January 2018, 14(1): 349-369. doi: 10.3934/jimo.2017050

Pricing and ordering strategies of supply chain with selling gift cards

School of Management and Economics, University of Electronic Science and Technology of China, Chengdu, 611731, China

* Corresponding author: Jingming Pan

Received  April 2016 Revised  May 2016 Published  June 2017

Gift cards is frequently used to replace traditional gift cash and gift products, especially when gift givers do not know gift receivers' performances. Basing on this phenomenon, we analyze the supplier's and the retailer's strategies with selling gift cards. First, we develop a Stackelberg model without selling gift cards. Next, we develop two models with selling gift cards when unredeemed gift cards balances become the retailer's property and the state's property, respectively. We present the optimal solutions and exam the impacts of parameters on the optimal decisions and the supply chain performance. When the retailer sells gift cards, the optimal order quantity is smaller than that without selling gift cards. The optimal wholesale price with selling gift cards is related to the treatment of unredeemed gift card balances. When unredeemed gift cards balances become the retailer's property, the wholesale price is lower than that without selling gift cards. However, when unredeemed gift cards balances become the state's property, the wholesale price is lower than that without selling gift cards in some conditions. And with selling gift cards, the optimal expected profits of retailer and supply chain are better off, but the optimal expected profit of supplier is worse off.

Citation: Jingming Pan, Wenqing Shi, Xiaowo Tang. Pricing and ordering strategies of supply chain with selling gift cards. Journal of Industrial & Management Optimization, 2018, 14 (1) : 349-369. doi: 10.3934/jimo.2017050
References:
[1]

Gift Card Solutions for Small Business: Differentiate and Grow Your Brand with First Data, Report of First Data Corporation, 2015. Available from: https://www.firstdata.com/giftcards/index.html.

[2]

Gift Cards State of the Union 2014, Report of CEB, 2015. Available from: https://www.cebglobal.com/financial-services/tower-group/gift-cards-2014.html.

[3]

E. Alini, U. S. News: Governments Grab Unused Gift Cards, Wall Street Journey (Eastern Edition), Jun. 3, 2009. .

[4]

C. G. Austin and L. Huang, First choice? Last resort? Social risks and gift card selection, Journal of Marketing Theory and Practice, 20 (2014), 293-306. doi: 10.2753/MTP1069-6679200304.

[5]

G. A. Chua and Y. Liu, On the effect of demand randomness on inventory, pricing and profit, Operations Research Letters, 43 (2015), 514-518. doi: 10.1016/j.orl.2015.07.007.

[6]

C. Feinson, The steep rise of gift card purchases by the consumer is changing the method of accounting and reporting of gift card income by corporate the retailers, Journal of Business and Economics Research, 6 (2008), 7-12. doi: 10.19030/jber.v6i4.2405.

[7]

M. GhoreishiA. MirzazadehG. Weber and I. Nakhai-Kamalabadi, Joint pricing and replenishment decisions for non-instantaneous deteriorating items with partial backlogging, inflation-and selling price-dependent demand and customer returns, Journal of Industrial and Management Optimization, 11 (2015), 933-949. doi: 10.3934/jimo.2015.11.933.

[8]

D. Horne, Unredeemed gift cards and the problem of not providing customers with value, Journal of Consumer Marketing, 24 (2007), 192-193. doi: 10.1108/07363760710755977.

[9]

T. R. Kaplan and B. J. Ruffle, In search of welfare-improving gifts, European Economic Review, 53 (2009), 445-460. doi: 10.1016/j.euroecorev.2008.09.002.

[10]

M. KhoujaJ. PanB. T. Ratchford and J. Zhou, Analysis of free gift card program effectiveness, Journal of Retailing, 87 (2011), 444-461. doi: 10.1016/j.jretai.2011.06.002.

[11]

M. KhoujaJ. Pan and J. Zhou, Effects of gift cards on optimal order and discount of seasonal products, European Journal of Operational Research, 248 (2016), 159-173. doi: 10.1016/j.ejor.2015.07.016.

[12]

M. KhoujaS. Park and J. Zhou, A free gift card alternative to price discounts in the newsvendor problem, Omega, 41 (2013), 665-678. doi: 10.1016/j.omega.2012.08.005.

[13]

M. A. Lariviere and E. L. Porteus, Selling to the newsvendor: An analysis of price-only contracts, Manufacturing & Service Operations Management, 3 (2001), 293-305. doi: 10.1287/msom.3.4.293.9971.

[14]

J. P. Offenberg, Markets: Gift cards, Journal of Economic Perspectives, 21 (2007), 227-238.

[15]

K. E. Principe and J. G. Eisenhauer, Gift-giving and deadweight loss, Journal of Socio-Economics, 38 (2009), 215-220. doi: 10.1016/j.socec.2008.12.005.

[16]

A. N. SadighS. K. Chaharsooghi and M. Sheikhmohammady, A game theoretic approach to coordination of pricing, advertising, and inventory decisions in a competitive supply chain, Journal of Industrial and Management Optimization, 12 (2016), 337-355. doi: 10.3934/jimo.2016.12.337.

[17]

S. M. Shugan and J. Xie, Advance pricing of services and other implications of separating purchase and consumption, Journal of Service Research, 2 (2000), 227-239. doi: 10.1177/109467050023001.

[18]

K. M. StilleyJ. J. Inman and K. L. Wakefield, Spending on the fly: Mental budgets, promotions, and spending behavior, Journal of Marketing, 74 (2010), 34-47. doi: 10.1509/jmkg.74.3.34.

[19]

K. M. StilleyJ. J. Inman and K. L. Wakefield, Planning to make unplanned purchases? The role of in-store slack in budget deviation, Journal of Consumer Research, 37 (2010), 264-278. doi: 10.1086/651567.

[20]

M. Tkacik, Christmas the retailer season's new bounce is the "Week After", Wall street Journey (Eastern edition), 2002.

[21]

L. M. Thomas and M. S. Dillenbeck, Best used by expiration date, Marketing Management, 13 (2004), 53-55.

[22]

E. K. Valentin and A. T. Allred, Giving and getting gift cards, Journal of Consumer Marketing, 29 (2012), 271-279. doi: 10.1108/07363761211237344.

[23]

J. Waldfogel, The deadweight loss of Christmas, The American Economic Review, 83 (1993), 1328-1336.

[24]

J. Waldfogel, Gifts, cash, and stigma, Economic Inquiry, 40 (2002), 415-427.

[25]

J. Waldfogel, Does consumer irrationality trump consumer sovereignty?, The Review of Economics and Statistics, 87 (2005), 691-696. doi: 10.1162/003465305775098107.

[26]

P. WebleyS. E. G. Lea and R. Portalska, The unacceptability of money as a gift, Journal of Economic Psychology, 4 (1983), 223-238. doi: 10.1016/0167-4870(83)90028-4.

[27]

K. Wertenbroch, Consumption self-control by rationing purchase quantities of virtue and vice, Marketing Science, 17 (1998), 317-337. doi: 10.1287/mksc.17.4.317.

[28]

J. R. White, Format matters in the mental accounting of funds: The case of gift cards and cash gifts, SSRN Electronic Journal 948587, (2006), 1-40. doi: 10.2139/ssrn.948587.

[29]

R. J. White, The mental accounting of gift card versus cash gift funds, Advances in Consumer Research, 35 (2008), 722-723.

[30]

Q. Yao and R. Chen, Gift cards and gifted cash: The impact of fit between gift type and message construal, Journal of Retailing, 90 (2014), 481-492. doi: 10.1016/j.jretai.2014.07.001.

show all references

References:
[1]

Gift Card Solutions for Small Business: Differentiate and Grow Your Brand with First Data, Report of First Data Corporation, 2015. Available from: https://www.firstdata.com/giftcards/index.html.

[2]

Gift Cards State of the Union 2014, Report of CEB, 2015. Available from: https://www.cebglobal.com/financial-services/tower-group/gift-cards-2014.html.

[3]

E. Alini, U. S. News: Governments Grab Unused Gift Cards, Wall Street Journey (Eastern Edition), Jun. 3, 2009. .

[4]

C. G. Austin and L. Huang, First choice? Last resort? Social risks and gift card selection, Journal of Marketing Theory and Practice, 20 (2014), 293-306. doi: 10.2753/MTP1069-6679200304.

[5]

G. A. Chua and Y. Liu, On the effect of demand randomness on inventory, pricing and profit, Operations Research Letters, 43 (2015), 514-518. doi: 10.1016/j.orl.2015.07.007.

[6]

C. Feinson, The steep rise of gift card purchases by the consumer is changing the method of accounting and reporting of gift card income by corporate the retailers, Journal of Business and Economics Research, 6 (2008), 7-12. doi: 10.19030/jber.v6i4.2405.

[7]

M. GhoreishiA. MirzazadehG. Weber and I. Nakhai-Kamalabadi, Joint pricing and replenishment decisions for non-instantaneous deteriorating items with partial backlogging, inflation-and selling price-dependent demand and customer returns, Journal of Industrial and Management Optimization, 11 (2015), 933-949. doi: 10.3934/jimo.2015.11.933.

[8]

D. Horne, Unredeemed gift cards and the problem of not providing customers with value, Journal of Consumer Marketing, 24 (2007), 192-193. doi: 10.1108/07363760710755977.

[9]

T. R. Kaplan and B. J. Ruffle, In search of welfare-improving gifts, European Economic Review, 53 (2009), 445-460. doi: 10.1016/j.euroecorev.2008.09.002.

[10]

M. KhoujaJ. PanB. T. Ratchford and J. Zhou, Analysis of free gift card program effectiveness, Journal of Retailing, 87 (2011), 444-461. doi: 10.1016/j.jretai.2011.06.002.

[11]

M. KhoujaJ. Pan and J. Zhou, Effects of gift cards on optimal order and discount of seasonal products, European Journal of Operational Research, 248 (2016), 159-173. doi: 10.1016/j.ejor.2015.07.016.

[12]

M. KhoujaS. Park and J. Zhou, A free gift card alternative to price discounts in the newsvendor problem, Omega, 41 (2013), 665-678. doi: 10.1016/j.omega.2012.08.005.

[13]

M. A. Lariviere and E. L. Porteus, Selling to the newsvendor: An analysis of price-only contracts, Manufacturing & Service Operations Management, 3 (2001), 293-305. doi: 10.1287/msom.3.4.293.9971.

[14]

J. P. Offenberg, Markets: Gift cards, Journal of Economic Perspectives, 21 (2007), 227-238.

[15]

K. E. Principe and J. G. Eisenhauer, Gift-giving and deadweight loss, Journal of Socio-Economics, 38 (2009), 215-220. doi: 10.1016/j.socec.2008.12.005.

[16]

A. N. SadighS. K. Chaharsooghi and M. Sheikhmohammady, A game theoretic approach to coordination of pricing, advertising, and inventory decisions in a competitive supply chain, Journal of Industrial and Management Optimization, 12 (2016), 337-355. doi: 10.3934/jimo.2016.12.337.

[17]

S. M. Shugan and J. Xie, Advance pricing of services and other implications of separating purchase and consumption, Journal of Service Research, 2 (2000), 227-239. doi: 10.1177/109467050023001.

[18]

K. M. StilleyJ. J. Inman and K. L. Wakefield, Spending on the fly: Mental budgets, promotions, and spending behavior, Journal of Marketing, 74 (2010), 34-47. doi: 10.1509/jmkg.74.3.34.

[19]

K. M. StilleyJ. J. Inman and K. L. Wakefield, Planning to make unplanned purchases? The role of in-store slack in budget deviation, Journal of Consumer Research, 37 (2010), 264-278. doi: 10.1086/651567.

[20]

M. Tkacik, Christmas the retailer season's new bounce is the "Week After", Wall street Journey (Eastern edition), 2002.

[21]

L. M. Thomas and M. S. Dillenbeck, Best used by expiration date, Marketing Management, 13 (2004), 53-55.

[22]

E. K. Valentin and A. T. Allred, Giving and getting gift cards, Journal of Consumer Marketing, 29 (2012), 271-279. doi: 10.1108/07363761211237344.

[23]

J. Waldfogel, The deadweight loss of Christmas, The American Economic Review, 83 (1993), 1328-1336.

[24]

J. Waldfogel, Gifts, cash, and stigma, Economic Inquiry, 40 (2002), 415-427.

[25]

J. Waldfogel, Does consumer irrationality trump consumer sovereignty?, The Review of Economics and Statistics, 87 (2005), 691-696. doi: 10.1162/003465305775098107.

[26]

P. WebleyS. E. G. Lea and R. Portalska, The unacceptability of money as a gift, Journal of Economic Psychology, 4 (1983), 223-238. doi: 10.1016/0167-4870(83)90028-4.

[27]

K. Wertenbroch, Consumption self-control by rationing purchase quantities of virtue and vice, Marketing Science, 17 (1998), 317-337. doi: 10.1287/mksc.17.4.317.

[28]

J. R. White, Format matters in the mental accounting of funds: The case of gift cards and cash gifts, SSRN Electronic Journal 948587, (2006), 1-40. doi: 10.2139/ssrn.948587.

[29]

R. J. White, The mental accounting of gift card versus cash gift funds, Advances in Consumer Research, 35 (2008), 722-723.

[30]

Q. Yao and R. Chen, Gift cards and gifted cash: The impact of fit between gift type and message construal, Journal of Retailing, 90 (2014), 481-492. doi: 10.1016/j.jretai.2014.07.001.

Figure 1.  Decision behaviors in supply chain without gift cards
Figure 2.  Decision behaviors in supply chain with gift cards
Figure 3.  $w^*$, $q^*$ and $\pi^*$ vs. $CV$ (Note: $c=5, \theta=0.15, \alpha=0.8, \beta=0.5$ and $m=0.3$)
Figure 4.  $w^*$, $q^*$ and $\pi^*$ vs. $c/p$ (Note: $\sigma=40, \theta=0.15, \alpha=0.8, \beta=0.5$ and $m=0.3$)
Figure 5.  $w^*$, $q^*$ and $\pi^*$ vs. $\alpha$ (Note: $\sigma=40, c=5, \theta=0.15, \beta=0.5$ and $m=0.3$)
Figure 6.  $w^*$, $q^*$ and $\pi^*$ vs. $\beta$ (Note: $\sigma=40, c=5, \theta=0.15, \alpha=0.5$ and $m=0.3$)
Figure 7.  $w^*$, $q^*$ and $\pi^*$ vs. $\beta$ (Note: $\sigma=40, c=5, \theta=0.15, \alpha=0.8$ and $m=0.3$)
Figure 8.  $w^*$, $q^*$ and $\pi^*$ vs. $m$ (Note: $\sigma=40, c=5, \theta=0.15, \alpha=0.8$ and $\beta=0.5$)
Table 1.  Notation
Decision Variables:
q order quantity of gift product of the retailer
w wholesale price of gift product of the supplier
Parameters:
x demand for gift product/gift cards from gift givers before the holiday
f(x), F(x) the pdf and cdf of demand from gift givers before the holiday
p sale price of unit gift product
c cost of unit gift product
v salvage value of unit gift product
θ return rate of gift product/probability of a gift giving consumer buying gift card before the holiday
β probability of gift product buyers buying gift cards when gift product is stock-out before the holiday
α average redemption rate of gift cards after the holiday
m profit margin of non-gift products
Decision Variables:
q order quantity of gift product of the retailer
w wholesale price of gift product of the supplier
Parameters:
x demand for gift product/gift cards from gift givers before the holiday
f(x), F(x) the pdf and cdf of demand from gift givers before the holiday
p sale price of unit gift product
c cost of unit gift product
v salvage value of unit gift product
θ return rate of gift product/probability of a gift giving consumer buying gift card before the holiday
β probability of gift product buyers buying gift cards when gift product is stock-out before the holiday
α average redemption rate of gift cards after the holiday
m profit margin of non-gift products
Table 2.  Optimal solutions for uniformly distributed demand
Optimal wholesale price Optimal order quantity Conditions
$w_{NG}^* = \frac{1}{2}\left[ {c + \left( {1 - \theta } \right)p + \theta v} \right]$ $q_{NG}^* = \frac{{b\left[ {\left( {1 - \theta } \right)p + \theta v - c} \right]}}{{2\left( {1 - \theta } \right)\left( {p - v} \right)}}$ --
$w_{RG}^* = \frac{1}{2}\left[ {c + \left( {1 - \beta - m\alpha \beta + \alpha \beta } \right)p} \right]$ $q_{RG}^* = \frac{{b\left( {1 - \theta } \right)\left[ {\left( {1 - \beta - m\alpha \beta + \alpha \beta } \right)p - c} \right]}}{{2\left( {1 -\beta- m\alpha \beta + \alpha \beta } \right)p - v}}$ $\left( {1 - \beta - m\alpha \beta + \alpha \beta } \right)p - v \ge 0$
$w_{SG}^* = \frac{1}{2}\left[ {c + \left( {1 - m\alpha \beta } \right)p} \right]$ $q_{SG}^* = \frac{{b\left( {1 - \theta } \right)\left[ {\left( {1 - m\alpha \beta } \right)p - c} \right]}}{{2\left( {1 - m\alpha \beta } \right)p - v}}$ $\left( {1 - m\alpha \beta } \right)p - v \ge 0$
Optimal wholesale price Optimal order quantity Conditions
$w_{NG}^* = \frac{1}{2}\left[ {c + \left( {1 - \theta } \right)p + \theta v} \right]$ $q_{NG}^* = \frac{{b\left[ {\left( {1 - \theta } \right)p + \theta v - c} \right]}}{{2\left( {1 - \theta } \right)\left( {p - v} \right)}}$ --
$w_{RG}^* = \frac{1}{2}\left[ {c + \left( {1 - \beta - m\alpha \beta + \alpha \beta } \right)p} \right]$ $q_{RG}^* = \frac{{b\left( {1 - \theta } \right)\left[ {\left( {1 - \beta - m\alpha \beta + \alpha \beta } \right)p - c} \right]}}{{2\left( {1 -\beta- m\alpha \beta + \alpha \beta } \right)p - v}}$ $\left( {1 - \beta - m\alpha \beta + \alpha \beta } \right)p - v \ge 0$
$w_{SG}^* = \frac{1}{2}\left[ {c + \left( {1 - m\alpha \beta } \right)p} \right]$ $q_{SG}^* = \frac{{b\left( {1 - \theta } \right)\left[ {\left( {1 - m\alpha \beta } \right)p - c} \right]}}{{2\left( {1 - m\alpha \beta } \right)p - v}}$ $\left( {1 - m\alpha \beta } \right)p - v \ge 0$
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