Cost-benefit associations in consumer inventory problem with uncertain benefit

Journal of Retailing and Consumer Services 51 (2019) 271–284

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Cost-benefit associations in consumer inventory problem with uncertain benefit

T

Haonan Hea, Shanyong Wangb,∗ a b

School of Economics and Management, Chang'an University, 710064, PR China School of Management, University of Science and Technology of China, 230026, PR China

ARTICLE INFO

ABSTRACT

Keywords: Consumer inventory decision Cost-benefit associations Newsvendor problem Benefit uncertainty Laboratory experiments

Newsvendor problems always describe a situation in which the vendor needs to predict the demand by a buyer when a constant unit profit is predetermined. However, sometimes, the vendor can effectively affect the demand as well as the unit profit, that is, when he is also the buyer simultaneously. Should he purchase more or less in advance when both the demand and unit benefit are uncertain? In this paper, we study how the vendor/buyer (consumer hereafter) would make this inventory decision when the unit profit is uncertain. We first analyze the evaluating process of consumers by conducting a mathematical model to contribute to the understanding of how the cost-benefit association affects consumer inventory decisions. Consumers would experience an immediate pain of payment (cost) at the order time, which is associated to thoughts of the uncertain pleasure (benefit) such payment may provide at the consumption time. The result shows the cost-benefit association might encourage consumers to either over- or underestimate the pain of paying and thereby take economically sub-optimal decisions. Based on this finding, we conduct three laboratory experiments to analyze the parameters in our model. Contrary to the existing literature, we find that the demand uncertainty may enhance consumer inventory decisions. Specifically, when the benefit uncertainty is really high, a strong cost-to-benefit link caused by the small probability of a great outcome would prevail against a weak benefit-to-cost link, leading to more deviation from the theoretical optimal quantity. Interestingly, we also show that changes to the benefits can lead to more deviation in order quantity, that is, a direct effect of benefit and an indirect impact on demand would jointly make changes to the benefits more effective than changes to the cost. Our finding has important implications on how firms should set prices and inventories of seasonal goods and how much money should invest in promoting pre-purchase behaviors (e.g., store cards).

1. Introduction Consumers usually buy seasonal products before actual consumption, such as purchasing a prepaid card for several trips to a gym or a swimming pool due to a special discount offered currently. In other words, the payment and consumption occasions are not always synchronous. Newsvendor problem captures a similar situation in which a vendor needs to predict the demand by a buyer when a constant unit profit (e.g., both retail price and wholesale price are known) is predetermined. It is one of the fundamental problems tackled in inventory management literature (Fisher and Raman, 1996), and is applicable to a broad array of settings, including retailing and manufacturing (e.g., Bolton and Katok (2008); Xiang et al. (2015)). For instance, a retailer should thoroughly determine the inventory before launching a new product, and a greengrocer must supply an appropriate wholesale

∗

volume before a selling season. Our understanding of how a vendor makes inventory decisions in this kind of setting has advanced significantly in recent years. For example, the seminal work of Eeckhoudt et al. (1995) compared vendors with different risk preferences and demonstrated that risk-averse vendor orders less than the expectedprofit-maximizing solution, whereas risk-seeking vendor orders beyond expectation. Schweitzer and Cachon (2000) revealed that even if the cost parameters are directly specified, vendors’ choices never correspond to those that maximize the expected profit. Moritz et al. (2013) further applied a theory of cognitive reflection to explain the wide observed variation among individual orders. Above all, most of the literature focuses on price-independent market demand. However, the vendor can effectively affect the demand as well as the unit profit, that is, when he is also the buyer simultaneously. Besides, a buyer may act as the vendor to decide the supply, and the pleasure derived from

Corresponding author. E-mail address: [email protected] (S. Wang).

https://doi.org/10.1016/j.jretconser.2019.06.013 Received 21 August 2018; Received in revised form 22 March 2019; Accepted 20 June 2019 0969-6989/ © 2019 Elsevier Ltd. All rights reserved.

Journal of Retailing and Consumer Services 51 (2019) 271–284

H. He and S. Wang

consumption could be unresolved due to the inherent product quality variability until the actual consumption time (Roberts and Urban, 1988). Furthermore, due to the technology innovations and consumer preference heterogeneity, the life cycle of products has been significantly reduced, and the actual demand is not only random but also sensitive to the pleasure consumer perceive at the consumption time (Hu et al., 2018). Therefore, this paper attempts to study a consumer inventory problem, that is, we first validate if the inventory decision would deviate consistently from the pre-specified optimal level when the demand is significantly affected by the consumer. Besides, in this setting, the unit benefit that a product may provide at the consumption time would differ among individual consumers significantly, even for products with perfectly known physical attributes or quality (Hauser and Wernerfelt, 1990). Therefore, unlike traditional newsvendor problem in which the retail price, as well as the unit profit, are always assumed to be predetermined, our study extends this assumption by considering an uncertain unit benefit that consumer would perceive while consuming the product. How does a consumer make inventory decision when the unit profit is uncertain and the demand can be significantly affected by himself? Clearly, a change in product price or product quality may affect the inventory decision for perfectly rational reasons (due to the change of the net profit). However, will such a change also induce a specific behavioral effect? If so, to what extent? Finding answers to these questions can help inform the pricing and product design strategy of seasonal goods and how much money should invest in promoting prepurchase behaviors. Based on the inventory management literature, consumers tend to mentally segregate payment transaction problems into two-time periods before and after consumption (Fisher and Raman, 1996). They manage transaction by assessing the outcome which comprises groups of costs and benefits (Heath and Soll, 1996). Therefore, the evaluation and the decision process heavily depend on pain of payment and the perceived benefit (Prelec and Loewenstein, 1998). That is, consumers would experience an immediate pain of payment at the order time, which is associated with thoughts of the uncertain pleasure such payment may provide at the consumption time. They have to choose an inventory level to meet a future demand related to an uncertain unit pleasure the product will provide and have no opportunity for further replenishment, for instance, the product line will be discontinued, the product will be no longer sold, or the discount will expire soon. Kamleitner et al. (2009) systematically discussed the concept of costbenefit association and divided it into a benefit-to-cost link and cost-tobenefit link. Specifically, a robust benefit-to-cost link implies that people tend to emphasize the expenditure and increase the perception of cost. By contrast, a robust cost-to-benefit link amplifies consumer’s perception of benefit, implying that people are likely to look forward to the pleasure derived from consumption. Because of these two opposite effects, we reason that altering the price and benefit (while keeping the net profit constant) will lead to significantly different inventory decisions by consumers. Chen et al. (2013) discussed the effect of payment schemes on the newsvendor problem and presented a “prospective accounting” behavior that predicts consumers would underestimate the order-time payments monotonically. Schweitzer and Cachon (2000), however, predicted that individuals might be loss averse concerning the order-time payments, thereby tend to overestimate the pain of paying. The expected-reward-maximizing solution for such an inventory problem is well known. However, there are many potentials to further analyze consumer perception during transactions and its behavioral effect on actual decisions. Besides, a clearer understanding of these different psychological association would help firms and decision makers to know how to exacerbate and mitigate the potential judgment inaccuracies that stem from this behavior. To illustrate this behavioral effect, we build a mathematical model to study how the decision maker takes these sorts of costs and benefits

into account. We also analytically determine such effect. We observe the actual purchase decisions by three laboratory experiments, in which consumers determine purchase quantities of a product with uncertain benefit and demand before actual consumption. Specifically, the pain of payment can weaken the pleasure derived from consumption or even prevent the purchase altogether (through the benefit-to-cost link). Similarly, the benefit derived from consumption would also be attenuated by the thought of the cost (through the cost-to-benefit link). Consumers would regret keeping lean inventories when the unit benefit that was generated reaches a relatively high level because they have missed several rewards. However, little demand would exist when the benefit drops to a relatively low level, and they must regard the excessive purchases as a loss. We can measure consumer’s individual payment perception by comparing their actual inventory decisions to the theoretical optimal decisions and then determine the behavioral effect of cost-benefit associations. Compared with a vendor’s revenue discussed in previous newsvendor problems, which equals the realized demand times retail price, the pleasure derived from consumption in this paper is more complicated. On the one hand, Nigam (2012) indicated that product quality positively influences peoples subjective demand. Therefore, similar to a stochastic market demand before, the subjective demand of the consumer himself in this paper is also not unchanged, causing a possible mismatch between the order quantity and demand. Specifically, a relatively high purchase quantity may exceed the low demand generated by low quality, making the excess inventory to be perceived as idle and worth nothing at all. On the contrary, the order quantity would be insufficient when the product shows excellent quality and generates a high subjective demand. In that situation, consumers forgo some revenues from this transaction. On the other hand, different from previous literature in which a constant retail price provided straightly before a price-independent demand, this paper considers an uncertain unit “retail price” (unit pleasure derived from consumption in our paper) as well as the unit “profit” (unit pleasure-unit price). Moreover, different from a price-independent demand that widely assumed in the classical newsvendor literature, the unit pleasure and the subjective demand in this paper is considered interrelated. Although a few recent articles already provided extensions for a pricedependent demand distribution, it is commonly found that the optimal inventory level is monotonically negative-related to demand uncertainty with exogenous quality (e.g., Jammernegg and Kischka (2013); Bhowmick (2016)). In this paper, we will show how the demand uncertainty would enhance the inventory decision in turn. Besides, although Jerath et al. (2017) presented a substitute relationship between quality and inventory and also showed that demand uncertainty also might have an effect of increasing inventory through reducing product quality, their endogenous demand is assumed to be negatively related to the retail price. However, it is entirely unsuitable in a consumer inventory problem, since the demand this time always arises synchronously with consumer’s pleasure derived from consumption. Therefore, by extending their assumptions, we show the opposite conclusion. Meanwhile, they considered neither the mental evaluations on purchase and consumption occasions nor experimental validations, as we do. Above all, a distinctive revenue form, which is composed of interrelated and both uncertain demand and benefit, distinguishes our work from traditional newsvendor literature and leads to novel results. From the perspective of the cost-benefit association and through various newsvendor experiments, this paper also shows an overall positive effect of demand/benefit uncertainty on practical inventory level, that comprises a general effect of reducing inventory and a mental effect of increasing it. The rest of the paper is organized as follows. The next section presents a consumer inventory model to explain how an individual consumer associates costs and benefits and makes inventory decisions. In Section 3, the primary analysis and results are computed by three newsvendor experiments. Discussions and implications of our study are 272

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Fig. 1. Inventory Decisions of traditional newsvendor and Individual Consumer.

proposed in Section 4. Finally, the last section concludes the findings, limitations, and discusses potential directions for future studies.

Agrawal and Seshadri (2000) and Cachon and Kök (2007). This condition is common in some inexpensive consumables, such as jam, fruits, and cookies. The unit purchase price of the product is c, and the unit benefit in the future is v. The benefit is stochastic and dependent on nuanced factors, such as functional, conditional, social, emotional, and epistemic components (Mathwick et al., 2001). Thus, v is a random variable with cumulative distribution function F (x). Specifically, we assume that v follows a normal distribution with mean μ and standard deviation σ. Meanwhile, given that the perceived benefit positively influences consumption intention (Keng et al., 2007), we assume that the subjective demand is proportional to the realized benefit for simplicity, which is d = kv, where k is a specific coefficient that is needed to fulfill the demand given a specific benefit v. A summary of notations used in this paper is presented in Table 1. This paper also considers the following three essential marketing strategies to simulate various cost-benefit association. In marketing strategy N (The retailer offers neither price discount nor additional benefit), the consumer pays the cost v per unit at order-time and receives a benefit v per unit after the demand realization. In marketing

2. Model of consumer inventory decisions In this section, we first construct a series of theoretical accounts of payment-consumption interactions in a newsvendor problem setting to predict consumer inventory decisions. As shown in Fig. 1, similar to a traditional newsvendor problem, both two inventory decisions depend on two accounts. Both accounts are comprised of two parts. For example, the “cost” account in consumer inventory decision is determined by inventory quantity and unit purchase price, whereas the “benefit” account depends on unit benefit and achieved demand resolved at the consumption time. In our consumer inventory model, we consider an individual consumer who chooses a purchase quantity q of a product to meet a future subjective demand d; we also assume that the unmet demand is lost and that the pending benefit cannot be inventoried, that is, the leftover inventory has zero salvage value and cannot be carried over to the subsequent period. Same assumptions are also made in 273

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Table 1 Model notation.

R (q, v) = Explanation

c q v d k s m

Unit purchase price Inventory quantity Unit benefit derived by consumption Subjective demand based on the consumption experience Coefficient between the demand and benefit Discount offered by the retailer Additional benefit offered by the retailer Loss-aversion coefficient on pain of payment Time-discounting coefficient on consumption benefit Benefit-to-cost link coefficient on pain of payment

Rˆ (q, v ) =

Payments at Order-time

Benefits at Consumption-time

N D E

−cq −(c − s)q −cq

v min (q, d) v min (q, d) (v + m) min (q, d + km)

(4)

1 (0)

(5)

1

q km k

(c

s) q+

k( x+ m)2f(x)dx

0

+

+q

(x+ m)f(x)dx q km k

(6)

Specifically, we have: 2

q N =

N

1 (0),

1c + 2

N (q) =

( qk µ) 2

2 2

e

+µ 1

q k

µ

2

q D=

q E=

E

D

1 (0),

1 (0),

D (q) =

E (q) =

1 (c 2

1 c+ 2

( qk µ ) s) +

( qk 2

e

2

e

m µ 2 2

2 2

+µ 1

q k

µ

q k

m

2

)

+ (µ + m) 1

µ

(7)

The model is reduced to an expected-reward-maximizing model when 1/ 2 = 1, which implies that the costs are equally as psychologically powerful as the benefits when the individual evaluates an outcome that comprise both. When 1/ 2 > 1, our model indicates that the subject strongly prefers avoiding losses as compared with acquiring benefits at a same amount. By contrast, 1/ 2 < 1 indicates that individuals do not fully consider payments that have previously been made. Moreover, according to Equation (7), given the general loss aversion and time-discounting factors, we can estimate the weighting factor = 1/ 2 by substituting the observed purchase quantity in Section 4 into this equation. Under marketing strategies introduced in the following experimental section, Fig. 2 lists the optimal purchase quantity as a theoretical benchmark, which maximizes the expected reward. As it shows, people should purchase 17.99 units of product at 14 each in Scenario N to maximize their reward when the distributions of future benefit and subjective demand are both distributed according to N(19.5, 35.76). Moreover, following Olivares et al. (2008), we attribute their order variability to a constant weighting factor β and noisy errors in the purchase quantity. Therefore, based on their purchase quantities under a specific scenario, we obtain a weighting factor of each and further estimate the overall weighting factor of consumers under such a scenario. Fig. 3 shows the relationship between the amount of possible advance purchase quantities and the corresponding β that is derived from the model. For instance, if a person decides to purchase 18 pieces of such product in Scenario N, his/her corresponding weighting factor at this time is estimated to be about one. However, if another person purchases 25 pieces, his/her weighting factor would be about 0.4. After several rounds of decision-making, the overall personal weighting factor can be obtained.

(1)

Therefore, the optimal purchase quantity, which maximizes Ri (q, v) ,

q

s ) q + min(q, k (v + m))(v + m)

2

1 cq

q *i = argmaxE v (Ri (q, v))

(c

E v (Rˆ (q, v)) =

strategy D (The retailer offers a price discount of s per unit), the consumer pays c − s per unit at order-time and receives a benefit v per unit. In marketing strategy E (The retailer offers an additional benefit of m per unit), the consumer achieves a benefit v + m per unit and pays the cost c. Following the behavioral operations management literature, the cost and benefit perceived in mental are not simply the numeric equivalent of the net cost and benefit. Based on the expected-profitmaximizing model in the newsvendor problem, we describe the consumer inventory model in terms of a reward function Ri(q, v), which denotes how the consumer evaluates costs and benefits. Four additional parameters are involved. First, both relative strength and the resulting patterns presumably vary across domains. Thus, the benefit-to-cost link and cost-to-benefit link should be measured separately. Following (Prelec and Loewenstein, 1998) prospective double-entry theory, we capture the benefit-to-cost link using a coefficient 1 ( 1 1) , which represents the degree to which consumption buffers the pain of payment. Second, 2 ( 2 1) also captures the cost-to-benefit link, which represents the degree to which payment attenuates enjoyment upon consumption. Third, Kahneman and Tversky (1979) prospect theory indicates that the individual may be averse to loss concerning pay1) to the payments at orderments. Thus, we assign a coefficient ( time. Fourth, considering the interest rate or behavior preferences, the individual discounts benefits at consumption-time because the individual becomes experienced later (Read, 2001). The degree of dis1) . counting is denoted by ( Consequently, given quantity q and perceived benefit v under marketing strategy i {N , D , E , M } , the reward of the transaction Ri (q , v ) can be simply calculated by:

is:

(3)

k( v+ m))( v+ m)

where E v (Rˆ (q, v) is defined as:

Marketing Strategy

+ 2 min(q , d ) v , i = N s ) q + 2 min(q, d ) v, i = D 2 min(q , d + km)(v + m), i = E

1

E v (Rˆ (q, v )) ,q = q

(q ) =

Marketing strategy applied by the retailer Overall outcome of the inventory decision

1 (c cq + 1

2 min(q,

In this case, the weighting factor of cost-benefit associations = 1/ 2 , represents that the result of cost-benefit associations is a genuine shift of the pain of payment. Thus, the optimal purchase quantity q* can be obtained as follow (see Appendix A for further details):

Table 2 Net payments and benefits under different marketing strategies.

Ri (q , v ) =

s) q+

2

Cost-to-benefit link coefficient on consumption benefit

2

i {N , D , E , M } R

c

It can be transformed as:

Notation

1

1(

(2)

where E is the expected value. Given that d = kv, the general form of the objective function R (q, v ) is as follows: 274

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Fig. 2. Expected-Reward-Maximizing Purchase Quantities across Different Marketing Strategies. Note. As set in Study 2, the unit prices of product and expectations of unit benefits upon consumption are (14, 19.5), (10, 19.5), (14, 23.5), and (10, 15.5) in Scenarios N, D, E, and M, respectively.

3. Newsvendor experiments

whether consumer makes similar decisions in a more general situation, where the subjective demand is no longer determined in advance. We replicate the experiments under four traditional marketing strategies to examine the effectiveness of these strategies and their behavioral effects on inventory decisions. Moreover, in Study 3, we change the volatility of the stochastic demand and the unit benefit derived from product consumption to further validate our results and study how the degree of uncertainty would affect the cost-benefit association and consumer inventory decisions.

In this section, three experiments were present to study the behavioral effect of cost-benefit associations on consumer inventory decisions and determine the critical coefficient 1/ 2 . To isolate and illustrate the strength of cost-benefit links and their effects on inventory decisions, in this paper, we eliminate factors such as time discounting and loss aversion in our experimental designs. Specifically, there would be only a short delay inherent to the order of things occurs, and thus the time-discounting factor can be assumed to be one. We also control the loss aversion factor to be one by providing straight payment transfers during the experiment processes. In Study 1, we consider a pre-determined exogenous product demand as a benchmark to eliminate the effect of demand uncertainty from the overall outcome uncertainty. According to the purchase quantities and the expected-reward-maximizing solutions, subject’s payment perception could be measured by the coefficient 1/ 2 in our model. In Study 2 we further analyze

3.1. Study 1 3.1.1. Experimental design We first consider a constant product demand in Study 1 as a benchmark situation to eliminate the demand uncertainty from the outcome uncertainty. Different product prices and qualities are considered to analyze the changes in the subjects’ cost-benefit links.

Fig. 3. Amount of Possible Advance Purchase Quantities and its Corresponding Weighting Factor β 275

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Table 3 Observed purchase quantities across scenarios 1 to 5. Scenario (Population)

Product Price

Mean of Dice (S.D.)

Maximum Order

Minimum Order

Mean order (S.D.)

1 2 3 4 5

14 14 14 16 18

19.00 22.88 23.38 19.25 18.75

19 19.5 19.5 17 13

10 14 15 5 2

14.75 (1.932) 16.79 (1.875) 17.96 (1.203) 11.68 (2.643) 9.64 (2.359)

(16) (24) (16) (22) (16)

(4.877) (7.014) (5.394) (3.918) (7.478)

Furthermore, by comparison of observed purchase quantities and the theoretical reward-maximizing solution, we determine the overall coefficient of the cost-benefit association and predict subjects’ payment perceptions. Specifically, subjects in Scenario 1 (c = 14 and d = 19.5) are asked to roll three dodecahedral (12-sided) dice with the numbers from 1 to 12 on their faces, the sum of which represents the unit benefit derived from consumption v1. The numbers are approximately independent and identically distributed from a uniform distribution with a mean of 6.5 and a variance of 11.92. Following the Lindeberg-Levy theorem (Billingsley, 1961), three dice together make up a stochastic benefit following a normal distribution with mean μ = 19.5 and standard deviation σ = 5.98. To facilitate subject’s comprehension of the uncertainty, we determine to execute active manipulation of rolling dice instead of computer simulation. Then, we replicated this pattern under parameters c = 14, d = 19.5 and v2 = v1 + 2 (Scenario 2); c = 14, d = 19.5 and v3 = v1 + 4 (Scenario 3); c = 16, d = 19.5 and v4 = v1 (Scenario 4); and c = 18, d = 19.5 and v5 = v1 (Scenario 5). The substantial promotional benefits (approximately 10% at least in Scenario 5) in Scenarios 1 to 5 would provide typical purchase conditions that consumers expect (Raghubir, 1998) and facilitate their information processing during the purchase (Hardesty and Bearden, 2003).

eliminate the loss aversion and time-discounting effects. Transactions in other scenarios were conducted analogously. Furthermore, subjects in Scenarios 2 and 3 were able to purchase a higher version of that product at the discounted price, which generates 2 and four more unit benefit at the time of consumption. Subjects in Scenarios 4 and 5 were told that the retailer discounted the initial product at 2 and 0. Thus it was sold at 16 and 18 each then, respectively. The reward in this round equals the payment to subjects after deducting the payment to the assistant, which could be positive or negative. In exchange for their service, the subjects received anywhere from 5 to 10 CNY as a bonus, depending on their reward. Finally, a follow-up question for each subject was administered, that is, “What is the minimum point you can get with the three dice?” We then filtered the data and calculated the average purchase quantities under each scenario. By comparing these results, we distinguished the specific directions of cost-benefit association and analyzed their effect on the prediction of consumers purchase behavior. Furthermore, according to the observed purchase quantities, we identified the value of β to match the expected-reward-maximizing solutions (see Table 2). 3.1.3. Results Subjects were randomly divided into five groups, and all of them successfully completed the experiment with their assistants. Decisions made by subjects who answered the follow-up question wrongly would be regarded as invalid and removed from the analysis because they seem to have failed in clearly recognizing the mechanism of the game. After removing the incomplete and invalid decisions, we obtained 94 pieces of valid data. The results of purchase quantities in different scenarios are shown in Table 3. We adopted several measures to analyze the decisions in different scenarios. As Table 3 shows, the mean of the dice scores, which represents the mean benefit derived from consumption, was consistent with the theoretical value, 19.5 (21.5 and 23.5 in Scenarios 2 and 3, respectively). Given that the mean benefit was higher than the selling price in all scenarios, people should have purchased as much as possible to meet the maximum demand, that is, the optimal decision is 19.5. However, we found that the purchase behaviors in these scenarios are significantly different (F (4, 89) = 49.499, p < 0.01). Specifically, we found that the mean values of the purchase quantities were highest in Scenario 3 and lowest in Scenario 5. A consistently increasing pattern was observed in the purchase quantities in the order of Scenarios 1, 2, and 3 (F12(1, 38) = 11.103, p < 0.01; F23(1, 38) = 4.922, p < 0.05) and a decreasing pattern in the order of Scenarios 1, 4, and 5 (F14(1, 36) = 15.482, p < 0.001; F45(1, 36) = 6.034, p < 0.05). Analogous trends were also evident in the maximum and minimum orders. These descriptive trends raise doubts about the relationship between the costbenefit association and the purchase behavior.

3.1.2. Experimental process A total of 96 undergraduate and graduate students participated in this experiment and were divided into groups that correspond to the five scenarios. Bolton et al. (2010) found that senior managers with lots of experience tend to make, and repeat, the same mistakes as novices in making newsvendor decisions. Accordingly, Feng et al. (2011) and Gavirneni and Isen (2010) also used students at top universities to study managerial behaviors. Thus we believe that it is justifiable to recruit qualitatively student without professional working experience as subjects of our experiments. We initially asked them to introduce their areas of specializations and to respond to several simple questions of the random distribution to ensure their comprehension of the experiment. Then, the experimental condition was introduced to them. On average, subjects took about 10 min to complete the experiment. To avoid potential demand effects during the administration of the study (Boulding and Kirmani, 1993), we assigned an experimental assistant to guide the subject. The assistant was not informed of the purpose and predictions of the study. Before the experiment started, the assistants read the written instruction sheet that explains the details of the marketing strategies to facilitate subjects understanding of the game. During the experiment, they facilitated the transactions and recorded the dice rolls and decisions. Meanwhile, in all of the scenarios, subjects were informed that the maximum subjective demand d was 19.5. The unit benefit derived from consumption was represented by the three dice rolled by their assistants. Subjects in Scenario 1 received a discount at four provided by the retailer. Considering the stochastic unit benefit, they ordered products at a discounted price of 14 each and were asked to pay the cost (−cq) immediately with a type of game currency. The decision was always kept concealed from other subjects. Then, the assistant rolled the dice, determined how much benefit v1 was derived from consuming a product, and returned the outcome (min(q, d)v) to the subject with the game currency. These direct payment transfers between subjects and assistants fix the values of λ and δ to one to

3.1.4. Parameter estimation and analysis As a particular case, the uncertainty of individuals subjective demand was eliminated from the model. We estimated the weighting factor = 1/ 2 of a subject, which fulfills a specific observed purchase quantity given the optimal decision. For example, subjects in Scenario 1 revealed a weighting factor of 1.3 when they purchased 16 pieces of the product. The average results from estimation are shown in Table 4. The estimated value of βˆ measures the effect of the cost-benefit association on individual order decisions, including the cost-to-benefit 276

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Table 4 Average weighting factor estimates and significance tests for study 1. Study 1

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

ˆ

1

Scenario 1

Scenario 2

Scenario 3

Scenario 4

Scenario 5

1.346(0.447)

1.175(0.360)

1.090(0.270)

1.783(0.756)

2.434(0.543))

−0.171**

−0.256**

0.437**

1.088**

−0.085*

0.608*

1.259**

0.693*

1.344*

2

3

0.651**

4

Note. Standard deviations are placed in parentheses; ∗p < 0.05,∗∗ p < 0.01.

link and benefit-to-cost link. Subjects who chose to order 16 pieces of the product in Scenario 1 may perceive the payment of 224 as it costs about 300, whereas subjects in Scenarios 4 and 5 may perceive that payment costs are about 390 and 550, respectively. We attributed the differences in payment perceptions to the cost-benefit association. Thoughts related to the same distribution of benefit in Scenarios 1, 4, and 5 brought to mind thought of payment, thereby generating a constant benefit-to-cost link. However, thoughts of the higher selling prices in Scenarios 4 and 5 strongly attenuated benefits that are perceived from consumption, thereby attenuating the cost-to-benefit link. Consequently, β1 remains unchanged, whereas β2 decreases rapidly. Thus, their ratio (that is, β) increases significantly (F14(1, 36) = 8.514, p < 0.05; F45(1, 36) = 10.496, p < 0.01). The strong benefit-to-cost link prevails against the cost-to-benefit link and attenuates consumption pleasure, thereby inducing subjects in Scenario 4 and 5 to experience the pain of paying several times. On the contrary, we found that β decreases significantly in the order of Scenarios 1, 2, and 3 (F12(1, 38) = 10.731, p < 0.01; F23(1, 38) = 5.478, p < 0.05). The reason is that the additional benefits offered in Scenarios 2 and 3 buffered the pain of paying given the same product price, and thus decreased β. If the product helps people establish a strong cost-to-benefit link, this result will make people think of consuming pleasure and attenuating the pain of paying.

3.2. Study 2 3.2.1. Experimental design The objective of Study 2 is to analyze whether consumer makes similar decisions in a more general situation, where the subjective demand is no longer determined in advance as in Study 1. That is, consumers tend to understand their subjective demand and product quality in the process of consumption. Therefore, both the product demand and the unit benefit derived from consumption are uncertain in this section. Subjects would certainly regret missing some rewards when the subjective demand is only partially met. However, little demand occurs when the benefit drops to a relatively low level, and the subjects must regard the excessive purchases as a loss. We implement nearly the same design as Study 1 except for four changes. First, the sum of these dice determines not only the unit benefit that is derived from consumption but also their future subjective demand (that is k=1). Second, we consider four marketing strategies, namely, N (a benchmark), D (a separate discount), E (a separate additional benefit), and M (a mixed strategy). Intuitively, compared to the benchmark strategy N, a change in the product price (D, M ) or product quality (E, M ) may affect the inventory decision for perfectly rational reasons (due to the change of the net profit). In addition, to capture the behavioral effect induced by such a change, the marketing strategies D and E, as well as N and M in Study 2 are equivalent in pairs in the sense that they produce identical net profits or losses for any given ordering decision and demand realization. Third, the experiments are conducted for 20 rounds to obtain an estimation of the weighting factor for an individual consumer. Each round denotes an independent purchasing period; subjects are not able to carry over their earnings to make purchase decisions in the next round. Therefore, unmet demand is assumed to be lost before the next round and leftover products have zero salvage value, which is consistent with Agrawal and Seshadri (2000). Fourth, an additional one-period decision will be asked at the end of the experiment to weed out the endowment effect (Kahneman et al., 1991), which predicts that subjects’ decisions could be contingent on their overall rewards in previous rounds.

3.1.5. Discussion We adopted an experimental method to determine the effect of costbenefit association on consumer inventory decisions and measure the deviation of consumer payment perception. Specifically, we contribute to the cost-benefit associations literature by empirically showing that a robust cost-to-benefit link (a larger β2) generated by a low product price would induce the hedonic experience and make people pay less attention to the payment; On the contrary, a robust benefit-to-cost link (a larger β1) caused by a low expected pleasure would make people perceive more pain of paying at the order time. The overall coefficient β is positively related to the discount in product price and is negatively related to the additional future benefit. Furthermore, an increased selling price would attenuate the cost-to-benefit link and induce utilitarian behavior, thus generating a lower β2. However, an additional benefit would attenuate the benefit-to-cost link, thereby generating a lower β1 and increase hedonic experience. In addition, we also found that all the average βs exceed one, which implies that most subjects would overestimate the pain of paying and tend to sacrifice a small amount of expected reward in certain demand cases. This result is consistent with the waste-averse preferences introduced by Arkes (1996). It predicts that consumers particularly dislike salvaging excess inventory and would reduce purchase quantities in view of an uncertain outcome. However, our findings in a newsvendor setting can be widely expanded to firm’s pricing, product line design of seasonal goods.

3.2.2. Experimental process We tested the effect of the cost-benefit association under four marketing strategies with parameter c = 14 in a repeated newsvendor setting. A total of 79 undergraduate and graduate students participated in the experiment and were divided into four groups. Fifty-five of the subjects were randomly divided into three essential marketing strategies, namely, N,D,E. The other 24 subjects were scheduled to respond to the mixed strategy M. Game play was for 20 rounds, and the sum of three dice represents the unit benefit and the subjective demand in each round. The mean subjective demand was directly provided to the subjects to test the pull-to-center effect, that is, whether subjects tend to anchor to it. The discount and the additional benefit were set at 4 under Scenarios D and E, respectively. That is, subjects in Scenario D were told that the retailer recently discounted the product at 4 each. Meanwhile, subjects in Scenario E would obtain a free update of the product that 277

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latter rounds with a better and more comprehensive understanding of the game. The results indicate that such decision deviation is robust over 20 rounds (FN (1, 34) = 0.230, p = 0.635; FD(1, 34) = 0.536, p = 0.469; FE(1, 34) = 2.761, p = 0.106 and FM (1, 46) = 0.451, p = 0.505). Moreover, although the endowment effect may be attributed to the ups and downs of subjects decisions, no significant difference was observed between the mean quantities and the one-period decision results (FN (1, 34) = 0.288, p = 0.595; FD(1, 34) = 0.602, p = 0.443; FE(1, 34) = 1.363, p = 0.251 and FM (1, 46) = 0.627, p = 0.431), which indicates that the one-period decision leads to the mean value of the repeated decisions, which is consistent with the concept of demand censoring (Rudi and Drake, 2014). We then compared the observed purchase quantities with the systematic mean demand to test the pull-to-center effect (Bostian et al., 2008). The average subjective demand generated by the dice are 19.52, 19.38, 19.67 (plus 4), and 19.43 (minus 4) under N, D, E, and M, respectively, which are nearly consistent with the theoretical value, 19.5. Results in Table 3 show that a significant pull-to-center effect occurs under strategies N and M (tN (359) = −0.662, p = 0.508; tM (479) = 0.79, p = 0.431). However, decisions under the two promotion strategies D and E are significantly greater than 19.5 and 23.5, respectively (tD(359) = 27.418, p < 0.001; tE(359) = 20.765, p < 0.001). Furthermore, we found that the purchase quantity under E was significantly higher than that under D (F (1, 34) = 39.592, p < 0.001). Therefore, given the costs of increasing the quality and offering a straight discount are equivalent for retailers, offering additional benefit induces more purchases because of the direct effect of benefit on demand and an indirect effect of the weak benefit-to-cost link. However, a straight discount can only increase sales by enhancing the cost-to-benefit link. We are currently interested in whether optimal solutions deviate from the benchmark assuming the expected-reward-maximizing model (that is, λβ1/δβ2 = 1), which are 17.99, 21.09, 23.58, and 15.63 under N, D, E, and M, respectively. Similarly, we investigate the differences between the optimal quantities and the observed purchase quantities under the same marketing strategy. In Table 6, the observed quantities are significantly higher than their corresponding theoretical optimal purchase quantities that maximize the reward (t’N(359) = 9.625, p < 0.001; t’E(359) = 32.842, p < 0.001; t’D(359) = 16.838, p < 0.001; t’M(479) = 4.141, p < 0.01). Therefore, our finding confirms the existence of a consistent deviated purchase decisions, and the degree of such deviation can be measured by β in our model.

they purchase, which provided an additional benefit m = 4 per unit and simultaneously generated a larger subjective demand v + m. Therefore, the future benefit and demand in Scenario E approximately follow normal distribution with mean μ = 23.5 and standard deviation δ = 5.98. Furthermore, a mixed strategy was introduced to subjects in the fourth group. Specifically, discount in the selling price of products and decreases in the unit benefit simultaneously occurred, which implies that the subjective demand was reduced by the same degree. The expected cost performance, that is, the ratio of mean benefit to the selling price, is increased. Such a condition is similar to the promotional strategy currently being implemented in the market. For example, some companies constantly launch low-end products with lower configuration and a lower price (e.g., iPhone SE to iPhone 6s) to attract more consumers. Following Heath (1995), each subject received a loan of 7,200 units of faux money, which serves as an initial fund for subsequent transactions. To assure their motivation, they were rewarded 10CNY for their participation and a bonus of 1CNY for every 100 units of faux money that they had at the end of the game after repaying the loan. Payment transfers were conducted in the form of this currency, and transactions were conducted analogously to eliminate the effect of loss aversion and time discounting. At the end of that round, benefit was scheduled to expire, and the assistants cleared the inventory to begin the next round. Subjects could always obtain a clear understanding of their total reward and can adjust their purchase quantities for the next round to ameliorate their decisions. “How many goods will you purchase if you could get one more chance to play?” would be asked as a follow-up question once they complete the experiment. Game play was for 20 rounds, and information exchange was prohibited during the experiment. Finally, the assistants offered the bonus to them in terms of the faux money that they held at the end of the game. 3.2.3. Results On average, subjects took approximately 20 min to complete the experiment with assistants. We obtained 78 pieces of valid data finally. The results of average purchase quantities in each round are shown in Fig. 4. The average purchase quantities exhibit a consistently decreasing pattern in the order of marketing strategies E, D, N, and M. Table 5 shows that these similar trends are present in the average purchase quantity and in the follow-up question. Furthermore, we calculated the average purchase quantities from rounds 17 to 20 to test the effect of the round, that is, whether subjects make different decisions in the

Fig. 4. Average purchase quantities in each round under marketing strategies N, D, E, and M. 278

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Table 5 Observed purchase quantities under marketing strategies N, D, E, and M. Scenario (Population)

Product Price

Mean of Dice (S.D.)

Mean of One-Period Decisions (S.D.)

Mean of Latter Rounds Decisions (S.D.)

Mean of All Rounds Decisions (S.D.)

N (18) D (18) E (18) M (24)

14 10 14 10

19.52 19.38 23.67 15.43

19.33 23.22 27.28 16.33

19.17 23.23 27.54 16.54

19.40 23.61 26.85 16.26

(5.723) (6.112) (5.947) (6.086)

(1.415) (1.555) (1.778) (1.606)

3.2.4. Parameter estimation and analysis The loss aversion and time-discounting factors were continuously fixed at 1 in this study. After verifying the deviation of payment perception in a variation of the newsvendor problem, we estimated the parameter β to evaluate the weighting factor. We assumed that each consumer had a unique β and attributed his/her purchase quantity variability to a noise and errors in the purchase quantity. According to Fig. 2, we obtained the corresponding relationship between the possible advance purchase quantities q and the weighting factor β. The results of personal average β under marketing strategies N, D, E, and M are indicated in an ascending order in Fig. 5. We obtained a βˆ by method of moments in Scenario N, thereby giving a mean value of 0.857, which indicates that a subject who purchases 20 units at 14 each may perceive this payment of 280 because the product only costs about 240. Similarly, βˆ under D is estimated to be about 0.693, and is about 0.662 under E, which is slightly smaller. We test the difference of βˆ among three groups, and the result shows that βˆ in Scenario N is significantly different with in Scenarios D and E (FND(1, 34) = 54.869, p < 0.001; FNE(1, 34) = 80.760, p < 0.001). Building on findings in Study 1, we propose that the discount enhanced the cost-to-benefit link, thereby inducing hedonic behavior, whereas the additional benefit attenuated the benefit-to-cost link, which induces consumers to pay less attention to the payment. Specifically, consumers in Scenario D tend to perceive about 138 in their mind when purchasing 20 units at 10 each with an actual cost of 200. Subjects in Scenario E largely underestimated the pain of paying 280 for 20 units because it only costs them 185 on average; thinking about the benefit derived from consumption may blunt the pain of paying. Moreover, significant differences are observed among βˆ under Scenarios D, E, and M (FDM (1, 40) = 90.370, p < 0.001; FEM (1, 40) = 122.583, p < 0.001), which also validate the robustness of conclusions in Study 1. By comparison of Scenarios N and M, we found that a simultaneous decrease in price and benefit resulted in a more intense pain of paying (FNM (1, 40) = 4.077, p < 0.05). We propose that the decrease in benefits, along with the decreased demand, leads to a strong benefit-to-cost link and induces more payment pain, even when the cost-to-benefit link is simultaneously intensified by the discount. Furthermore, Darke and Chung (2005) indicated that both discount and benefit reduction offers were vulnerable to consumers perception of deal value, thereby affecting the effectiveness of these promotional strategies. Therefore, subjects significantly reduced purchase quantities (F (1, 40) = 162.833, p < 0.001); however, this behavior seems unwise from a normative perspective considering that expected profitability is actually enhanced.

(1.783) (1.157) (1.082) (1.267)

(1.305) (1.243) (1.045) (1.148)

3.2.5. Discussion In Study 2 we extended the assumptions in Study 1 by examining a more general, uncertain product demand. Four equivalent marketing strategies that produce identical net profits were considered to eliminate the economic effect and measure the behavioral effect of the costbenefit association on consumer inventory decisions. We found that the coefficient β in Study 2 is consistently lower than one, implying that subjects tend to pay more attention to future benefits than the past in this case and unconsciously purchase more. For example, consumers who buy 20 units at 14 each may perceive this payment of 280 because it only costs about 240 in this case. Interestingly, contrary to previous literature, we noticed that the purchase quantity in an uncertain demand situation (i.e., Scenario N ) could be even higher than in a certain demand situation (i.e., Scenario 1 in Study 1). Our analysis showed that in this general case, the mean outcome increases when the individual demand is proportional to the stochastic benefit and would generate a weaker benefit-to-cost link in the consumer’s mind. Therefore, although the same product price in Scenario N and 1 would generate an identical cost-to-benefit link, the reduction of the benefit-to-cost link promotes the average β to fell below one sharply in Scenario N, facilitating subjects’ payment underestimation. Besides, we also found that a direct effect of benefit and an indirect impact on demand would jointly make changes to the benefits more effectively. In other words, changes to the benefits can lead to more deviation in order quantity than changes to the product prices at the same level in this case. These results have meaningful implications in marketing strategy design and can help inform firm’s inventory management. 3.3. Study 3 3.3.1. Experimental design It is commonly found in the inventory literature that inventory monotonically decreases as demand uncertainty increases (e.g., Carlton and Dana (2008)). However, in Study 1 and 2, we have shown that the purchase quantity in an uncertain demand situation (i.e., Scenario N ) could be even higher than in a certain demand situation (i.e., Scenario 1 in Study 1). Therefore, in Study 3, we implement three more repeated newsvendor scenarios to validate our results further and show how the degree of uncertainty would affect the cost-benefit association and consumer inventory decision. Subjects are divided into three groups, namely, V1, V2, and V3, to make purchase decisions facing different volatility of future benefit and demand. Other aspects of the experimental design are the same as Study 2. We show a departure from this conventional wisdom that the inventory decision in an uncertain

Table 6 Significance tests for differences between the observed purchase quantities, systematical mean demand, and optimal purchase quantities in study 2.

q q

M O

Scenario N All (Final)

Scenario D All(Final)

Scenario E All(Final)

Scenario M All(Final)

−0.12(0.19) 1.41***(1.34***)

4.18**(3.84**) 2.52***(2.30***)

3.33**(3.61**) 3.27***(3.70***)

−3.17***(-3.30***) 0.63**(0.70*)

Note. M refers to the systematic mean demands generated by three dice. O refers to the optimal purchase quantities considering the expected-reward-maximizing model (that is, β = 1). Tests of final round are placed in parentheses; ∗p < 0.05,∗∗ p < 0.01,∗∗∗ p < 0.001.

279

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Fig. 5. Personal Average Weighting Factor β under Marketing Strategies N, D, E, and M. (in an ascending order).

demand situation can be more than its counterpart in a more stable demand.

weighting factors in all groups are shown in ascending order in Fig. 7. Interestingly, there is not even one subject who overestimated the cost in scenario V3.

3.3.2. Experimental process A total of 72 undergraduate and graduate students participated in this study and were divided into three groups. Assistants in Group V1 rolled three identical 12-sided dice having the numbers 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, and 12 on each face. Therefore, parameters v and d in Group V1 approximately follow a normal distribution with standard deviation σ = 5.98. However, three new identical 12-sided dice were used in Group V2, which have numbers 0, 1, 2, 4, 5, 6, 7, 8, 9, 11, 12, and 13 on their face, which implies that the volatility of future outcomes is bigger (σ = 7.12). As for the Group V3, another three same dice have 0, 1, 2, 3, 4, 5, 8, 9, 10, 11, 12, and 13 (σ = 7.52) on their every face. However, the mean value of the benefit and the expected outcome remains constant (μ = 19.5) among three groups. Payment transfers were conducted same as Study 2. At the end of the experiment, the one-period decision was asked as a follow-up question, and bonuses were allocated to the subjects according to the faux money they held at the end of the game.

3.3.4. Discussion Conventional wisdom predicts that the inventory would monotonically decrease as demand uncertainty increases (Jerath et al., 2017). In Study 3, we examined the effect of the degree of demand and benefit uncertainty on consumer inventory decisions, and the finding indicated that higher volatility of demand and benefit could be even beneficial to the excessive purchase stimulation. In fact, the higher the benefit volatility is, the higher the demand volatility it induces. As a result, not only the observed inventory decisions but also the theoretical optimal solutions increase with the volatility of demand in this case. Based on our analysis, it is the extremely high outcome with a relatively small probability that enhances the expectation of overall outcome and weakens the benefit-to-cost link. Therefore, by considering an uncertain and quality-related demand in inventory decisions, our result showed that a great majority of subjects might have a strong incentive to underestimate the payment and make more-thanoptimal inventory decisions when the volatility of product demand and benefit become bigger. This finding will help companies to introduce strategies to guide consumers’ purchase behavior and more accurately determine inventory in advance, especially when the quality and price of its product varies a lot from season to season.

3.3.3. Parameter estimation and analysis All 72 undergraduate and graduate students correctly completed the experiment. The information of observed purchase quantities in the three groups is listed in Table 7. Meanwhile, the results of average purchase quantities in each round are shown in Fig. 6. The optimal purchase quantities of Groups V1, V2, and V3 under assumption 1/ 2 = 1 are 17.99, 18.16, and 18.24, respectively. Table 7 shows the observed results of purchase quantities, indicating that the purchase quantities in all groups are significantly higher than optimal purchase quantity (approximately 18). Then, we calculated out the approximate values of the mean weighting factors, that is, 0.887, 0.772, and 0.714 for Groups V1, V2, and V3, respectively (see results of β estimations and significance tests in Table 8). It shows that the payment perception of subjects significantly reduced with the increase of the degree of demand uncertainty. Results of personal average

4. General discussions and implications This paper contributes to newsvendor decision literature by developing a consumer inventory model to determine the purchase behavior with uncertain benefit derived from consumption. Meanwhile, inspired by the cost-benefit association theory (Kamleitner et al., 2009), we analyzed the directions and strength of the cost-benefit association and determined the overall effect by several newsvendor experiments, thus advanced current knowledge of the effect of the cost-benefit association

Table 7 Observed purchase quantities in study 3. Scenario (Population)

Product Price

Mean of Dice (S.D.)

Mean of One-Period Decisions (S.D.)

Mean of Latter Rounds Decisions (S.D.)

Mean of All Rounds Decisions (S.D.)

V1 (24) V2 (24) V3(24)

14 14 14

19.33(5.723) 19.41(5.451) 19.57(4.026)

19.23(1.433) 20.11(1.070) 21.15(1.327)

19.17(1.046) 27.54 (1.082) 20.05(1.233)

19.08(1.143) 20.12(1.018) 21.10(1.013)

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Fig. 6. Average purchase quantities in each round of groups V1, V2, and V3.

on consumer inventory behavior. Specifically, three newsvendor experiments are conducted to observe the actual purchase decisions, in which consumers determine purchase quantities of a product with uncertain benefit and demand before actual consumption. The findings validate the existence of a deviation from real purchase decision from the pre-specified optimal level. We show that a strong cost-to-benefit link makes a consumer think more about the pleasure that is derived from consumption and achieve high hedonic efficiency, whereas a robust benefit-to-cost link induce consumers to pay more attention on the payment and perceive more pain at the order time. When the subjective demand is pre-determined and constant, and the volatility of benefit becomes exceptionally high, consumers would perceive the pain of payment several times, in line with the risk aversion behavior. However, when the subjective demand is no longer constant but influenced by the consumption benefit, the small probability of a great outcome would induce consumers to underestimate the pain of paying and purchase excessive products. Furthermore, with the rise of the volatility of benefit the product may produce in the consumption time, our research found that both the optimal purchase quantity and the observed inventory decision are increasing. A direct effect and an indirect effect of benefit, through the benefit-to-cost link, on subjective demand, facilitated more consumers to feel at ease and pay less attention to the cost. Eventually, when the volatility reaches a relatively high level, all the people would no longer overestimate the pain of paying and purchase more-than-optimal products. Besides, the experimental design also contributes a lot to previous empirical literature. For instance, most interpretations and predictions of them rest on a single selling price p and fixed buying price c, such as Chen et al. (2013). However, this study shows how sensitive results

react to price and benefit variations by replicating the experiment at very different discount or benefit levels. Besides, most of the newsvendor experiments fail to take the volatility of future benefit into account due to the abstractness of the distribution generated by computer manipulation. However, the demand and benefit in this study are explicitly created by rolling dice to provide subject an explicit recognition of the volatility and its alternation. Moreover, the payment transfers between subjects and assistants were executed right after the decisions were made to facilitate the subject’s comprehension of the outcome their decisions generated. Faux money transaction during the whole experiment process further eliminated the difference of thoughts that come to mind when talking about a discount or additional benefit. These results are practically meaningful in marketing strategy design and inventory management. First of all, as for promotional strategy design, some firms often launch a higher-end product at the same price as the old version, whereas the others prefer offering the original one a discount. Building on our findings, we indicated that the additional benefit positively affects subjective demand and attenuates the benefitto-cost link at the same time. However, the discount offered could only enhance the cost-to-benefit link and have no significant effect on consumers subjective demand since consumer tends to allocate cost and benefit into different accounts in their mind. Therefore, the former method would induce consumers to underestimate the pain of paying more efficiently than the latter and facilitate higher purchases. Besides, these common underestimations would stimulate consumers to pay in advance or over-consume. That is the reason why the idea of sharing economic would arise. Most car owners or house buyers cannot make the best of their payments, these idled cars and houses forthrightly suggest people share unnecessary purchases and reallocate their resources. Second, the findings could also be applied to explain the

Table 8 Weighting factor estimates and significance tests for studies 2 and 3. Study 2

Study 3

N

D

E

M

V1

V2

V3

ˆ— ˆ

0.857 (0.047) –

0.693 (0.053) −0.164***

0.662 0.662 −0.195***

0.904 (0.059) 0.047*

0.887 (0.071) 0.030

0.772 (0.075) −0.085**

0.714 (0.064) −0.143***

ˆ— ˆ

–

–

−0.031

0.211***

0.194***

0.079**

0.021

ˆ— ˆ

–

–

–

0.242***

0.225***

0.110**

0.052*

−0.017

−0.132***

−0.190***

−0.115**

−0.173***

ˆ N D

E

ˆ— ˆ

M

–

ˆ— ˆ

V1

−0.058*

ˆ— ˆ

V2

Note. Standard deviations are placed in parentheses; ∗p < 0.05,∗∗ p < 0.01,∗∗∗ p < 0.001. 281

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Fig. 7. Personal average weighting factor in Groups V1, V2, and V3 (in an ascending order).

rationality of various store cards. Under the normative behavioral theory, people would prefer a discount upon consumption rather than the same discount at the time that they buy a pre-paid card in store. However, considering the existence of the weighting factor described in this paper, realizing that offering a discount for pre-paid items is more effective than a straight discount on products is essential to maximize their profit for some necessity retailers. It is interesting to find that a 10% discount on such a card will outweigh (concerning promoting overall sales) a 15% on-purchase discount while providing more profit and capital pool. Another application may appear in the supply chain contract design and coordination. Firms have to store larger-than-optimal or less-than-optimal inventory according to their consumers’ costbenefit association influenced by their product and strategy design, to reduce some of the supply chain inefficiency. Moreover, if retailers can obtain the consumers weighting factor in advance as we did in the experiment section, they may adjust their trade-off between improving retail price and offering additional benefit to achieve more profit effectively.

reward, implying that consumers this time tended to underestimate the pain of paying and unconsciously purchased more. For example, consumers who buy 20 units at 14 each may perceive this payment of 280 because it only costs about 240 in this case. In contrast to the certain demand condition, a higher expected outcome that is determined by the proportional demand and benefit attenuates the benefit-to-cost link, and thereby a dominating cost-to-benefit link could induce people to feel less pain of payment. We speculate that overestimating a small probability of high reward will further intensify this underestimation. Moreover, we found that changes to the benefits affect inventory more strongly and lead to more deviation than changes to the cost. It is because people tend to allocate achieved demand into the benefit account in their mind. Thus an extra benefit offered to consumers has a direct effect on consumer’s individual demand. Besides, the additional benefit also has an indirect effect, through attenuating the benefit-to-cost link, on inventory decision. Finally, we conducted the third experiment to test the effect of volatility of benefit and demand. The result shows that the degree of uncertainty could even induce excessive purchase. Although the optimal inventory level does not change a lot, the small probability of an extremely high outcome could weaken the benefit-to-cost link, which induces people to concentrate more on the future pleasure and thus underestimate the payment right now. Meanwhile, when the product price remains unchanged, the benefit-to-cost link would be congruently enhanced with the disappearance of demand and benefit uncertainty. Consequently, consumers underestimation of the pain of paying gradually disappears, and in turn overestimate the payment. These findings contribute to determining how consumers associate costs and benefits in an inventory problem and how different marketing strategies affect the cost-benefit association and thereby induce payment underestimation or overestimation, which are inconsistent with some predictions of risk-aversion preferences, prospective accounting, and prospect theory. Several extensions to this study may merit further research. First, the absolute monetary values of the products may also be influential. If the product is sold at 140 or 1.4 and provides 195 or 1.95 as a mean benefit, would the weighting factor be the same? Further research should reexamine the effect of the cost-benefit association on payment perception using different levels of absolute value. Second, this study assumes a positive correlation with a constant parameter one between subjective demand and perceived benefit for the implementation of the experiments. Such assumption limits the category of accessible products, and discussions regarding the weighting factor with otherwise benefit-demand relations may be meaningful. Third, costs and benefits coincided within a short time frame in our experimental setting. A

5. Conclusions To measure the effect of cost-benefit association on consumer inventory decision, we expanded the expected-reward-maximizing model and formulated a consumer inventory model that includes stochastic demand and future benefit. Subsequently, three newsvendor experiments were conducted to determine the parameters of the model. First of all, We picked apart the demand uncertainty from the overall outcome derived from consumption. Subjects are asked to order some products with a stochastic future benefit at a constant price. Experimental results reveal that consumers tend to perceive the pain of paying several times in these conditions and inventory decisions do not always reach a theoretically pre-specified optimal level. Changes to costs and benefits might further encourage the consumer to take economically sub-optimal choices. The extent to which people deviate from reaching this optimal inventory level varies depending on how the costs or benefits are changed. In particular, increasing the product price could weaken the cost-to-benefit link. A relatively strong benefit-to-cost link would prevail against a weak cost-to-benefit link. Therefore, the pain associated with payment would be overestimated, and the inventory decision would further diminish. However, offering an extra benefit could induce consumers to feel at ease and order more by attenuating the benefit-to-cost link. Then, we considered an uncertain, subjective demand to analyze a more general decision problem. The observed purchase quantities in this case consistently exceeded those that maximize the expected 282

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considerable temporal distance would intensify the time-discounting effect and reduce the impact of cost and benefits, which then hamper

their combination. Therefore, decisions in a delayed consumption pattern could be entirely different.

Appendix A The optimal quantity is defined as

q = argmax E v (Ri (q, v ))

(A.1)

q

whereE v (Ri (q, v )) is the expected value, which is

Ev (Ri (q, v ))= (c

s) q +

0

q km k

+ q km k

k (x + m)2f (x ) dx+q

(x + m) f (x ) dx

(A.2)

Its first derivation with respect toq is Ev (Ri (q, v)) = q

(c

q km k k (x + m)2f (x ) dx

0

s) +

+ q km (x + m) f (x ) dx k

+q

q

+

q

+ q km k

(x + m ) f (x ) dx

(A.3)

Then we have Ev (Ri (q, v)) q

+

+ q km k

=

(c

s) + k

(

q

km k

) ( 2

+m f

q

km k

) + q( (

q

km k

)(

+m f

q

km k

))

(x + m ) f (x ) dx

(A.4)

After simplification,

E v (Ri (q, v )) = q

(c

+ q km k

s) +

(x + m) f (x ) dx

(A.5)

Since v follows normal distribution with mean µ and standard deviation , we have

(q ) =

Ev

(Ri (q,

v ))

q

=

(c

s) +

2

(

e

q km k

µ

2 2

2

)

q

+ (µ + m) 1

km k

µ (A.6)

Then the optimal quantity is 2

qN

=

N

1 (0),

N (q )

=

c+

2

e

( kq µ) 2 2

+µ 1 2

qD

qE =

=

E

D

1 (0),

1 (0),

D (q )

E (q )

=

=

c+

(c

s) +

2

e

( qk

2 m µ 2 2

e

( qk µ ) 2 2

+µ 1

2

)

+ (µ + m) 1

q k

µ

q k

µ

q k

m

µ

(A.7)

Appendix B. Supplementary data Supplementary data related to this article can be found at https://doi.org/10.1016/j.jretconser.2019.06.013.

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