impact of consumer loss aversion on operations in the context...

Research ArticleImpact of Consumer Loss Aversion on Operations in theContext of Remanufacturing

Bi-feng Liao 1 and Bing-zhang Wang 2

1School of Economics and Management Yantai University Yantai China2School of Mathematics and Information Sciences Yantai University Yantai China

Correspondence should be addressed to Bing-zhang Wang wbzhyt163com

Received 14 March 2020 Revised 30 September 2020 Accepted 4 October 2020 Published 19 October 2020

Academic Editor Michele Scarpiniti

Copyright copy 2020 Bi-feng Liao and Bing-zhang Wang -is is an open access article distributed under the Creative CommonsAttribution License which permits unrestricted use distribution and reproduction in anymedium provided the original work isproperly cited

Loss aversion is an important psychological characteristic that has become well supported in finance and marketing -is paperintroduces consumer loss aversion into the game model with two substitutable products in a remanufacturing system -e loss-averse consumers gain utility from comparing the price and value dimensions with the superior product Our model highlightsalternative products competition product selections and consumption psychology in a remanufacturing environment -eresults show that consumer loss aversion has important implications on key decisions in the remanufacturing system When themanufacturer faces loss-averse consumers there is a tendency to charge higher prices for two types of products At the same timethe sales prices increase with the degree of loss aversion Further analysis reveals that if the manufacturer manipulates consumerswith a high probability of purchase the feature of loss aversion usually benefits him Our theoretical analyses are proven bynumerical computation and some useful conclusions are summarized in this paper

1 Introduction

Driven by the regulations around the world devoted toforcing producers to take the responsibility for their end-of-life (EOL) products researchers are increasingly investi-gating the Closed-Loop Supply Chain (CLSC) in recentdecades [1ndash3] In addition to the conventional ForwardSupply Chain (FSC) it includes Reverse Supply Chain (RSC)in CLSC FSC does not account for EOL products HoweverRSC manages EOL products in the most environmentallyfriendly manner possible which involves activities such asacquisition collection and reprocessingmdashreuse recyclingor remanufacturing [4ndash7] CLSC integrates both the FSC andRSC simultaneously [8 9] Remanufacturing is the mosteffective form for EOL product recovery and it is generallyaccepted that remanufacturing is one important means forestablishing resources-saving society [10ndash13] -erefore ourpaper addresses the concern of the operations in CLSC basedon remanufacturing

Remanufacturing is a process of fully extracting theadditional value from EOL products and applies advancedremanufacturing technology to the production of newproducts It achieves energy-saving and emission reductionwhich greatly benefits the enterprises and the society[14 15] Both Lenovo and Apple Inc implement RecyclingProgram Several successful examples from the industryhave already highlighted the high-profit margin for rema-nufactured products for instance Kodak Xerox and IBM

Although a large number of theory studies and practicesfrom the industry at home and abroad indicate that there aregreat prospects for development in remanufacturing thedecision-making to remanufacture is difficult because thereis a great diversity of industry practice and little guidance forremanufacturers to go forward It is well known that profit isthe key point of the operation and the driving force for thedevelopment of enterprises It is affected by many factorsAnd among all the market share is of utmost importance[14]

HindawiComplexityVolume 2020 Article ID 3065819 10 pageshttpsdoiorg10115520203065819

-is paper aims to provide guidelines for manufacturersto make optimal decision-making Considering the complexcharacteristics of the remanufacturing system we addressthe following three problems to identify the drives forremanufacturing (1) consumer perception of price andvalue dimensions for new and remanufactured products (2)consumer preference for the two types of products and (3)the influence of consumer loss aversion on operations

11 Price and Value Dimensions of New and RemanufacturedProducts Remanufacturing has been identified to be themost effective way to minimize the consumption of energyand raw materials leave less air pollution and reduce wastedisposal treatments [16] -e remanufactured product is anew alternative environment-friendly product -e low costand low price are their competitive advantages Althoughremanufactured products affect the market share of theprimary new products it may be an important path to realizethe sustainable development -is issue is discussed ex-haustively in this paper -e results show that remanu-facturing is a new growth point

12 Consumer Preference for New and RemanufacturedProducts -e raw materials for remanufacturing are EOLproducts It is no surprise that consumers perceive newproducts to be of a higher quality standard and they usuallyhave lower valuation for remanufactured products Beforepurchasing or using remanufactured products consumersare often uncertain about the actual performance andphysical reliability and hold the idea that new products havebetter properties As such if the new product is available it istaken for granted that the new product is the best choiceConsumers can clearly distinguish new and remanufacturedproducts -eir willingness to pay (WTP) for remanufac-tured products is obviously lower than that for new onesWTP difference plays a significant role in demands for bothproducts and supply chain performance

13 Consumer Loss Aversion -e important characteristicsof loss aversion are that people are reluctant to accept lossesand tend to choose avoiding losses It is well supported infinance and marketing and has extensive and profoundinfluence [17 18] As loss aversion obviously exists in realityit attracts researchersrsquo interests significantly [19ndash21] In thecase of utilizing remanufactured products most customersare often uncertain about the product properties It istherefore of no surprise that the consumers usually have alower valuation for remanufactured products -e instinctthat consumers as far as possible avoid losses leads them tohardly make purchase decisions for remanufactured prod-ucts and significantly affects the operation performance ofCLSC

-e outline of our paper is as follows We provide anexhaustive literature review in Section 2 In the next sectionwe lay out the features of the market demand Section 4presents the gamemodels and obtains the equilibrium-ennumerical examples and environmental assessment are

presented in Sections 5 and 6 respectively Finally our paperbriefly concludes in Section 7 and offers some possible di-rections for future work in this area

2 Relevant Literature

Our paper is closely related to the following two researchfields in CLSC consumer preference and remanufacturingAt present a variety of articles are carried out to investigatethe remanufacturing profitability from the perspective of themanufacturer Ferguson and Toktay [22] investigate rema-nufacturing and collection decisions to derive conditionsunder which strategy is profitable In a stochastic demandsetting Kaya [23] considers the decision-making with theincentive strategy and product remanufacturing Accordingto a variety of different parameters the impacts on systemperformance are taken into account in the paper Chen andChang [24] present several game models to identify theeconomic benefits of the remanufacturing system Pietro andGeorges [25] develop CLSC game models to investigate theoperational performance Mitra [26] develops theoreticalmodels to show that the profit is always higher in theremanufacturing setting Pietro [27] develops incentivegames to investigate product recycling and economic ben-efits Raz et al [28] investigate the economic environmentaland social impact of remanufacturing

Interestingly all these articles concentrate on the stra-tegic research of the remanufacturing system under thegeneral concept of value Due to the imperfection of theremanufactured products we cannot easily measure theirvalue in common sense Atasu et al [14] introduce consumerWTP to study the profitability of the remanufacturingsystem Given that consumer WTP for new and remanu-factured products is different Ferrer and Swaminathan [29]propose game models with differentiated prices for themAgrawal et al [30] investigate that the existence of rema-nufactured products has a direct influence on the con-sumersrsquo perceived value for new ones Abbey et al [31]discuss the optimal decision-making in CLSC consideringconsumer preferences -ey reveal that the original equip-ment manufacturer can reap high profits through makingdifferent prices for them Gan et al [32] reveal that thecognition and attitudes to remanufactured products play animportant role in enhancing the profit of players Kovachet al [33] present a salesforce incentive model to investigatethe salesforce incentives and the enterprisersquos decision-making Ma et al [34] introduce consumer WTP to in-vestigate pricing and recycling strategies in CLSC Tang et al[35] conduct a full analysis to examine the impacts of pricingand warranty decisions on profitability and consumersurplus in the context of remanufacturing Ramırez et al[36] propose economicmodels to demonstrate the economicoutputs and environmental impacts

All these papers mentioned above mainly investigate theperformance in CLSC operations considering loss-neutralconsumers and they ignore the psychological characteristicsof loss aversion Brooks and Zank [37] demonstrate thebehavior of consumers in themarket and point out that mostconsumers are loss averse -e analysis and consequences of

2 Complexity

consumer loss aversion have become an important part ofthe economic applications [38] -ere is as mentionedabove a growing number of research works devoted toextending their research in the loss aversion context Heid-hues and Koszegi [39] study the choice process of loss-averseconsumers Kotonya et al [40] propose a model describingthe consumer choice impact of loss aversion -ey point outthat cheaper product is more likely to attract loss-averseconsumers Kim and Lee [41] investigate the effects of con-sumer loss aversion on enterprisersquos decisions Antonia [42]identifies the production management and pricing strategieswhen a retailer faces loss-averse consumers Fabrizi et al [43]present game models to show the great influence of referencedependence on consumer preferences Marz [44] proposes amodel to investigate the effects of persuasive advertisingtargeted at loss-averse consumers Ghesla et al [45] conduct afield experiment to evaluate the effectiveness pro-environmental incentives in a loss frame

Inspired by these findings we analyze the strategic be-havior of a profit-maximizing manufacturer facing loss-averse consumers We contribute to the research by pro-viding a new perspective and method to the remanu-facturing system and the main concern on the factors of ourresearch is associated with the demand side -e combi-nation of these factors is embodied in three aspects First weconsider the value dimension of products Second wecapture the WTP difference for new and remanufacturedproducts Finally we analyze the influence of consumer lossaversion on the decision-making So far as we know this isthe first paper that integrates the above three factors si-multaneously in a remanufacturing context

3 Model Description

We illustrate the game between the consumers and themanufacturer in Figure 1 Based on consumer preference aconsumer first forms his valuation and learns his referencepoint -en the manufacturer charges differential prices fortwo types of products Finally the consumer makes a choiceand hence the market demand is realized

Now assume that the market capacity is normalized toone and it is uniformly distributed on [0 1] Consumers areclassified into two basic categories depending on their in-dividual psychological characteristics the most commontype of loss-neutral consumers and rarely mentioned type ofloss-averse consumers We use N and L to indicate the twotypes of consumers respectively

Consider an OEM who manufactures remanufacturedproducts along with original new products -e two types ofproducts are sold in the same market and we furtherhypothesise that they are not available for sale elsewhere-etwo types of products are partially substitutable and con-sumer valuations are different for them Consumers are freeto make the choice between the two types of products

Case 1 Loss-neutral consumers

We first consider the market with the loss-neutralconsumers and take this as a benchmark scenario Our goal

is to help identify the parameters that will impact decision-making

Suppose that consumers distinguish between new andremanufactured products -e WTP is subjected to uniformdistribution on [0 1] In general consumers perceiveremanufactured products as having less quality -ereforewhen consumers are loss-neutral theWTP for new productsis v and that for remanufactured products is θv where0 lt θ lt 1 -at is the perceived value of remanufacturedproducts to consumers is not higher than that of new ones

-is paper describes consumersrsquo preferences with utilityfunctions un and ur If the selling price of a new product is pna loss-neutral consumer gets net utility un v minus pn And if theselling price of a remanufactured product is pr a loss-neutralconsumer gets net utility ur θv minus pr -e net utility is equalto zero when the loss-neutral consumer does not purchaseany products Consumer utility is the standard notion ineconomics which depends only on the absolute outcomes

Consumers tend to choose to buy new products ifun gt ur and un gt 0 Otherwise consumers will switch toremanufactured products if ur gt 0 We illustrate the utilityfunction in Figure 2

-en consumer preference is summarized in the fol-lowing lemma

Lemma 1 In the loss-neutral benchmark

(a) consumers with v isin [((pn minus pr)(1 minus θ)) 1] plan topurchase new products

(b) consumers with v isin [(prθ) ((pn minus pr)(1 minus θ))) planto purchase remanufactured products

(c) consumers with v isin [0 [prθ)) plan to purchasenothing

We obtain the demand functions for two types ofproducts are as follows [15 35 46]

qNn 1 minus

pn minus pr

1 minus θ

qNr

pn minus pr( 1113857

(1 minus θ)minus

pr

θ

(1)

Case 2 Loss-averse consumers

Loss-averse can explain the anomalous behavior accordingto classical economic theory and researchers recently showgreat interest in the market implications of nonstandardconsumer behavior Behavioral economics has accumulatedabundant evidence of reference dependence with loss aversion-is paper assumes the reference dependence is determinedendogenously which is given by the rational expectations [47]-is paper introduces reference dependence by consideringproducts sequentially When consumers value the laterproduct the new onemdashthe first product they are willing topurchasemdashmay become the reference point It is known to allthat new products are enjoying broadmarket acceptance todayand consumers generally prefer new products to remanufac-tured products And so it is reasonable to take the new product

Complexity 3

as a reference point We employ utility as the carrier of lossaversion -is view is adopted in Tversky and Kahneman [48]Hardie et al [49] Kobberling and Wakker [50] Horst andPeter [20] and so on

It is obviously different from the standard loss-neutralconsumers -e total utility of loss-averse consumers comesin two additive parts First is the intrinsic consumer surpluswhen a consumer buys the product Second is the gain-lossutility when consumers compare the actual outcome withrational expectations It captures reference dependence andloss aversion As such if a consumer purchases a newproduct at a price pn the consumer utility is

un v minus pn (2)

If a consumer purchases the remanufactured productthe preferred new product is the reference point of thetransaction -e utility is derived from the reference pointSuppose consumers measure gains and losses with price andvalue dimensions separately As consumers value theremanufactured products less than the new ones they suffera loss in the product dimension On the other handmanufacturers always charge a lower price for a remanu-factured product than a new one and consumers benefitfrom the price dimension -erefore the consumer totalutility of purchasing a remanufactured product is as follows

ur θv minus pr + μ(θv minus v) + μ pn minus pr( 1113857 (3)

where

μ x minus x0( 1113857 x minus x0 xgex0

λ x minus x0( 1113857 x lt x01113896 (4)

is gain-loss utility [51] -e parameter λ represents the degreeof consumer loss aversion and λ gt 1 captures the characteristicthatmakes consumersmore concerned about losses than gains

-erefore consumers total utility of purchasing rema-nufactured products is given by

ur θv minus pr minus λ(v minus θ)v + pn minus pr( 1113857 (5)

Consumers are willing to buy new products if un gt 0 andun gt ur Otherwise consumers will switch to remanufac-tured products if ur gt u0 where u0 is the utility of pur-chasing nothing for loss-averse consumers -e utilityfunction is illustrated in Figure 3

In order to describe the consumer preference associatedwith the prices of the two types of products the valuediscount and consumer loss aversion we present a usefullemma as follows

Lemma 2 In the loss-averse situation

(A) consumers with v isin [2(pn minus pr)((1 minus θ)(1 + λ)) 1]

plan to purchase new products(B) consumers with v isin [(2pr(θ(1 + λ))) (2(pn minus pr)

(1 + λ)(1 minus θ))) plan to purchase remanufacturedproducts

(C) consumers with v isin [0 (2prθ(1 + λ))) plan topurchase nothing

Similarly the demand functions can be written as

qLn 1 minus

2 2pn minus pr( 1113857

(1 minus θ)(1 + λ)

qLr

2 2pn minus pr( 1113857

(1 minus θ)(1 + λ)minus

2pr

θ(1 + λ)

(6)

4 Analysis Results

Recall that consumers are reference dependent and loss-averse -e market share of the two types of productsmanufacturer decision-making process and equilibriumanalysis are presented next

41 Market Share

Proposition 1 If the manufacturer keeps the prices fixedthen

Time

Consumer utility is realized andhe makes purchase decision

Consumer formshis reference point

Manufacturer commits to newand remanufactured products

Manufacturer marksprices for products

Figure 1 -e timing of the game

qnun = v ndash pn

ur = θv ndash pr

v

qr

pn (pn ndash pr)(1 ndash θ)prθ0 1

Nodemand

u

Figure 2 -e loss-neutral consumer utility

4 Complexity

(1) some additional market share is picked up under lossaversion

(2) there is a greater demand for new products in theloss-averse situation than in the loss-neutralbenchmark

Proof It is easy to see that (2(1 + λ)) lt 1 since λ gt 1-erefore we have

2pr

θ(1 + λ)lt

pr

θ

2 pn minus pr( 1113857

(1 minus θ)(1 + λ)lt


(1 minus θ)

qLn 1 minus


(1 minus θ)(1 + λ)gt q

Nn 1 minus

pn minus pr

1 minus θ

(7)

-is concludes the proof

Proposition 1 shows that loss-neutral consumers do notidentify any losses when purchasing nothing But if loss-averseconsumers purchase nothing they feel a loss compared togetting a product -is leads to increased market share

Due to the uncertainty factors which influence theperception of remanufactured products loss-averse con-sumers prefer new ones As such there is a greater demandfor new products in the loss-averse situation than in the loss-neutral benchmark

42OptimalDecisions -emanufacturerrsquos profit is given bythe following equation

maxpnpr

π pn minus cn( 1113857qn + pr minus cr( 1113857qr (8)

According to the first-order conditions we obtain thefollowing results

Proposition 2 When consumers are loss-neutral the stra-tegic equilibrium and profit are given by

qNn

1 minus θ minus cn + cr

2(1 minus θ)

qNr

θcn minus cr

2θ(1 minus θ)

pNn

1 + cn

2

pNr

θ + cr

2

πN1 minus 2cn

4+

c2r

4θ+

cn minus cr( 11138572

4(1 minus θ)

(9)

Proposition 3 9e manufacturerrsquos optimal decisions andprofit in the loss-averse situation are given by

qLn

t minus θt minus cn + cr

2t(1 minus θ)12

minuscn minus cr

2t(1 minus θ)

qLr

θcn minus cr

2θt(1 minus θ)

pLn

t + cn

2

pLr

θt + cr

2

πL

t minus 2cn

4+

c2r

4θt+


4t(1 minus θ)

(10)

where t ((1 + λ)2) gt 1

43 Equilibrium Analysis Having discovered the results ofthe game equilibrium of the two cases we are interested inanalyzing the impact of consumer loss aversion -e fol-lowing propositions are derived from the equilibrium of thetwo scenarios

Proposition 4 9e manufacturer charges a higher price fornew products under loss aversion than loss-neutrality and theprice goes up with consumer loss aversion

Proof

pLn minus p

Nn

t + cn

2minus1 + cn

2

t minus 12gt 0

zpLn

zλ

zpLn

zt

zt

zλ14gt 0

(11)

We compute the difference in their prices under con-sumer loss aversion and loss-neutrality and find that they arepositive for all parameter values under our assumptions

(1 ndash θ)(pn ndash pr)

pn(pn)λ

u

qnun = v ndash pn

ur = θv ndash pr ndash λ (v ndash θv) +(pn ndash pr)

1v

prθ (2pr)θ (1 + λ)

u0 = ndashλv + pn

No demand

Figure 3 -e loss-averse consumer utility

Complexity 5

-us we have the result that the manufacturer charges ahigher price in the loss-averse situation

We differentiate pLn with respect to λ and check the sign

It suffices to demonstrate that the price goes up with con-sumer loss aversion

From Proposition 4 we can obtain the followingcorollary

Corollary 1 9e scale of price dispersion for new productswidens with consumer loss aversion

Proposition 5 A manufacturer charges a higher price forremanufactured products in the loss-averse situation And theprice increases with the degree of consumer loss aversion

Proof

pLr minus p

Nr

θt + cr

2minusθ + cr

2θ(t minus 1)

2gt 0

zpLr

zλ

zpLr

zt

zt

zλθ4gt 0

(12)

Propositions 4 and 5 show that consumers are expectedto purchase a product in the loss-averse situation and themanufacturer would charge higher prices for the two typesof products

Proposition 6 Consumer loss aversion boosts sales of newproducts and the sales of new products are larger under lossaversion than loss neutrality But it is the contrary for theremanufactured products

Proof It is similar to Proposition 5

Proposition 6 points out that consumers might pull theirchoices out of the remanufacturing sales market to avoidincurring losses and purchase new products instead Con-sequently the market share of the remanufactured ones willbe reduced sharply -is gives new products the opportunityto grab a big market share

5 Numerical Results

To get a better understanding of our analytical findings andcomplement them with new insights under such two dif-ferent consumer markets we next discuss the equilibriumresulting in profit using numerical experiments

Countless instances indicate that consumer WTP andcost savings may vary with product features[4 14 31 52 53]

We obtain the estimates of λ in various scenarios A valueof λ greater than one shows that consumers are loss-averseAnd the greater the value the more the loss aversion[42 49 54]

Based on the survey data of the remanufacturingmarketsand related literature [46 55 56] we give the parametervalues as follows cn 04 cr 02 θ 06 λ 2 -e redcurve with diamonds and the black curve with asterisks in

13

12

11

1

09

08

07

1 15 2 25 3

Loss-neutralityLoss-aversion

λ

pn

Figure 4 Impact of λ on pn

07

1 15 2 25 3


λ

pr

065

06

055

05

045

04

075

Figure 5 Impact of λ on pr

1 15 2 25 3


λ

n

038

036

034

032

03

028

026

024

Figure 6 Effect of λ on qn

6 Complexity

the following figures mean the loss-neutral and loss-aversemarket respectively

Figures 4 and 5 show that consumer loss aversion has amajor influence on prices In the loss-averse situation con-sumers are willing to pay higher prices for products -egreater the level of loss aversion themore the prices go up-isis because consumers can predetermine new products as thereference point and unsupplied customers experience a lossAccordingly it increases the consumerrsquos willingness to pay forproducts and even pay far more than the productrsquos worth -eprice dispersion increases with the growth of loss aversion andit helps to visualize the results in Propositions 4 and 5

Figures 6 and 7 show the dependence between the de-mands and consumer loss aversion As can be seen inFigure 6 we conclude that loss aversion gives new productsan opportunity to pick up some additional market share

Observing from Figure 7 we can find that the demandfor remanufactured products is decreasing in λ -e morethe loss aversion is the more difficult it is to violate con-sumer original intention to purchase remanufacturedproducts To avoid losses loss-averse consumers purchaserelatively expensive new products instead of choosing thelower-priced remanufactured products At a higher con-sumer loss aversion level the manufacturer will focus onnew products and then skip the remanufacturing planFurthermore the manufacturer will charge a higher price fornew products

Obviously Figures 8 and 9 show that loss aversionsignificantly impacts profits Loss-averse consumers do notnecessarily lead to lower profit and it is always better off forthe manufacturer facing loss-averse consumers -e profitdispersion increases with the value of λ and decreases withthe consumer WTP In the presence of uncertainty it seemsthat a profit-maximizing manufacturer can manipulate theconsumersrsquo expectations and would have incentive to exploitthe consumer loss aversion-is enables them to reap higherprofits easily

-e higher WTP for remanufactured products and themore consumer loss aversion level imply a relatively higher

price advantage for remanufactured and new productsrespectively -is makes it easier for the manufacturer toseize the chance to charge a higher price and the operationperformance also increases

6 Environmental Performance

Remanufacturing is generally perceived as an environ-mentally friendly management option for EOL productsWhen compared to manufacturing remanufacturing itselfuses less energy and reduces environmental pollution Herethe total environmental impacts of CLSC in these two casesenter into our discussion

In the whole lifecycle the process of production userecycling and remanufacturing all have a degree of envi-ronmental impact We assume that the environmentalimpact factors borne by each unit of new products are N andof remanufactured ones are R As remanufactured productsare green products we may wish to set up R lt N

1 15 2 25 3


λ

r

0085

008

0075

007

0065

006

0055

005

0045

004

Figure 7 Effect of λ on qr


θ

π

026

024

022

02

018

016

014

012

01

00805 055 06 065 07 075 08 085 09

Figure 8 Effect of θ on π

1 15 2 25 3


λ

π

04

035

03

025

02

015

01

005

Figure 9 Effect of λ on π

Complexity 7

Figures 10ndash12 illustrate the environmental impact of the twoconsumer markets with different parameters

As can be seen from Figures 10ndash12 the environmentaleffect of consumer loss aversion is negative -is is because

consumer loss aversion brings about more new productionand hence an increase in the total energy What is importantis that the relative energy consumption per unit of productdecreases and this growth in the total energy is sustainableAs the development of remanufacturing lies largely on thesnatch of the incumbent market and the exploitation of thenewmarket it is necessary to mitigate consumer uncertaintyand consumer loss aversion that is depressing demand forremanufacturing products To achieve a ldquowin-winrdquo situationthe manufacture will more likely adopt strategies to attractconsumers to buy remanufactured products such as fixed-price subsidy advertising and promotion

7 Concluding Remarks

-e ldquoloss aversionrdquo theory is one of the representativetheories about behavioral finance It accounts for a varietyof economic phenomena which includes the equity pre-mium puzzle and important economic markets -is paperintroduces consumer loss aversion to investigate theplayersrsquo decision-making in CLSC with remanufacturingWe combine the products competition WTP differenceand consumer loss aversion in our model -is researchshows that if consumers cannot obtain the product whatthey expect they feel they suffer a loss and are very sensitiveto this loss-is not only increases consumerWTP but alsoboosts the immediate demand for new products -usconsumer loss aversion can be used to exploit future marketsize and a higher degree of loss aversion leads to higherprofit -e results in this paper provide a useful referencefor remanufacturers arousing consumer loss aversion toreap economic benefits

-is paper is contributing some insights into decision-making when faced with loss-averse consumers howeverthere are several aspects that are not taken into accountOur model shows better operational performance andworse environmental performance and one natural pos-sibility would be to consider an environmental regulationIn our model new and remanufactured products are inplentiful supply in the market In view of the supply ofremanufactured products it is bounded by the number ofEOL products recycled from consumers -ereforeremanufactured products facing supply constraints wouldseem to be more appropriate in CLSC with remanu-facturing Loosening the restriction that consumers arewilling to purchase new products can also bring aboutsomewhat different explanations -ese hypotheses aremore objective and in line with reality and they are excitingavenues for research Similarly one could consider thatmanufacturers are loss-averse As to the situation with lossaversion of both consumer and manufacturer it will bemore complicated and therefore be completed in the fol-low-up study Finally we assume consumers prefer newproducts as reference points in this paper -e measures toimprove consumer acceptance of remanufactured prod-ucts as well as the alternative new products as referencepoints to remanufactured products are also potentiallyinteresting extensions All the possible cases consideredmay come to entirely different conclusions -is provides a


219181716151413

1 12 14 16 18 2 22 24 26 28 3λ

E

Figure 10 Effect of λ on environment (N 5 and R 1)

08

075

07

065

06

0551 12 14 16 18 2 22 24 26 28 3

λ

E



23

22

21

19

18

17

16

15

2

1 12 14 16 18 2 22 24 26 28 3λ

E



8 Complexity

new insight for the following study and plays a guiding rolein remanufacturing practice

Data Availability

All data models and codes generated or used during thestudy are included within the article

Conflicts of Interest

-e authors declare that they have no conflicts of interest

Acknowledgments

-is work was supported by the National Natural ScienceFoundation of China (Grant no 71672166) and ShandongSocial Science Planning Project (Grant no 20CSDJ10)

References

[1] M Fleischmann P Beullens J M Bloemhof-Ruwaard andL N Van Wassenhove ldquo-e impact of product recovery onlogistics network designrdquo Production and Operations Man-agement vol 10 no 2 pp 156ndash173 2001

[2] V D R Guide T P Harrison and L N Van Wassenhoveldquo-e challenge of closed-loop supply chainsrdquo Interfacesvol 33 no 6 pp 3ndash6 2003

[3] K Govindan H Soleimani and D Kannan ldquoReverse logisticsand closed-loop supply chain a comprehensive review toexplore the futurerdquo European Journal of Operational Researchvol 240 no 3 pp 603ndash626 2015

[4] M Radhi Impact of Quality Grading and Uncertainty onRecovery Behaviour in a Remanufacturing EnvironmentUniversity of Windsor Windsor Canada 2012

[5] R Bhattacharya A Kaur and R K Amit ldquoPrice optimizationof multi-stage remanufacturing in a closed loop supply chainrdquoJournal of Cleaner Production vol 186 pp 943ndash962 2018

[6] Y Wang Z Wang B Li Z Liu X Zhu and Q WangldquoClosed-loop supply chain models with product recovery anddonationrdquo Journal of Cleaner Production vol 227 pp 861ndash876 2019

[7] L Yang Y Hu and L Huang ldquoCollecting mode selection in aremanufacturing supply chain under cap-and-trade regula-tionrdquo European Journal of Operational Research vol 287no 2 pp 480ndash496 2020

[8] S Dowlatshahi ldquoDeveloping a theory of reverse logisticsrdquoInterfaces vol 30 no 3 pp 143ndash155 2000

[9] V D R Guide and L N van Wassenhove ldquoOR FORUM-theevolution of closed-loop supply chain researchrdquo OperationsResearch vol 57 no 1 pp 10ndash18 2009

[10] G Ferrer D ClayWhybark and CM Dalton ldquoFrom garbageto goods successful remanufacturing systems and skillsrdquoBusiness Horizons vol 43 no 6 pp 55ndash64 2000

[11] V D R Guide ldquoProduction planning and control forremanufacturing industry practice and research needsrdquoJournal of OperationsManagement vol 18 no 4 pp 467ndash4832000

[12] A L Larson E O Teisberg and R R Johnson ldquoSustainablebusiness opportunity and value creationrdquo Interfaces vol 30no 3 pp 1ndash12 2000

[13] Z Zhang B Gong J Tang Z Liu and X Zheng ldquo-e jointdynamic green innovation and pricing strategies for a hybridsystem of manufacturing and remanufacturing with carbon

emission constraintsrdquo Kybernetes vol 48 no 8pp 1699ndash1730 2019

[14] A Atasu M Sarvary and L N Van Wassenhove ldquoRema-nufacturing as a marketing strategyrdquo Management Sciencevol 54 no 10 pp 1731ndash1746 2008

[15] Z Wang Y Wang Z Liu J S Cheng and X T ChenldquoStrategic management of product recovery and its envi-ronmental impactrdquo International Journal of Production Re-search 2020

[16] S V Nagalingam S S Kuik and Y Amer ldquoPerformancemeasurement of product returns with recovery for sustainablemanufacturingrdquo Robotics and Computer-IntegratedManufacturing vol 29 no 6 pp 473ndash483 2013

[17] D Kahneman and A Tversky ldquoProspect theory an analysis ofdecision under riskrdquo Econometrica vol 47 no 2 pp 263ndash2911979

[18] E C Yurewicz F Matsuura and K S Moghissi ldquoLossaversion and individual characteristicsrdquo Environmental andResource Economics vol 49 no 4 pp 573ndash596 2011

[19] U Schmidt and H Zank ldquoWhat is loss aversionrdquo Journal ofRisk and Uncertainty vol 30 no 2 pp 157ndash167 2005

[20] Z Horst and B Peter ldquoLoss averse behaviorrdquo Journal of Riskand Uncertainty vol 31 no 3 pp 301ndash325 2005

[21] A Tversky and D Kahneman ldquoLoss aversion in risklesschoice a reference-dependent modelrdquo 9e Quarterly Journalof Economics vol 106 no 4 pp 1039ndash1061 1991

[22] M E Ferguson and L B Toktay ldquo-e effect of competition onrecovery strategiesrdquo Production and Operations Managementvol 15 no 3 pp 351ndash368 2010

[23] O Kaya ldquoIncentive and production decisions for remanu-facturing operationsrdquo European Journal of Operational Re-search vol 201 no 2 pp 442ndash453 2010

[24] J-M Chen and C-I Chang ldquo-e economics of a closed-loopsupply chain with remanufacturingrdquo Journal of the Opera-tional Research Society vol 63 no 10 pp 1323ndash1335 2012

[25] D G Pietro and Z Georges ldquoA two-period game of a closed-loop supply chainrdquo European Journal of Operational Researchvol 232 no 1 pp 22ndash40 2014

[26] S Mitra ldquoModels to explore remanufacturing as a competitivestrategy under duopolyrdquo Omega vol 59 pp 215ndash227 2015

[27] D G Pietro ldquoClosed-loop supply chain coordination throughincentives with asymmetric informationrdquo Annals of Opera-tions Research vol 253 pp 133ndash167 2017

[28] G Raz A Ovchinnikov and V Blass ldquoEconomic environ-mental and social impact of remanufacturing in a competitivesettingrdquo IEEE Transactions on Engineering Managementvol 64 no 4 pp 476ndash490 2017

[29] G Ferrer and J M Swaminathan ldquoManaging new and dif-ferentiated remanufactured productsrdquo European Journal ofOperational Research vol 203 no 2 pp 370ndash379 2010

[30] V V Agrawal A Atasu and K van Ittersum ldquoRemanu-facturing third-party competition and consumersrsquo perceivedvalue of new productsrdquo Management Science vol 61 no 1pp 60ndash72 2015

[31] J D Abbey J D Blackburn and D R Guide ldquoOptimalpricing for new and remanufactured productsrdquo Journal ofOperations Management vol 36 no 1 pp 130ndash146 2015

[32] S S Gan I N Pujawan Suparno and B Widodo ldquoPricingdecision for new and remanufactured product in a closed-loop supply chain with separate sales-channelrdquo InternationalJournal of Production Economics vol 190 pp 120ndash132 2016

[33] J J Kovach A Atasu and S Banerjee ldquoSalesforce incentivesand remanufacturingrdquo Production and Operations Manage-ment vol 27 no 3 pp 516ndash530 2018

Complexity 9

[34] J Ma H Ren M Yu and M Zhu ldquoResearch on the com-plexity and chaos control about a closed-loop supply chainwith dual-channel recycling and uncertain consumer per-ceptionrdquo Complexity vol 2018 Article ID 9853635 13 pages2018

[35] J Tang B Y Li K W Li Z Liu and J Huang ldquoPricing andwarranty decisions in a two-period closed-loop supply chainrdquoInternational Journal of Production Research vol 58 no 6pp 1688ndash1704 2020

[36] F J Ramırez J A Aledo and D T Pham ldquoEconomicmodelling of robotic disassembly in end-of-life product re-covery for remanufacturingrdquo Computers and Industrial En-gineering vol 142 Article ID 106339 2020

[37] P Brooks and H Zank ldquoLoss averse behaviorrdquo Journal of Riskand Uncertainty vol 31 no 3 pp 301ndash325 2005

[38] D Kahneman and A Tversky ldquoChoices values and framesrdquoAmerican Psychologist vol 39 no 4 pp 341ndash350 2000

[39] P Heidhues and B Koszegi 9e Impact of Consumer LossAversion on Pricing CEPR Discussion Papers (SP II 2004-17)London UK 2005

[40] G Kotonya S Lock and J Mariani ldquoLoss aversion andconsumption choice theory and experimental evidencerdquoAmerican Economic Journal Microeconomics vol 7 no 2pp 101ndash120 2012

[41] S H Kim and J Lee ldquoFirm behavior under consumer lossaversionrdquo Social Science Electronic Publishing vol 27 no 2pp 171ndash186 2014

[42] R Antonio ldquoSelling substitute goods to loss-averse con-sumers limited availability bargains and rip-offsrdquo9e RANDJournal of Economics vol 47 no 3 pp 709ndash733 2016

[43] S Fabrizi S Lippert C Puppe and S Rosenkranz ldquoManu-facturer suggested retail prices loss aversion and competi-tionrdquo Journal of Economic Psychology vol 53 pp 141ndash1532016

[44] O Marz ldquoCompetitive persuasive advertising under con-sumer loss aversionrdquo Economics Letters vol 185 Article ID108690 2019

[45] C Ghesla M Grieder and M Stadelmann ldquoPro-environ-mental incentives and loss aversion a field experiment onelectricity saving behaviorrdquo Energy Policy vol 137 Article ID111131 2020

[46] Z Liu K W Li B-Y Li J Huang and J Tang ldquoImpact ofproduct-design strategies on the operations of a closed-loopsupply chainrdquo Transportation Research Part E Logistics andTransportation Review vol 124 pp 75ndash91 2019

[47] B Koszegi and M Rabin ldquoA model of reference-dependentpreferencesrdquo Quarterly Journal of Economics vol 121 no 4pp 1133ndash1165 2006

[48] A Tversky and D Kahneman ldquoAdvances in prospect theorycumulative representation of uncertaintyrdquo Journal of Risk andUncertainty vol 5 no 4 pp 297ndash323 1992

[49] B G S Hardie E J Johnson and P S Fader ldquoModeling lossaversion and reference dependence effects on brand choicerdquoMarketing Science vol 12 no 4 pp 378ndash394 1993

[50] V Kobberling and P P Wakker ldquoAn index of loss aversionrdquoJournal of Economic 9eory vol 122 no 1 pp 119ndash131 2005

[51] L P Metzger and M O Rieger ldquoNon-cooperative games withprospect theory players and dominated strategiesrdquoGames andEconomic Behavior vol 115 pp 396ndash409 2019

[52] R Giutini and K Gaudette ldquoRemanufacturing the next greatopportunity for boosting us productivityrdquo Business Horizonsvol 46 no 6 pp 41ndash48 2003

[53] S Bernard ldquoRemanufacturingrdquo Journal of EnvironmentalEconomics and Management vol 62 no 3 pp 337ndash351 2011

[54] C F Camerer ldquoBehavioral economicsrdquo Current Biologyvol 24 no 18 pp R867ndashR871 2014

[55] X-X Zheng D-F Li Z Liu F Jia and J-B Sheu ldquoCoor-dinating a closed-loop supply chain with fairness concernsthrough variable-weighted Shapley valuesrdquo TransportationResearch Part E Logistics and Transportation Review vol 126pp 227ndash253 2019

[56] O Samuel ldquoLoss aversion and market crashesrdquo EconomicModelling vol 92 pp 70ndash86 2020

10 Complexity

-is paper aims to provide guidelines for manufacturersto make optimal decision-making Considering the complexcharacteristics of the remanufacturing system we addressthe following three problems to identify the drives forremanufacturing (1) consumer perception of price andvalue dimensions for new and remanufactured products (2)consumer preference for the two types of products and (3)the influence of consumer loss aversion on operations

11 Price and Value Dimensions of New and RemanufacturedProducts Remanufacturing has been identified to be themost effective way to minimize the consumption of energyand raw materials leave less air pollution and reduce wastedisposal treatments [16] -e remanufactured product is anew alternative environment-friendly product -e low costand low price are their competitive advantages Althoughremanufactured products affect the market share of theprimary new products it may be an important path to realizethe sustainable development -is issue is discussed ex-haustively in this paper -e results show that remanu-facturing is a new growth point

12 Consumer Preference for New and RemanufacturedProducts -e raw materials for remanufacturing are EOLproducts It is no surprise that consumers perceive newproducts to be of a higher quality standard and they usuallyhave lower valuation for remanufactured products Beforepurchasing or using remanufactured products consumersare often uncertain about the actual performance andphysical reliability and hold the idea that new products havebetter properties As such if the new product is available it istaken for granted that the new product is the best choiceConsumers can clearly distinguish new and remanufacturedproducts -eir willingness to pay (WTP) for remanufac-tured products is obviously lower than that for new onesWTP difference plays a significant role in demands for bothproducts and supply chain performance

13 Consumer Loss Aversion -e important characteristicsof loss aversion are that people are reluctant to accept lossesand tend to choose avoiding losses It is well supported infinance and marketing and has extensive and profoundinfluence [17 18] As loss aversion obviously exists in realityit attracts researchersrsquo interests significantly [19ndash21] In thecase of utilizing remanufactured products most customersare often uncertain about the product properties It istherefore of no surprise that the consumers usually have alower valuation for remanufactured products -e instinctthat consumers as far as possible avoid losses leads them tohardly make purchase decisions for remanufactured prod-ucts and significantly affects the operation performance ofCLSC

-e outline of our paper is as follows We provide anexhaustive literature review in Section 2 In the next sectionwe lay out the features of the market demand Section 4presents the gamemodels and obtains the equilibrium-ennumerical examples and environmental assessment are

presented in Sections 5 and 6 respectively Finally our paperbriefly concludes in Section 7 and offers some possible di-rections for future work in this area

2 Relevant Literature

Our paper is closely related to the following two researchfields in CLSC consumer preference and remanufacturingAt present a variety of articles are carried out to investigatethe remanufacturing profitability from the perspective of themanufacturer Ferguson and Toktay [22] investigate rema-nufacturing and collection decisions to derive conditionsunder which strategy is profitable In a stochastic demandsetting Kaya [23] considers the decision-making with theincentive strategy and product remanufacturing Accordingto a variety of different parameters the impacts on systemperformance are taken into account in the paper Chen andChang [24] present several game models to identify theeconomic benefits of the remanufacturing system Pietro andGeorges [25] develop CLSC game models to investigate theoperational performance Mitra [26] develops theoreticalmodels to show that the profit is always higher in theremanufacturing setting Pietro [27] develops incentivegames to investigate product recycling and economic ben-efits Raz et al [28] investigate the economic environmentaland social impact of remanufacturing

Interestingly all these articles concentrate on the stra-tegic research of the remanufacturing system under thegeneral concept of value Due to the imperfection of theremanufactured products we cannot easily measure theirvalue in common sense Atasu et al [14] introduce consumerWTP to study the profitability of the remanufacturingsystem Given that consumer WTP for new and remanu-factured products is different Ferrer and Swaminathan [29]propose game models with differentiated prices for themAgrawal et al [30] investigate that the existence of rema-nufactured products has a direct influence on the con-sumersrsquo perceived value for new ones Abbey et al [31]discuss the optimal decision-making in CLSC consideringconsumer preferences -ey reveal that the original equip-ment manufacturer can reap high profits through makingdifferent prices for them Gan et al [32] reveal that thecognition and attitudes to remanufactured products play animportant role in enhancing the profit of players Kovachet al [33] present a salesforce incentive model to investigatethe salesforce incentives and the enterprisersquos decision-making Ma et al [34] introduce consumer WTP to in-vestigate pricing and recycling strategies in CLSC Tang et al[35] conduct a full analysis to examine the impacts of pricingand warranty decisions on profitability and consumersurplus in the context of remanufacturing Ramırez et al[36] propose economicmodels to demonstrate the economicoutputs and environmental impacts

All these papers mentioned above mainly investigate theperformance in CLSC operations considering loss-neutralconsumers and they ignore the psychological characteristicsof loss aversion Brooks and Zank [37] demonstrate thebehavior of consumers in themarket and point out that mostconsumers are loss averse -e analysis and consequences of

2 Complexity



3 Model Description
















qNn 1 minus

pn minus pr

1 minus θ

qNr


(1 minus θ)minus

pr

θ

(1)



Complexity 3



un v minus pn (2)



where


λ x minus x0( 1113857 x lt x01113896 (4)












qLn 1 minus

2 2pn minus pr( 1113857

(1 minus θ)(1 + λ)

qLr

2 2pn minus pr( 1113857


2pr

θ(1 + λ)

(6)

4 Analysis Results


41 Market Share


Time






qnun = v ndash pn

ur = θv ndash pr

v

qr


Nodemand

u


4 Complexity




2pr

θ(1 + λ)lt

pr

θ




(1 minus θ)

qLn 1 minus



Nn 1 minus

pn minus pr

1 minus θ

(7)





maxpnpr




qNn


2(1 minus θ)

qNr

θcn minus cr

2θ(1 minus θ)

pNn

1 + cn

2

pNr

θ + cr

2

πN1 minus 2cn

4+

c2r

4θ+


4(1 minus θ)

(9)


qLn


2t(1 minus θ)12

minuscn minus cr

2t(1 minus θ)

qLr

θcn minus cr

2θt(1 minus θ)

pLn

t + cn

2

pLr

θt + cr

2

πL

t minus 2cn

4+

c2r

4θt+


4t(1 minus θ)

(10)

where t ((1 + λ)2) gt 1



Proof

pLn minus p

Nn

t + cn

2minus1 + cn

2

t minus 12gt 0

zpLn

zλ

zpLn

zt

zt

zλ14gt 0

(11)



pn(pn)λ

u

qnun = v ndash pn


1v

prθ (2pr)θ (1 + λ)

u0 = ndashλv + pn

No demand


Complexity 5







Proof

pLr minus p

Nr

θt + cr

2minusθ + cr

2θ(t minus 1)

2gt 0

zpLr

zλ

zpLr

zt

zt

zλθ4gt 0

(12)





5 Numerical Results





13

12

11

1

09

08

07

1 15 2 25 3


λ

pn


07

1 15 2 25 3


λ

pr

065

06

055

05

045

04

075


1 15 2 25 3


λ

n

038

036

034

032

03

028

026

024


6 Complexity











1 15 2 25 3


λ

r

0085

008

0075

007

0065

006

0055

005

0045

004



θ

π

026

024

022

02

018

016

014

012

01

00805 055 06 065 07 075 08 085 09


1 15 2 25 3


λ

π

04

035

03

025

02

015

01

005


Complexity 7








219181716151413

1 12 14 16 18 2 22 24 26 28 3λ

E


08

075

07

065

06

0551 12 14 16 18 2 22 24 26 28 3

λ

E



23

22

21

19

18

17

16

15

2

1 12 14 16 18 2 22 24 26 28 3λ

E



8 Complexity


Data Availability




Acknowledgments


References



































Complexity 9
























10 Complexity



3 Model Description
















qNn 1 minus

pn minus pr

1 minus θ

qNr


(1 minus θ)minus

pr

θ

(1)



Complexity 3



un v minus pn (2)



where


λ x minus x0( 1113857 x lt x01113896 (4)












qLn 1 minus

2 2pn minus pr( 1113857

(1 minus θ)(1 + λ)

qLr

2 2pn minus pr( 1113857


2pr

θ(1 + λ)

(6)

4 Analysis Results


41 Market Share


Time






qnun = v ndash pn

ur = θv ndash pr

v

qr


Nodemand

u


4 Complexity




2pr

θ(1 + λ)lt

pr

θ




(1 minus θ)

qLn 1 minus



Nn 1 minus

pn minus pr

1 minus θ

(7)





maxpnpr




qNn


2(1 minus θ)

qNr

θcn minus cr

2θ(1 minus θ)

pNn

1 + cn

2

pNr

θ + cr

2

πN1 minus 2cn

4+

c2r

4θ+


4(1 minus θ)

(9)


qLn


2t(1 minus θ)12

minuscn minus cr

2t(1 minus θ)

qLr

θcn minus cr

2θt(1 minus θ)

pLn

t + cn

2

pLr

θt + cr

2

πL

t minus 2cn

4+

c2r

4θt+


4t(1 minus θ)

(10)

where t ((1 + λ)2) gt 1



Proof

pLn minus p

Nn

t + cn

2minus1 + cn

2

t minus 12gt 0

zpLn

zλ

zpLn

zt

zt

zλ14gt 0

(11)



pn(pn)λ

u

qnun = v ndash pn


1v

prθ (2pr)θ (1 + λ)

u0 = ndashλv + pn

No demand


Complexity 5







Proof

pLr minus p

Nr

θt + cr

2minusθ + cr

2θ(t minus 1)

2gt 0

zpLr

zλ

zpLr

zt

zt

zλθ4gt 0

(12)





5 Numerical Results





13

12

11

1

09

08

07

1 15 2 25 3


λ

pn


07

1 15 2 25 3


λ

pr

065

06

055

05

045

04

075


1 15 2 25 3


λ

n

038

036

034

032

03

028

026

024


6 Complexity











1 15 2 25 3


λ

r

0085

008

0075

007

0065

006

0055

005

0045

004



θ

π

026

024

022

02

018

016

014

012

01

00805 055 06 065 07 075 08 085 09


1 15 2 25 3


λ

π

04

035

03

025

02

015

01

005


Complexity 7








219181716151413

1 12 14 16 18 2 22 24 26 28 3λ

E


08

075

07

065

06

0551 12 14 16 18 2 22 24 26 28 3

λ

E



23

22

21

19

18

17

16

15

2

1 12 14 16 18 2 22 24 26 28 3λ

E



8 Complexity


Data Availability




Acknowledgments


References



































Complexity 9
























10 Complexity



un v minus pn (2)



where


λ x minus x0( 1113857 x lt x01113896 (4)












qLn 1 minus

2 2pn minus pr( 1113857

(1 minus θ)(1 + λ)

qLr

2 2pn minus pr( 1113857


2pr

θ(1 + λ)

(6)

4 Analysis Results


41 Market Share


Time






qnun = v ndash pn

ur = θv ndash pr

v

qr


Nodemand

u


4 Complexity




2pr

θ(1 + λ)lt

pr

θ




(1 minus θ)

qLn 1 minus



Nn 1 minus

pn minus pr

1 minus θ

(7)





maxpnpr




qNn


2(1 minus θ)

qNr

θcn minus cr

2θ(1 minus θ)

pNn

1 + cn

2

pNr

θ + cr

2

πN1 minus 2cn

4+

c2r

4θ+


4(1 minus θ)

(9)


qLn


2t(1 minus θ)12

minuscn minus cr

2t(1 minus θ)

qLr

θcn minus cr

2θt(1 minus θ)

pLn

t + cn

2

pLr

θt + cr

2

πL

t minus 2cn

4+

c2r

4θt+


4t(1 minus θ)

(10)

where t ((1 + λ)2) gt 1



Proof

pLn minus p

Nn

t + cn

2minus1 + cn

2

t minus 12gt 0

zpLn

zλ

zpLn

zt

zt

zλ14gt 0

(11)



pn(pn)λ

u

qnun = v ndash pn


1v

prθ (2pr)θ (1 + λ)

u0 = ndashλv + pn

No demand


Complexity 5







Proof

pLr minus p

Nr

θt + cr

2minusθ + cr

2θ(t minus 1)

2gt 0

zpLr

zλ

zpLr

zt

zt

zλθ4gt 0

(12)





5 Numerical Results





13

12

11

1

09

08

07

1 15 2 25 3


λ

pn


07

1 15 2 25 3


λ

pr

065

06

055

05

045

04

075


1 15 2 25 3


λ

n

038

036

034

032

03

028

026

024


6 Complexity











1 15 2 25 3


λ

r

0085

008

0075

007

0065

006

0055

005

0045

004



θ

π

026

024

022

02

018

016

014

012

01

00805 055 06 065 07 075 08 085 09


1 15 2 25 3


λ

π

04

035

03

025

02

015

01

005


Complexity 7








219181716151413

1 12 14 16 18 2 22 24 26 28 3λ

E


08

075

07

065

06

0551 12 14 16 18 2 22 24 26 28 3

λ

E



23

22

21

19

18

17

16

15

2

1 12 14 16 18 2 22 24 26 28 3λ

E



8 Complexity


Data Availability




Acknowledgments


References



































Complexity 9
























10 Complexity




2pr

θ(1 + λ)lt

pr

θ




(1 minus θ)

qLn 1 minus



Nn 1 minus

pn minus pr

1 minus θ

(7)





maxpnpr




qNn


2(1 minus θ)

qNr

θcn minus cr

2θ(1 minus θ)

pNn

1 + cn

2

pNr

θ + cr

2

πN1 minus 2cn

4+

c2r

4θ+


4(1 minus θ)

(9)


qLn


2t(1 minus θ)12

minuscn minus cr

2t(1 minus θ)

qLr

θcn minus cr

2θt(1 minus θ)

pLn

t + cn

2

pLr

θt + cr

2

πL

t minus 2cn

4+

c2r

4θt+


4t(1 minus θ)

(10)

where t ((1 + λ)2) gt 1



Proof

pLn minus p

Nn

t + cn

2minus1 + cn

2

t minus 12gt 0

zpLn

zλ

zpLn

zt

zt

zλ14gt 0

(11)



pn(pn)λ

u

qnun = v ndash pn


1v

prθ (2pr)θ (1 + λ)

u0 = ndashλv + pn

No demand


Complexity 5







Proof

pLr minus p

Nr

θt + cr

2minusθ + cr

2θ(t minus 1)

2gt 0

zpLr

zλ

zpLr

zt

zt

zλθ4gt 0

(12)





5 Numerical Results





13

12

11

1

09

08

07

1 15 2 25 3


λ

pn


07

1 15 2 25 3


λ

pr

065

06

055

05

045

04

075


1 15 2 25 3


λ

n

038

036

034

032

03

028

026

024


6 Complexity











1 15 2 25 3


λ

r

0085

008

0075

007

0065

006

0055

005

0045

004



θ

π

026

024

022

02

018

016

014

012

01

00805 055 06 065 07 075 08 085 09


1 15 2 25 3


λ

π

04

035

03

025

02

015

01

005


Complexity 7








219181716151413

1 12 14 16 18 2 22 24 26 28 3λ

E


08

075

07

065

06

0551 12 14 16 18 2 22 24 26 28 3

λ

E



23

22

21

19

18

17

16

15

2

1 12 14 16 18 2 22 24 26 28 3λ

E



8 Complexity


Data Availability




Acknowledgments


References



































Complexity 9
























10 Complexity







Proof

pLr minus p

Nr

θt + cr

2minusθ + cr

2θ(t minus 1)

2gt 0

zpLr

zλ

zpLr

zt

zt

zλθ4gt 0

(12)





5 Numerical Results





13

12

11

1

09

08

07

1 15 2 25 3


λ

pn


07

1 15 2 25 3


λ

pr

065

06

055

05

045

04

075


1 15 2 25 3


λ

n

038

036

034

032

03

028

026

024


6 Complexity











1 15 2 25 3


λ

r

0085

008

0075

007

0065

006

0055

005

0045

004



θ

π

026

024

022

02

018

016

014

012

01

00805 055 06 065 07 075 08 085 09


1 15 2 25 3


λ

π

04

035

03

025

02

015

01

005


Complexity 7








219181716151413

1 12 14 16 18 2 22 24 26 28 3λ

E


08

075

07

065

06

0551 12 14 16 18 2 22 24 26 28 3

λ

E



23

22

21

19

18

17

16

15

2

1 12 14 16 18 2 22 24 26 28 3λ

E



8 Complexity


Data Availability




Acknowledgments


References



































Complexity 9
























10 Complexity











1 15 2 25 3


λ

r

0085

008

0075

007

0065

006

0055

005

0045

004



θ

π

026

024

022

02

018

016

014

012

01

00805 055 06 065 07 075 08 085 09


1 15 2 25 3


λ

π

04

035

03

025

02

015

01

005


Complexity 7








219181716151413

1 12 14 16 18 2 22 24 26 28 3λ

E


08

075

07

065

06

0551 12 14 16 18 2 22 24 26 28 3

λ

E



23

22

21

19

18

17

16

15

2

1 12 14 16 18 2 22 24 26 28 3λ

E



8 Complexity


Data Availability




Acknowledgments


References



































Complexity 9
























10 Complexity








219181716151413

1 12 14 16 18 2 22 24 26 28 3λ

E


08

075

07

065

06

0551 12 14 16 18 2 22 24 26 28 3

λ

E



23

22

21

19

18

17

16

15

2

1 12 14 16 18 2 22 24 26 28 3λ

E



8 Complexity


Data Availability




Acknowledgments


References



































Complexity 9
























10 Complexity


Data Availability




Acknowledgments


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Complexity 9
























10 Complexity
























10 Complexity

impact of consumer loss aversion on operations in the context...

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