support Corollary 9.

We next rely on Corollary F to propose the following.

Hypothesis 2

The optimal promised delivery time is shorter when ratings are available than when ratings are not available.

We test this hypothesis with another regression model. Specifically, we use the average promised delivery time as the dependent variable and find that it is 3.912  h shorter ( p - value ≤ 0.01 ) when delivery-time ratings are available (see Table 2). This difference amounts to 7.4 % of the average promised delivery time, equal to 52.95  h (see Table 4 in Appendix A). Because these results are consistent with Corollary F and support Corollary 7, they provide empirical support for the implications of our theoretical model.

6. Summary and concluding remarks

In this paper, we consider a two-echelon supply chain consisting of a supplier and a retailer who serve an online market under the drop-shipping fulfillment model, which has been commonly adopted in online retailing. We rely on data from the Tmall supply chain to model and analyze consumer utility and to derive expected demand functions for both cases with and without delivery-time ratings. We allow the promised delivery time to affect consumer utility directly through its effect on expected waiting times and also indirectly through the effect of delivery-time ratings on expected delivery-time conformance. In agreement with the drop-shipping model, the supplier is in charge of product delivery and the retailer is only responsible for enabling transactions. Accordingly, the supplier determines the wholesale price and promised delivery time, whereas the retailer determines the retail price. We find that, under this scenario, the optimal promised delivery time is increasing in both consumer sensitivities to delivery time and to delivery-time conformance.

As extant publications have shown the optimal promised delivery time to be decreasing in consumer sensitivity to delivery time, in this paper we analyze additional models to explain the discrepancy. We find that the trade-off between delivery time and delivery-time conformance arises from the combination of delivery-time rating availability and the endogeneity of pricing (i.e., the ability of the supply chain to coordinate prices and promised delivery times). We show that this result also holds for the retailer-fulfillment model, in which the retailer rather than the supplier makes the promised delivery-time decision (see Appendix B), and also for a two-retailer case in which one retailer publishes product-quality and delivery-time ratings whereas the other one does not (see Appendix C). We further validate the result in a context of Nash bargaining where the retailer and the supplier bargain over the wholesale price and promised delivery time (see Appendix D). Next, we find conditions for delivery-time rating availability to improve sales and profitability. Finally, we analyze the Tmall dataset to provide empirical support for two testable implications of our theoretical models.

The main implications of our analyses are summarized as follows:

Optimal promised delivery times are decreasing in consumer sensitivity to delivery time, no matter whether prices are endogenous or exogenous and no matter whether delivery-time ratings are available or not.

Optimal promised delivery times are increasing in consumer sensitivity to delivery-time conformance, unless pricing is endogenous and delivery-time ratings are available. If these two conditions hold, optimal promised delivery times are decreasing in consumer sensitivity to delivery conformance, and there is no trade-off between delivery times and delivery-time conformance.

Regardless of whether the supply chain uses the drop-shipping model or the retailer-fulfillment model, the optimal promised shipping time is shorter when rating information is disclosed than when it is not. For both fulfillment models, the impacts of information disclosure on the wholesale and retail prices are similar. If the information disclosure makes consumers’ total utility increase greater than the supplier’s unit shipping-cost increase, then the supplier and the retailer raise their prices when disclosing rating information. If consumers incur a medium total utility reduction after information disclosure, then the supplier raises the wholesale price whereas the retailer decreases the retail price. Otherwise, if consumers experience a sufficiently large total utility reduction, both the supplier and the retailer reduce their prices to compensate consumers for this loss.

For both the drop-shipping and the retailer-fulfillment models, the supplier’s and the retailer’s incentives to disclose rating information depend on the system-wide value (i.e., the sum of consumers’ total utility increase and the supply chain’s unit shipping-cost reduction).

Because making delivery-time ratings available can shorten optimal delivery times, this strategy may not be profitable for online marketplaces that lack affordable access to a high delivery-speed infrastructure (e.g., marketplaces that operate in remote geographic areas or that lack capital to develop the capability in-house). Likewise, making delivery-time ratings available may not be profitable when short delivery times are cost-prohibitive or pricing restrictions are enforced (i.e., prices are exogenous or capped). These two possible scenarios could explain why some online retailers make delivery-time ratings available while others do not.

Supplemental Material

sj-pdf-1-pao-10.1177_10591478261460106 - Supplemental material for Retailer–supplier coordination of pricing and delivery ratings availability decisions in online marketplaces

Supplemental material, sj-pdf-1-pao-10.1177_10591478261460106 for Retailer–supplier coordination of pricing and delivery ratings availability decisions in online marketplaces by Chi Zhou, Rafael Becerril-Arreola and Mingming Leng in Production and Operations Management