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Online Consumer’s Optimal Purchasing Decisions Under Contingent Free Delay Shipping

Qianqian Liu* Wenliang Bian School of Economics and Management

Beijing Jiaotong University Beijing, China

[email protected]

Abstract—This paper considers the optimal purchasing decisions of a consumer when online retailers provide contingent free shipping service under delay delivery. A consumption decision model for online consumers is proposed by establishing net consumption surplus function under delay delivery, which comprehensively considering all of the conditions including the product price, delay time, free shipping threshold given by online retailers, as well as the consumer’s individual characteristics relate to the preference for the product and sensitivity on delay delivery, which can be used to analyze the best purchasing decisions of an online consumer. Finally, a numerical example proves the reliability of the model, and the result shows that a consumer’s optimal purchasing decisions mainly depend on the comparison of free shipping cut off level under delay delivery and consumer’s specific parameter about the preference for the product and sensitivity on delay time. Simultaneously, it indicates that free delay shipping service with a reasonable threshold could attract additional consumers with middle consumption desire to enlarge purchasing amount, which can be used as a reference for online retailers to set an effective free delay shipping strategy.

Keywords—purchasing decision; delay delivery; contingent free shipping; net consumption surplus

I. INTRODUCTION With the growing scale of online shopping, more and more

consumers are choosing to shop online for enjoying the convenience of the Internet. According to the "36th Statistical Report on Internet Development in China" released by China Internet Network Information Center (CNNIC), the data displays that China's online shopping users has reached 374 million till June 2015. Owing to the growing consumption demand for online shopping, the competition among online retailers has become increasingly fierce, in order to attract more consumers, online retailers have provided a variety of free shipping strategy. For example, the delivery strategy of "Free shipping on orders over 79 RMB" implemented by JD.com Inc, T-mall carrying out unconditional free shipping on Nov 11 each year, et al. Note that free shipping has not only become a competitive tool for E-commerce enterprises to attract consumers, but also bring consumers more and more preferential service. However, online shopping has taken the convenience to the public, but at the same time raised some new issues. Especially in recent years, delay in delivery is

becoming increasingly prominent. By analyzing the causes, it’s easy to find that on the one hand, the hot Internet shopping market leads to the frequency of occurrence on out of stock increasing, but retailers’ ability for rapid replenishment is limited; on the other hand, the nature of the Internet shopping requires its extreme dependence on logistics, the uncertainty of logistics often leads to delay in delivery. In particular, the later is the major cause as a result of the impacts of weather, traffic, delivery demand et al. In a word, delay delivery of online shopping is almost inevitable in the current environment.

Delay delivery would not only affect the consumers’ consumption experience, but also have negative impact on the service and reputation of online retailers. Therefore, in order to maintain and compensate consumers, offering free delay shipping may be feasible for online retailers. From this view, this paper considers consumer’s decision-making when retailers offer free shipping under delay delivery and investigate the best purchasing decisions for a consumer. Reference [2] suggests that contingent free shipping is the most effective strategy for online retailers to attract consumers and increase profit compared with the other two strategies, i.e. unconditional free shipping and shipping fees increasing with order size, which is consistent with the real delivery service mode taken by most retailers in online shopping environment. Generally, online consumers decide whether to choose free shipping service simply by considering the purchase quantity or purchase amount on the product under normal delivery. However, it varies under delay delivery, because the time factor will influence consumers' purchase decisions, where there is a necessary to re-analyze consumers’ decision rules.

On consumer’s decision-making, many scholars launch the research from the factors that influence online consumer’s consumption behavior, where the psychological characteristics of consumers is a focus of the research. Reference [1] has discussed the influence of consumers’ psychological characteristics including time-stressed behavior et al on online shopping behavior. In addition, reference [9] have investigated the impact of price factors on consumers’ online shopping behavior. Some others applied utility theory to the research of consumers' online shopping behavior, as [3] and [4] showed, there is a certain relationship between consumption utility and

the purchase quantity of products and the psychological expectations of consumers, and consumption utility function constructed by consumers’ psychological expectations and the purchase quantity of products is obtained according to marginal utility diminishing theory. Although utility theory didn’t raise consumer’s decision-making model, but proposed the "economic man" hypothesis, assuming that consumers in the market are all rational decision-makers with a series of constraints (such as income, et al.) and pursuit maximization consumption utility. Based on this, reference [5] proposed a net consumption surplus function capable of quantitative analysis on consumers’ decision-making, which just supports the mental accounting theory LI, HAO, LI and LING build [6]. In summary, although the study on consumer’s decision- making is no longer limited to qualitative analysis, also including gradually in-depth quantitative research, it still needs to further expand the application of the related research results to more specific problems, such as delay delivery.

Based on the above, this paper investigate the online consumer’s optimal purchasing decisions under the situation that retailers offer contingent free delay shipping. First, we provide a detail description for the problem, where we create free delay shipping rule for an online retailer combined with related research results and actual delivery strategy. Next, we analyze the consumer’s best purchasing decision by establishing net consumption surplus function under delay delivery according to product price, delay time, free shipping conditions and consumer’s characteristic about preference for product and sensitivity on delay. Finally, we perform a numerical example to examine the reliability of consumer’s decision-making model, as well as the influence of free delay shipping threshold on consumer’s best purchasing decision, and propose some managerial insights based on the analysis result.

II. SCENARIO DESCRIPTION In this section, we provide a detailed description of the

problem and a preliminary discussion on it. In order to facilitate the research, here simulate such a scenario: there is an online retailer selling single product with fixed-price, but because of some unavoidable factors, the retailer can’t provide consumers with timely delivery service in a short term. Therefore, delay delivery for all orders generated during that time will occur. To mitigate its negative impacts on sales, the online retailer provide all consumers shopping in this period contingent free delay delivery service as compensation. The online retailer disclose the delay delivery time and the conditions for free shipping to every consumer arriving at the shop in advance, and develop free shipping rule: if the purchase amount consumers spending in one transaction reach the free shipping threshold the retailer developed, then the consumers are qualified for free delay shipping, i.e. consumers only pay for the amount of shopping to retailers and the shipping fees are paid by online retailer, otherwise, the consumers are responsible for the shipping fees increasing with purchase values, which is the on-time delivery charges in usual the retailer followed. Then, in this context, according to product price, delay time in delivery and the free delay shipping conditions the online retailer reported, consumers will determine whether or not to consume and the best

purchasing decisions that maximize their own interests when they choose to consume by weighing the revenues to obtain and expenses to spend in a single transaction.

According to the above description of the problem, to fulfill the need for theoretical analysis, there is a necessary to make the following assumptions:

• The price of the product online retailer selling is constant, and there is no price discount;

• The consumers are full rational, and they make decisions to maximize their own interests in the consumption process;

• The consumers are in a state of complete information, i.e. they has been fully aware of the free delay shipping conditions, delay delivery time and the product information provided by the online retailer and they consume on their needs. So here only analyze consumer consumption behavior in the final decision- making process, regardless of consumer behavior carried out in pre-web browser to search for product information and other processes;

• In order to facilitate model derivation and analysis, we set the consumers’ purchase quantity or amount is a continuous variable, the slack variable assumed will not affect the nature of the solution;

• For the period discussed in this paper, retailer can’t provide on-time delivery service to any consumer;

• The standard shipping charges is related with the purchase amount of consumers, and the shipment formula in [5] is computed as:

sAsAS += 0)(  (1)

where 0

s and s denote the fixed value and variable value of shipment, respectively.

• To facilitate quantitative research, this paper only considers consumer purchase decision problem in a single transaction.

III. PURCHASING DECISION OF AN ONLINE CONSUMER IN A SINGLE TRANSACTION UNDER DELAY DELIVERY

According to the scenario described above, the final decision-making process of consumers is analyzed and the best purchasing decisions are investigated in this section. In the light of the information of product and shipping services provided by the retailer, consumers determine the purchasing quantity (or amount) of product and the form of shipping services on individual preferences. Since consumers are perfectly rational, the final decision of consumers must be the best purchasing decisions able to make their own benefit maximum. Based on this, the interests of consumers got in one transaction should be depicted firstly. More specifically, here denote c as the retailer’s unit acquisition cost of the product and m as the profit margin, then the price of the product can be easily computed as cmp )1( += . The delay time in delivery is denoted by T ( 0>T ), based on which the retailer

gives a contingent Free-Shipping(CFS) threshold T

x , and promises that consumers can enjoy free delay shipping as long as the amount spent on single order by consumers is not less than free shipping threshold, otherwise, the consumers should bear the shipping fee on their own. In view of this analysis, we have to characterize the profit obtained in one transaction for consumers through the establishment of consumer’ s net surplus function.

A. Net Consumption Surplus Function of a Consumer Net consumption surplus reflects the ultimate profit of

online consumer obtained in a single transaction, which is expressed as the total utility subtracts the total expenditure in the formula Leng and Rafael build [5]. Therefore, we should first calculate consumer’s total utility in delay delivery. Suppose a consumer with product-specific parameter θ buys q units of product from the retailer with purchase amount

cqmpqA )1( +== in a single transaction, then the consumer obtains a consumption utility qU θ= , where θ is a non- negative parameter to express the degree of consumer’s preference for product. Note that the square-root utility function is widely used in many areas. As online retailer can only provide all consumers with delay delivery during that period, and the delay time will dilute the value the consumer gets from online shopping, so the total utility of a consumer in the context of delay delivery should be the consumption utility considering the impact from the delay time,which means that the consumption utility need to be further quantified by delay discounting. The value of reward will be discounted with a delay realization of consumers achieving it, which is so-called delay discounting. From the above analysis, the consumption utility is reward that consumers are achieving in single transaction, but delay delivery will make the value of the consumption utility discounted. Thus, according to the concept of hyperbolic delay discounting Mazur builds [7], the total utility of consumers under delay delivery can be computed as

q kT

UT θ+ =

1 , where k is a coefficient on behalf of the

sensitive degree for individual on delay delivery time T . As to consumer’s total expenditure, i.e. the total amount that consumers should pay to the online retailer, it depends on comparison of, if consumer’s purchase amount A isn’t less than the cut-off level

T x , the consumer is qualified for free

delay shipping, and what consumer pay to the online retailer is just the purchase amount, otherwise, the consumers should pay additional shipping fee, at this time, the total expenditure not only includes the purchase amount A , but also the shipping fee )( AS .

Using the above, we can compute the net consumption surplus that the consumer with parameters θ , k derives from consuming q units of product from online retailer under delay delivery. Let G denote net consumption surplus and we have net consumption surplus under delay delivery as

 

 



<−+−θ +

≥+−θ +

= =

xAAScqmq kT

xAcqmq kT

G G

,)()1( 1

,)1( 1

(2)

It’s not difficult to find that the scenario when the retailer provide on time delivery is exactly a special case with 0=T . For ease of following discussion, we momentarily ignore the constraints in (2) to find the solution that maximizes 1G and

2G respectively. The proof of following theorem 1 and theorem 2 are with reference to Leng and Rafael [5], we don’t repeat them here.

Theorem 1. Net consumption surplus G is convex on q (the same on A ), and it satisfies:

When 222

1 )1()1(4

ˆ kTmc

q ++

θ = , the resulting

purchase amount 1Â and maximum net consumption surplus * 1G are, respectively,

ϕ+

φ ==

)1(4 ˆ

1 * 1

m AG ��(3)

Similarly, when 2222

2 )1()1()1(4

ˆ kTmsc

q +++

θ = ,

the resulting purchase amount 2Â and maximum net

consumption surplus *2G are,

0 * 2

)1)(1(4 s

sm G −

ϕ++ φ

(4)

ϕ++

φ =

22 )1)(1(4 ˆ

sm A (5)

where c

2θ =φ denotes the consumer-specific utility

parameter, and 2)1( kT+=ϕ denotes delay discounting

parameter.

B. Best Purchasing Decision of a Consumer Based on the above analysis, The comparison of CFS

threshold Tx and consumer’s total purchase amount A decides whether the consumer can obtain free delay shipping service or not. Since the parameter is different among consumers, consumer’s total purchase amount A is a random variable. According to the position of CFS threshold Tx and

consumer’s total purchase amount A ,there are the following four cases in Fig. 1.

2Â 1Â (a) 2ÂxT ≤

2Â 1Â (b) 12

ˆˆ AxA T ≤<

2Â 1Â (c) TxA <1ˆ and TxAGG =≤ |1

* 2

* 1G

* 2G

1G2G

2Â 1Â

TxA G |1

(d) TxA <1ˆ and TxAGG => |1

* 2

Fig. 1. Four cases for the optimal solution *A of the consumer with

parameter φ , ϕ

Combined with net consumption surplus function in (5),

analyze the above four cases, consumer’s optimal purchase amount *A maximizing G is shown in the following theorem 2.

Theorem 2. Given a unit acquisition cost c , a profit margin m , a delay time T , and a CFS cutoff level Tx , the optimal

purchase amount *A maximizing the net consumption surplus of the consumer with specific parameter φ ,

ϕ is as follows:

• When )1(4 0 ssxT +< ,then

(1) If it satisfies )1(4 mxT +≥ϕ φ

, the consumer’s

optimal purchase amount 1 * ÂA = .

(2) If it satisfies )1(4)1( mxmx TT +<ϕ φ

≤+ , the

consumer’s optimal purchase amount TxA = * .

(3) If it satisfies )1( mxT +<ϕ φ

, the consumer’s

best choice is to leave without buying anything.

• When )1(4 0 ssxT +≥ ,then

(1) If it satisfies )1(4 mxT +≥ϕ φ

, the consumer’s

optimal purchase amount 1 * ÂA = .

(2) If it satisfies

)1(4

))1()(1)(1(4 20

sxsxsms

+< ϕ φ

≤+−+++

the consumer’s optimal purchase amount TxA = * .

(3) If it satisfies

2 0

))1()(1)(1(4

)1)(1(4

TT sxsxsms

mss

+−+++

< ϕ φ

≤++

the consumer’s optimal purchase amount 2 * ÂA = .

(4) If it satisfies )1)(1(4 0 mss ++<ϕ φ

, the

consumer’s best choice is to leave without buying anything.

Theorem 2 suggests that consumer’s optimal purchasing decision depends on the specific parameter φ ,

ϕ relate to

consumer’s preference for the product sold by online retailer and sensitivity to delay delivery service respectively, as well as free shipping cutoff level. More specifically, if free delay shipping threshold set by the online retailer is low, then

consumer’s best purchasing decision maybe spending 1Â , Tx or abandoning the purchase to leave. Especially, for the consumer with much more preference for the product or rather low time-sensitive on delay delivery, who has strong desire to

purchase, a larger purchasing amount 1Â is the best purchasing decision, which not only maximize consumer’s profit, but also make the consumer obtain free delay shipping service. However, when the consumer doesn’t have much interest in the product, or be a little more on minding the delay time in delivery, and doesn’t want to purchase too much, but the free shipping threshold is at a lower level, to pursue maximum profit, it’s the best choice for the consumer to enlarge the purchase amount to free shipping threshold for free shipping service. As to the consumer whose preference for the product is very small, or he/she is completely sensitive to the delay time in delivery, the consumer had better to leave to abandon the purchasing behavior at this time. On the contrary, if the online retailer sets a higher free shipping threshold, the

optimal consumer’s purchasing decisions should be 1Â , 2Â ,

Tx , or not buying anything to leave. In this case, the increasing free shipping threshold doesn’t influence those who prefer a larger purchasing amount for product, or with little sensitivity on the delay time in delivery, and it’s the same as the consumer with lowest consumption desire, whose preference for the product is very small, or sensitivity on the delay time in delivery is high. But for the consumers with moderate consumption desire is totally affected, they may abandon free delay shipping service because the CFS cut off level is too high to reach for them.

IV. NUMERICAL EXAMPLE AND SENSITIVITY ANALYSIS To confirm the validity of the purchasing decision model

above, we introduce a numerical example and make a comprehensive analysis on the result. Given that a online retailer sells a single product and provide a contingent free

delay shipping service. The related parameters of the product and free delay shipping service take the values as shown in TableⅠ.

TABLE I. RELEVANT DATA FOR PARAMETERS FROM THE ONLINE RETAILER

Name

Parameters of Free Delay Shipping Parameters of

Product

CFS

( Tx )

Fixed Shipping

Fee

( 0s )

Variable Shipping

Fee ( s )

Delay Time

( T )

Profit Margin ( m )

Unit Acquisition

Cost ( c )

value 4.63 10.00 1.00 3.00 1.10 13.00

Next considering a consumer with product preference parameter 20=θ , delay-sensitive coefficient 1.0=k , the consumer’s net consumption surplus function under the situation that the delivery of product will delay three days is obtained when all data of parameters are applied into the formula in (2). It can be seen from Fig.2 that the change of net surplus above the black dotted line the affects consumer’s purchasing decision, which indicates that when spending

63.4* =A , the consumer will obtain the maximum profit, while that below the dotted line determines consumer’s leave without buy anything. On the other hand, we could draw the same conclusion that this consumer’s optimal purchasing

decision under current conditions is TxA = * , because it

satisfies )1(4 0 ssxT +< , )1(4)1( mxmx TT +<ϕ φ

≤+

according to theorem 2. At this point, the consistency of the two results proves the reliability of the purchasing decision model.

0 2.5 5 7.5 10 12.5 15 -14

-12

-10

-8

-6

-4

-2

X: 4.63 Y: 1.706

Purchase amount (A)

N e

t s u

rp lu

s (G

)

Fig. 2. Net surplus function G of consumer with 20=θ , 1.0=k .

0 1 2 3 4 5 6 7 8 9 10 0

X: 8.66 Y: 8.66

CFS thres hold (x T )

B e

st p

u rc

h a

se a

m o

u n

t ( A

*) , N

e t s

u rp

lu s

(G *)

X: 8.67 Y: 0

X: 2.17 Y: 2.17

A*—x T

G*—x T

Fig. 3. The impacts of CFS threshold ( T

x ) on best purchase amount ( *A ) and

maximum net surplus ( *G )

Since the free shipping threshold Tx set by the online retailer is one of the most important factors that determine the optimal purchasing decisions for the consumer. So we will examine its impact on the consumer’s optimal decisions and maximum net consumption surplus perform by performing sensitivity analysis to it. Figure 3 shows that, when

]10,0[∈Tx , it satisfies )1(4 0 ssxT +< , the variation of consumer’s optimal purchasing decision is consistent with the consumption decision rule in theorem 2, where with free shipping threshold

T x increasing, the maximum net

consumption surplus *G remains unchanged firstly, and then gradually decreases to zero; and correspondingly, the consumer’s optimal purchasing amount *A remains constant as

* ÂA = at first, and then increases linearly as TxA = * until

free shipping threshold T

x increases to a certain extent (Combined with the parameter conditions related to the consumer, the situation

* ÂA = doesn’t exist.), and the maximum net consumption surplus *G is reduced to zero, the consumer will abandon purchasing behavior. In addition, the sensitivity analysis of free shipping threshold

T x yields that

providing free delay shipping service could attract additional consumers with middle consumption desire when free shipping threshold reach a reasonable level but not too high, which is a reference to online retailers to develop an effective free shipping threshold under delay delivery.

V. SUMMARY AND CONCLUDING REMARKS

This paper launched a research problem about the consumer’s optimal purchasing decision under the online retailers providing free delay shipping service on the basis of the existing literature on the issue relate to consumer’s consumption decision and free shipping. We firstly established consumer’s net consumption surplus function, and then drew a conclusion on the consumer’s optimal purchasing decisions given the conditions of the product, delivery service provided by the online retailer as well as the consumer’s individual characteristics (relate to individual preference for the product

and sensitivity to delay delivery) through analyzing consumer’s decision-making process. Finally, we stimulated a numerical experiment to prove the reliability of consumer’s optimal purchasing decision model. Furthermore, the results show that: 1) The consumer’s optimal purchasing decision under delay delivery depends on consumer’s specific parameter φ ,

ϕ relate to consumer’s preference for the

product and sensitivity to delay delivery service respectively, as well as online retailer’s free delay shipping cutoff level

T x ,

profit margin m et al, where consumer’s specific parameter and free delay shipping threshold are two of the most important factors. According to the conclusion of best purchasing decisions of a consumer, there always exists the consumers with perfectly high preference for product and a little sensitivity on delay delivery being qualified for free delay shipping and those with little preference for product and much more sensitivity on delay delivery leaving without buying anything whatever the free delay shipping cut off level is set, but the others with middle consumption desire should trade off their own specific parameter and online retailer’s free delay shipping cutoff level to decide the best purchasing amount; 2) Providing free delay shipping service with a reasonable threshold could attract additional consumers with middle consumption desire to enlarge the expense for free delay shipping, which may lead to increasing profit for online retailers. This result also indicates that carrying out free delay shipping service has practical significance and implementation value. For further research, we will investigate the possibility of implementing free delay shipping from online retailers, and we will take a variety of product categories into account.

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[2] Lewis, M., V. Singh and S. Fay, “An empirical study of the impact of nonlinear shipping and handling fees on purchase incidence and expenditure decisions”, Market. Sci, vol. 25, no.1, pp. 51–64, 2006.

[3] Chung and J.W, Utility and Production Functions. Cambridge: Blackwell, 1994.

[4] Coto-Milla'n and P, Utility and Production: Theory and Applications. Heidelberg: Physica-Verlag, 1999.

[5] Mingming Leng and Rafael Becerril-Arreola, “Joint Pricing and Contingent Free-Shipping Decisions in B2C Transactions” , PRODUCTION AND OPERATIONS MANAGEMENT, vol. 19, no.4, pp. 390-405, 2010

[6] LI Ai-Mei, HAO Mei, LI Li and LING Wen-Quan, “A New Perspective on Consumer Decision:Double-entry Mental Accounting Theory”, Advances in Psychological Science, vol. 20, no.11, pp. 1709-1717, 2012.

[7] Mazur J E, “An adjusting procedure for studying delayed reinforcement”, Commons, ML.; Mazur, JE.; Nevin, JA, pp. 55-73, 1987.

[8] Basu, A. K., R. Lal, V. Srinivasan and R. Staelin, “Salesforce compensation plans: An agency theoretic perspective”, Market.Sci, vol. 4, no.4, pp. 267–291, 1985.

[9] Gupta, S., & Kim and H. W, “Value-driven Internet shopping: The mental accounting theory perspective”, Psychology and Marketing, vol. 27, pp. 13–35, 2010.

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