جایگزین کارت هدیه رایگان برای تخفیف قیمت در مساله پسر روزنامه فروش

In this paper, we develop a newsvendor model in which the retailer gives “free” gift cards to consumers who purchase a regularly priced product at the end of the selling season instead of discounting the product. The model is developed for a market with patient consumers. We derive the sufficient optimality condition for the retailer's stocking level in the first period and the optimal gift card value in the second period. We also investigate the conditions under which giving gift cards results in higher expected profits than discounting the product. We find that five factors determine the effectiveness of gift cards. The first three factors are consumers' valuation per $1 of gift card, gift card redemption rates, and the average gross margin of the retailer. The last two factors are the degree to which consumers use gift cards to pay for products which they would have purchased from the retailer in the future with cash, and the additional spending above the gift card value consumers make when they redeem the card. The last two factors have a strong interaction. We also find that gift cards can be profitable when patient consumers consistently value each $1 by their redemption probability, even with 100% redemption. Numerical analysis shows that in the presence of patient consumers, increases in the redemption rate may lead to an increase in the expected profit. Similar counter-intuitive behavior of the expected profit occurs with changes in other problem parameters. The analysis also shows that gift cards' profit advantage over discounting increases with the variability of demand. The analysis also indicates that gift cards are most effective for low to medium priced products sold by high margin retailers.

Recently, Cachon and Swinney [8] contributed to our understanding of the effect of strategic consumers on inventory and pricing policy of retailers and on their profits. In their model, strategic or rational consumers decide between purchasing the product at the regular price or waiting to purchase later, if the product is available, at a discounted but uncertain price depending on which action maximizes their expected gain. The effect of strategic consumers on retailer pricing and profitability has been the focus of much recent research. Levin et al. [22] distinguished strategic consumers from others by their awareness that pricing is dynamic and by timing their purchases accordingly. Strategic consumers are patient and can weigh the benefit of delaying purchases [5]. Cachon and Swinney [8] concluded from their model that in the presence of strategic consumers it is optimal for the retailer to order a smaller quantity and she will have a lower expected profit than if there are no strategic consumers. Retailers can use promotions such as “free” gift cards with the purchase of a product instead of discounting the product at the end of the period. Fig. 1 shows three examples of gift cards given free with the purchase of products by large retailers. Gift cards have several advantages for the retailer. When used as a promotional tool, they are not directly linked to a product and, therefore, do not create a perception of reduced value of the product like direct discounts and coupons [11]. The second advantage of gift cards is that they can be given by the recipient to another consumer, and thus have the potential to expand a retailer's consumer base. A third advantage of gift cards is that some consumers may redeem only part of the cards' full value and others may not use the card at all. Reasons for partial or no redemption include loss of cards, expiration of cards, and consumers' relocation. We refer to this partial redemption as slippage. Horne [17] estimates the slippage rate of the cards that go unredeemed nine month after issuance is 19%. This 19% slippage rate is for gift cards which consumers buy and use as gifts. A fourth advantage of gift cards is that consumers redeeming gift cards may spend more than the value of the gift card, creating additional sales. In a survey of more than 500 U.S. consumers conducted by Accenture [1], 45% of respondents said they spend more than the value of the gift card when they redeem it. One estimate of the average spending of consumers beyond the card value when redeeming cards is about 20% of card value [30]. Finally, when gift cards are redeemed, the retailer incurs only the cost of the goods sold with the card rather than the full face value of the card. The last two benefits are realized by the retailer when consumers use gift cards to make purchases they would not have made at the retailer in the future with cash. On the other hand, if purchases made with gift cards result in a reduction in future purchases that would have been made at the retailer with cash, then the last two benefits may altogether vanish.

We developed a model in which the retailer offers a “free” gift card along with a regularly priced product at the end of the selling season. We followed the model framework developed by Cachon and Swinney [8] and developed the sufficient optimality condition for the order quantity. We also compared the performance of the “free” gift card strategy with that of the discounting strategy. We found that under certain conditions, the gift card strategy can be a viable alternative to a discounting strategy for retailers facing patient consumers. Numerical analysis shows that in the presence of patient consumers, the expected profit function may exhibit a counter-intuitive behavior. For example, increases in the redemption rate in some range may lead to an increase in the expected profit. Also, the expected profit may decrease with increases in consumer spending beyond gift card value at redemption and decreases in future cash sales offset. This is because when these changes in problem parameters occur the retailer decreases (increases) the order quantity which decreases (increases) patient consumers' probability of finding a unit available in the second period, thus more (less) consumers buy the product in the first period. If patient consumers are consistent in the sense of valuing each $1 by the probability of redeeming it, offering gift cards can still be more profitable than discounting. The most important factor to this profitability is that sufficient number of consumers use the gift cards to buy something they would not normally buy from the retailer. When such is the case, this gift card profit advantage is larger for retailers with high average margins and more consumers spending beyond the cards' value. Gift cards' profit advantage over discounting increases with the variability of demand. Using gift cards can mitigate the risk of overstocking and, hence, the retailer orders a larger quantity relative to discounting as the demand variability increases. Gift cards are not always a good alternative to discounting. When the product price is high, the retailer has to offer a high value gift card when the realized demand is small. As a result, consumers are more likely to redeem their gift cards while their marginal valuation of gift cards is likely to be small. Our results indicate that for high price products, the retailer is better off by discounting the product instead of using gift cards. In addition, gift cards are more likely to result in lower expected profit when consumers are present-biased. Some extensions to our models are possible. One interesting extension would be incorporating a different behavior for bargain hunters from patient consumers. For example, the redemption rate and valuation for gift cards may be different for bargain hunters and patient consumers. Incorporating different redemption rates for bargain hunters and patient consumers would require modeling the arrival process of consumers when a large value gift card is offered. Demand for leftover inventory with a large value gift card can be assumed to form a queue of both types of consumers with a parameter which represents the proportion of each type of demand in the queue.