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Open AccessOpen Access JUSTC Research Articles:Management Science and Engineering

Quality and inventory decisions in loss-averse distribution channels considering consumer heterogeneity

  • 1.

    College of Transportation Engineering, Chang'an University, Xi'an 710064, China

  • 2.

    School of Economics and Management, Chang'an University, Xi'an 710064, China

  • 3.

    School of Public Affairs, University of Science and Technology of China, Hefei 230026, China

Cite this:
https://doi.org/10.52396/JUST-2021-0056
  • Received Date: 25 February 2021
  • Rev Recd Date: 22 March 2021
  • Publish Date: 31 March 2021
    Abstract

  • Abstract

    In this paper, we examine firms’ quality and inventory decisions with consumers who behave heterogeneously not only on the product’s valuation (horizontal) but also on the reference price setting (vertical). Through a three-stage Stackelberg leader-follower model, we derive cost-effective solutions for channel members in two distribution scenarios. Counter-intuitively, the analytical result illustrates that profit-maximizing inventory and quality decisions can be higher when the uncertainty of the market increases because the two-dimensional impacts of market uncertainty on demand are diametrically opposite to each other. Specifically, the vertical uncertainty (difference in reference effects) has a buffering effect on the aggregate market demand, which is further amplified by loss-aversion behaviors. However, the horizontal uncertainty (heterogeneity of consumer valuation) has a promoting effect on the market demand and induces firms to order more. The numerical result further shows that market demand may not inherit the behavioral bias of individual consumers, leading to an inconsistent relationship between the sensitivity of market demand to gain/loss and consumers’ loss-aversion behaviors. Our findings have implications not only for understanding the stochastic market demand with behaviorally biased consumers but also for determining the channel members’ optimal inventory and quality decisions.

    Abstract

    In this paper, we examine firms’ quality and inventory decisions with consumers who behave heterogeneously not only on the product’s valuation (horizontal) but also on the reference price setting (vertical). Through a three-stage Stackelberg leader-follower model, we derive cost-effective solutions for channel members in two distribution scenarios. Counter-intuitively, the analytical result illustrates that profit-maximizing inventory and quality decisions can be higher when the uncertainty of the market increases because the two-dimensional impacts of market uncertainty on demand are diametrically opposite to each other. Specifically, the vertical uncertainty (difference in reference effects) has a buffering effect on the aggregate market demand, which is further amplified by loss-aversion behaviors. However, the horizontal uncertainty (heterogeneity of consumer valuation) has a promoting effect on the market demand and induces firms to order more. The numerical result further shows that market demand may not inherit the behavioral bias of individual consumers, leading to an inconsistent relationship between the sensitivity of market demand to gain/loss and consumers’ loss-aversion behaviors. Our findings have implications not only for understanding the stochastic market demand with behaviorally biased consumers but also for determining the channel members’ optimal inventory and quality decisions.
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    • References(49)
  • [1]
    Eeckhoudt L, Gollier C, Schlesinger H. The risk-averse (and prudent) newsboy. Management Science, 1995, 41(5): 786-794.
    [2]
    Schweitzer M E, Cachon G P. Decision bias in the newsvendor problem with a known demand distribution: Experimental evidence. Management Science, 2000, 46(3): 404-420.
    [3]
    Chen L, Kök A G, Tong J D. The effect of payment schemes on inventory decisions: The role of mental accounting. Management Science, 2013, 59(2): 436-451.
    [4]
    Jerath K, Kim S H, Swinney R. Product quality in a distribution channel with inventory risk. Marketing Science, 2017, 36(5): 747-761.
    [5]
    Choi T M, Chiu C H. Mean-downside-risk and mean-variance newsvendor models: Implications for sustainable fashion retailing. International Journal of Production Economics, 2012, 135(2): 552-560.
    [6]
    Huang K L, Kuo C W, Lu M L. Wholesale price rebate vs. capacity expansion: The optimal strategy for seasonal products in a supply chain. European Journal of Operational Research, 2014, 234(1): 77-85.
    [7]
    Nouri M, Hosseini-Motlagh S M, Nematollahi M, et al. Coordinating manufacturer’s innovation and retailer’s promotion and replenishment using a compensation-based wholesale price contract. International Journal of Production Economics, 2018, 198: 11-24.
    [8]
    Popescu I, Wu Y. Dynamic pricing strategies with reference effects. Operations Research, 2007, 55(3): 413-429.
    [9]
    Nasiry J, Popescu I. Dynamic pricing with loss-averse consumers and peak-end anchoring. Operations Research, 2011, 59(6): 1361-1368.
    [10]
    Chen X, Hu P, Shum S, et al. Dynamic stochastic inventory management with reference price effects. Operations Research, 2016, 64(6): 1529-1536.
    [11]
    Cao Y, Duan Y. Joint production and pricing inventory system under stochastic reference price effect. Computers & Industrial Engineering, 2020, 143: 106411.
    [12]
    Zhou J, Xu X, Shen B. Selling luxury fashion to conspicuous consumers in the presence of discount sensitivity behavior. International Transactions in Operational Research, 2018, 25(6): 1763-1784.
    [13]
    Sajeesh S, Hada M, Raju J S. The effect of consumer heterogeneity on firm profits in conspicuous goods markets. International Journal of Research in Marketing,2020, 37(2): 258-280.
    [14]
    Shi H, Liu Y, Petruzzi N C. Consumer heterogeneity, product quality, and distribution channels. Management Science, 2013, 59(5): 1162-1176.
    [15]
    Collado P B, Martinnez-De-Albéniz V. Estimating and optimizing the impact of inventory on consumer choices in a fashion retail setting. Manufacturing & Service Operations Management, 2018, 22 (3): 582-597.
    [16]
    Fibich G, Gavious A, Lowengart O. Explicit solutions of optimization models and differential games with nonsmooth (asymmetric) reference-price effects. Operations Research, 2003, 51(5): 721-734.
    [17]
    Hu Z, Nasiry J. Are markets with loss-averse consumers more sensitive to losses? Management Science, 2018, 64(3): 1384-1395.
    [18]
    Wang C X. The loss-averse newsvendor game. International Journal of Production Economics, 2010, 124(2): 448-452.
    [19]
    He H, Wang S. Cost-benefit associations in consumer inventory problem with uncertain benefit. Journal of Retailing and Consumer Services, 2019, 51: 271-284.
    [20]
    Jeuland A P, Shugan S M. Managing channel profits. Marketing Science, 1983, 2(3): 239-272.
    [21]
    Villas-Boas J M. Product line design for a distribution channel. Marketing Science, 1998, 17(2): 156-169.
    [22]
    Carlton D W, Dana Jr J D. Product variety and demand uncertainty: Why markups vary with quality. The Journal of Industrial Economics, 2008, 56(3): 535-552.
    [23]
    Jammernegg W, Kischka P. The price-setting newsvendor with service and loss constraints. Omega, 2013, 41(2): 326-335.
    [24]
    Bhowmick J. Optimal inventory policies for imperfect inventory with price dependent stochastic demand and partially backlogged shortages. Yugoslav Journal of Operations Research, 2016, 22: 199-223.
    [25]
    Hua Z, Li S. Impacts of demand uncertainty on retailer’s dominance and manufacturer-retailer supply chain cooperation. Omega, 2008, 36(5): 697-714.
    [26]
    Briesch R A, Krishnamurthi L, Mazumdar T, et al. A comparative analysis of reference price models. Journal of Consumer Research, 1997, 24(2): 202-214.
    [27]
    Mazumdar T, Raj S P, Sinha I. Reference price research: Review and propositions. Journal of Marketing, 2005, 69(4): 84-102.
    [28]
    Gao S Y, Lim W S, Tang C S. Entry of copycats of luxury brands. Marketing Science, 2017, 36(2): 272-289.
    [29]
    Greenleaf E A. The impact of reference price effects on the profitability of price promotions. Marketing Science, 1995, 14(1): 82-104.
    [30]
    Rajendran K N, Tellis G J. Contextual and temporal components of reference price. Journal of Marketing, 1994, 58(1): 22-34.
    [31]
    Chen X, Hu Z Y, Zhang Y H. Dynamic pricing with stochastic reference price effect. Journal of the Operations Research Society of China, 2019, 7(1): 107-125.
    [32]
    Zhang J, Gou Q, Liang L, et al. Supply chain coordination through cooperative advertising with reference price effect. Omega, 2013, 41(2): 345-353.
    [33]
    URban T L. Coordinating pricing and inventory decisions under reference price effects. International Journal of Manufacturing Technology and Management, 2008, 13(1): 78-94.
    [34]
    Zhang Y. Essays on robust optimization, integrated inventory and pricing, and reference price effect.Urbana, IL: University of Illinois at Urbana-Champaign, 2010.
    [35]
    Taudes A, Rudloff C. Integrating inventory control and a price change in the presence of reference price effects: A two-period model. Mathematical Methods of Operations Research, 2012, 75(1): 29-65.
    [36]
    Güler M G, Bilgiç T, Güllü R. Joint inventory and pricing decisions with reference effects. IIE Transactions, 2014, 46(4): 330-343.
    [37]
    Chen X, Hu P, Hu Z. Efficient algorithms for the dynamic pricing problem with reference price effect. Management Science, 2017, 63(12): 4389-4408.
    [38]
    Tversky A, Kahneman D. Prospect theory: An analysis of decision under risk. Econometrica, 1979, 47(2): 263-291.
    [39]
    Tversky A, Kahneman D. Loss aversion in riskless choice: A reference-dependent model. The Quarterly Journal of Economics, 1991, 106(4): 1039-1061.
    [40]
    Prelec D, Loewenstein G. The red and the black: Mental accounting of savings and debt. Marketing Science, 1998, 17(1): 4-28.
    [41]
    Chang K, Siddarth S, Weinberg C B. The impact of heterogeneity in purchase timing and price responsiveness on estimates of sticker shock effects. Marketing Science, 1999, 18(2): 178-192.
    [42]
    BelL D R, LAttin J M. Looking for loss aversion in scanner panel data: The confounding effect of price response heterogeneity. Marketing Science, 2000, 19(2): 185-200.
    [43]
    Kopalle P K, Kannan P, Boldt L B, et al. The impact of household level heterogeneity in reference price effects on optimal retailer pricing policies. Journal of Retailing, 2012, 88(1): 102-114.
    [44]
    Huck S, Zhou J. Consumer behavioural biases in competition: A survey. NYU Working Paper, 2011: No. 2451/29989.
    [45]
    Koszegi B, Rabin M. A model of reference-dependent preferences. The Quarterly Journal of Economics, 2006, 121(4): 1133-1165.
    [46]
    Banker R D, Khosla I, Sinha K K. Quality and competition. Management Science, 1998, 44(9): 1179-1192.
    [47]
    Lin Q, He J. Supply chain contract design considering the supplier’s asset structure and capital constraints. Computers & Industrial Engineering, 2019, 137: 106044.
    [48]
    He H, Wang C, Wang S, et al. Does environmental concern promote EV sales? Duopoly pricing analysis considering consumer heterogeneity. Transportation Research Part D: Transport and Environment, 2021, 91: 102695.
    [49]
    Song H, Gao X. Green supply chain game model and analysis under revenue-sharing contract. Journal of Cleaner Production, 2018, 170: 183-192.
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    [1]
    Eeckhoudt L, Gollier C, Schlesinger H. The risk-averse (and prudent) newsboy. Management Science, 1995, 41(5): 786-794.
    [2]
    Schweitzer M E, Cachon G P. Decision bias in the newsvendor problem with a known demand distribution: Experimental evidence. Management Science, 2000, 46(3): 404-420.
    [3]
    Chen L, Kök A G, Tong J D. The effect of payment schemes on inventory decisions: The role of mental accounting. Management Science, 2013, 59(2): 436-451.
    [4]
    Jerath K, Kim S H, Swinney R. Product quality in a distribution channel with inventory risk. Marketing Science, 2017, 36(5): 747-761.
    [5]
    Choi T M, Chiu C H. Mean-downside-risk and mean-variance newsvendor models: Implications for sustainable fashion retailing. International Journal of Production Economics, 2012, 135(2): 552-560.
    [6]
    Huang K L, Kuo C W, Lu M L. Wholesale price rebate vs. capacity expansion: The optimal strategy for seasonal products in a supply chain. European Journal of Operational Research, 2014, 234(1): 77-85.
    [7]
    Nouri M, Hosseini-Motlagh S M, Nematollahi M, et al. Coordinating manufacturer’s innovation and retailer’s promotion and replenishment using a compensation-based wholesale price contract. International Journal of Production Economics, 2018, 198: 11-24.
    [8]
    Popescu I, Wu Y. Dynamic pricing strategies with reference effects. Operations Research, 2007, 55(3): 413-429.
    [9]
    Nasiry J, Popescu I. Dynamic pricing with loss-averse consumers and peak-end anchoring. Operations Research, 2011, 59(6): 1361-1368.
    [10]
    Chen X, Hu P, Shum S, et al. Dynamic stochastic inventory management with reference price effects. Operations Research, 2016, 64(6): 1529-1536.
    [11]
    Cao Y, Duan Y. Joint production and pricing inventory system under stochastic reference price effect. Computers & Industrial Engineering, 2020, 143: 106411.
    [12]
    Zhou J, Xu X, Shen B. Selling luxury fashion to conspicuous consumers in the presence of discount sensitivity behavior. International Transactions in Operational Research, 2018, 25(6): 1763-1784.
    [13]
    Sajeesh S, Hada M, Raju J S. The effect of consumer heterogeneity on firm profits in conspicuous goods markets. International Journal of Research in Marketing,2020, 37(2): 258-280.
    [14]
    Shi H, Liu Y, Petruzzi N C. Consumer heterogeneity, product quality, and distribution channels. Management Science, 2013, 59(5): 1162-1176.
    [15]
    Collado P B, Martinnez-De-Albéniz V. Estimating and optimizing the impact of inventory on consumer choices in a fashion retail setting. Manufacturing & Service Operations Management, 2018, 22 (3): 582-597.
    [16]
    Fibich G, Gavious A, Lowengart O. Explicit solutions of optimization models and differential games with nonsmooth (asymmetric) reference-price effects. Operations Research, 2003, 51(5): 721-734.
    [17]
    Hu Z, Nasiry J. Are markets with loss-averse consumers more sensitive to losses? Management Science, 2018, 64(3): 1384-1395.
    [18]
    Wang C X. The loss-averse newsvendor game. International Journal of Production Economics, 2010, 124(2): 448-452.
    [19]
    He H, Wang S. Cost-benefit associations in consumer inventory problem with uncertain benefit. Journal of Retailing and Consumer Services, 2019, 51: 271-284.
    [20]
    Jeuland A P, Shugan S M. Managing channel profits. Marketing Science, 1983, 2(3): 239-272.
    [21]
    Villas-Boas J M. Product line design for a distribution channel. Marketing Science, 1998, 17(2): 156-169.
    [22]
    Carlton D W, Dana Jr J D. Product variety and demand uncertainty: Why markups vary with quality. The Journal of Industrial Economics, 2008, 56(3): 535-552.
    [23]
    Jammernegg W, Kischka P. The price-setting newsvendor with service and loss constraints. Omega, 2013, 41(2): 326-335.
    [24]
    Bhowmick J. Optimal inventory policies for imperfect inventory with price dependent stochastic demand and partially backlogged shortages. Yugoslav Journal of Operations Research, 2016, 22: 199-223.
    [25]
    Hua Z, Li S. Impacts of demand uncertainty on retailer’s dominance and manufacturer-retailer supply chain cooperation. Omega, 2008, 36(5): 697-714.
    [26]
    Briesch R A, Krishnamurthi L, Mazumdar T, et al. A comparative analysis of reference price models. Journal of Consumer Research, 1997, 24(2): 202-214.
    [27]
    Mazumdar T, Raj S P, Sinha I. Reference price research: Review and propositions. Journal of Marketing, 2005, 69(4): 84-102.
    [28]
    Gao S Y, Lim W S, Tang C S. Entry of copycats of luxury brands. Marketing Science, 2017, 36(2): 272-289.
    [29]
    Greenleaf E A. The impact of reference price effects on the profitability of price promotions. Marketing Science, 1995, 14(1): 82-104.
    [30]
    Rajendran K N, Tellis G J. Contextual and temporal components of reference price. Journal of Marketing, 1994, 58(1): 22-34.
    [31]
    Chen X, Hu Z Y, Zhang Y H. Dynamic pricing with stochastic reference price effect. Journal of the Operations Research Society of China, 2019, 7(1): 107-125.
    [32]
    Zhang J, Gou Q, Liang L, et al. Supply chain coordination through cooperative advertising with reference price effect. Omega, 2013, 41(2): 345-353.
    [33]
    URban T L. Coordinating pricing and inventory decisions under reference price effects. International Journal of Manufacturing Technology and Management, 2008, 13(1): 78-94.
    [34]
    Zhang Y. Essays on robust optimization, integrated inventory and pricing, and reference price effect.Urbana, IL: University of Illinois at Urbana-Champaign, 2010.
    [35]
    Taudes A, Rudloff C. Integrating inventory control and a price change in the presence of reference price effects: A two-period model. Mathematical Methods of Operations Research, 2012, 75(1): 29-65.
    [36]
    Güler M G, Bilgiç T, Güllü R. Joint inventory and pricing decisions with reference effects. IIE Transactions, 2014, 46(4): 330-343.
    [37]
    Chen X, Hu P, Hu Z. Efficient algorithms for the dynamic pricing problem with reference price effect. Management Science, 2017, 63(12): 4389-4408.
    [38]
    Tversky A, Kahneman D. Prospect theory: An analysis of decision under risk. Econometrica, 1979, 47(2): 263-291.
    [39]
    Tversky A, Kahneman D. Loss aversion in riskless choice: A reference-dependent model. The Quarterly Journal of Economics, 1991, 106(4): 1039-1061.
    [40]
    Prelec D, Loewenstein G. The red and the black: Mental accounting of savings and debt. Marketing Science, 1998, 17(1): 4-28.
    [41]
    Chang K, Siddarth S, Weinberg C B. The impact of heterogeneity in purchase timing and price responsiveness on estimates of sticker shock effects. Marketing Science, 1999, 18(2): 178-192.
    [42]
    BelL D R, LAttin J M. Looking for loss aversion in scanner panel data: The confounding effect of price response heterogeneity. Marketing Science, 2000, 19(2): 185-200.
    [43]
    Kopalle P K, Kannan P, Boldt L B, et al. The impact of household level heterogeneity in reference price effects on optimal retailer pricing policies. Journal of Retailing, 2012, 88(1): 102-114.
    [44]
    Huck S, Zhou J. Consumer behavioural biases in competition: A survey. NYU Working Paper, 2011: No. 2451/29989.
    [45]
    Koszegi B, Rabin M. A model of reference-dependent preferences. The Quarterly Journal of Economics, 2006, 121(4): 1133-1165.
    [46]
    Banker R D, Khosla I, Sinha K K. Quality and competition. Management Science, 1998, 44(9): 1179-1192.
    [47]
    Lin Q, He J. Supply chain contract design considering the supplier’s asset structure and capital constraints. Computers & Industrial Engineering, 2019, 137: 106044.
    [48]
    He H, Wang C, Wang S, et al. Does environmental concern promote EV sales? Duopoly pricing analysis considering consumer heterogeneity. Transportation Research Part D: Transport and Environment, 2021, 91: 102695.
    [49]
    Song H, Gao X. Green supply chain game model and analysis under revenue-sharing contract. Journal of Cleaner Production, 2018, 170: 183-192.
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