سود دهی برنامه های پاداش وفاداری: بررسی تحلیلی

Loyalty programs, as a prevalent CRM strategy, aim to enhance customers’ loyalty and thereby increase a firm’s long-term profitability. Recent analytical and empirical studies demonstrate inconsistent findings on the efficacy of loyalty programs in fulfilling these goals. In this study, an analytical model is developed to analyze the effect of customers’ valuation and their post-purchase satisfaction level on a loyalty program’s profitability. The results reveal how customers’ satisfaction plays a significant role in profitability of loyalty programs. We consider a profit-maximizing firm selling a good or service through two periods. Valuation is modeled as a deterministic parameter, as well as a stochastic variable with two arbitrary distributions. Depending on the customers’ valuation distribution, the model results in either a linear or a nonlinear optimization problem. Optimization problems are solved analytically, in terms of the model parameters. The obtained solutions provide some useful insights into the effects of customers’ satisfaction on the profitability of loyalty programs. Specifically, it is shown that depending on the customers’ satisfaction level, it may be optimal not to offer a loyalty reward.

Loyalty programs are structured marketing efforts [1] that aim to enhance customers’ loyalty by rewarding their repeat purchase behavior. Since loyalty buying behavior is thought to be of benefit to the firm [1], [2], [3] and [4], loyalty reward programs are presumed to increase a firm’s long-term profitability. Since the time American Airlines lunched AAdvantage, the first contemporary loyalty program [5], loyalty programs have proliferated in various industries and markets [6] and [7]. Customers’ participation in such programs, on the other hand, has also substantially increased over the past decade [8], [9] and [10]. Despite the ubiquity of loyalty programs, researchers have not yet achieved consensus on whether these programs actually work [11], [12] and [13]. In other words, it is not apparent that loyalty programs are able to influence the established buying pattern of customers and increase a firm’s profitability. While empirical studies show contradictory findings on the effectiveness of loyalty programs [5], [12] and [14], there are only a few analytical studies on this important marketing field. This fact is evident from Kim et al. [15] (the first published analytical study on loyalty programs), who view their work “as an initial step, and clearly far removed from the ideal model in which the implications directly translate into managerial practice”. Loyalty programs, by offering rewards based on cumulative buying, create switching costs for customers. Thus, literature on the effects of switching cost is also relevant to our work. The effect of switching cost on the market competitiveness was first studied by Von Weizsacker [16]. Using a Hotelling model, Von Weizsacker [16] shows that the price sensitivity of customers and market competitiveness rise with the switching cost. These findings, however, depend on the underlying assumptions that firms are committed to maintaining the same price over time, and also customers randomly change their preferences for the competing goods within a market. However, by relaxing the constancy of price assumption and adding a segment of customers with fixed preferences over time, Klemperer [17] shows that the market may be less competitive than a market with no switching costs. Furthermore, Klemperer [17] concludes that the effect of switching cost on a firms’ profitability, similar to market competiveness, depends on the size of the segment with constant preference. Namely, firms may be either better off or worse off with switching costs than without them, depending on the proportion of customers whose preferences remain constant over time. In contrast to Von Weizsacker [16] and Klemperer [17], [18], [19] and [20], who take the switching costs as exogenous, Caminal and Matutes [21] treat them as endogenous. In essence, switching costs created by loyalty programs are endogenous because firms directly decide upon the amount of reward. Hence, we incorporate the amount of loyalty reward as a decision variable in our model, which distinguishes this study from those of Von Weizsacker [16] and Klemperer [17], [18], [19] and [20]. This paper builds on previous analytical studies on loyalty programs’ profitability, notably Kim et al. [15] and Singh et al. [13], by treating customers’ valuation as a random variable. In fact, except for Kopalle and Neslin [22], we are unaware of any other study that has considered valuation in the context of loyalty programs. Kopalle and Neslin [22], using numerical simulation, examine the viability of loyalty programs in a strategic competitive game by incorporating customers’ valuation as a logistically distributed random variable. Other previous studies on loyalty programs have either not incorporated the valuation as a factor in customers’ decision making (e.g., [13]) or have assumed that the valuation is sufficiently high that it exceeds the product price (e.g., [15]). Similarly, to the best of our knowledge, none of the studies on the switching cost includes a stochastic valuation. For instance, Klemperer [17], [18], [19] and [20] incorporates valuation as a parameter. Caminal and Matutes [21], who study the endogenous switching cost, assume that customers’ valuation is higher than the offered prices. Farrel and Shappiro [23] assume that buyers’ valuation is so high that it is not binding and state that their results are affected if the valuation binds. In this paper, however, we incorporate the valuation both as a deterministic and as a stochastic variable. Moreover, we study the impact of customers’ satisfaction with their past purchases on the profitability of loyalty programs. In the previous studies on loyalty programs, the customers’ purchase experience is not considered as a factor in their decision to buy. In other words, it is presumed that, no matter whether they are satisfied or dissatisfied with their past purchase, customers return to the firm with either the same valuation or a valuation independent from their past valuations. For instance, Kopalle and Neslin [22] assume that a customer’s valuation in each period is a random draw from the logistic distribution. This implies the assumption that a customer’s valuation changes independently from his/her previous valuations. In contrast to this underlying assumption, empirical studies have found that satisfied and dissatisfied customers perceive loyalty programs in different ways [24]. Moreover, based on the expectation disconfirmation theory (EDT) proposed by Oliver [25], customers’ satisfaction with the actual product or service experience is the primary determinant of their post-purchase intentions [26]. Au et al. [27] also state that customer satisfaction results in repeat business and increases the firm’s profitability. Likewise, Nie [28] posits that customer dissatisfaction hurts repeat business and, as a result, jeopardizes the company’s long-term profitability. Thus, the customer satisfaction level is an important factor that may affect the effectiveness of a loyalty program in driving repeat purchase behavior and increasing the firm’s profitability [29]. As pointed out earlier, some studies on switching costs allow for customers to randomly change their preferences over time. For instance, Klemperer [17] assumes that a fraction of customers change their position on the Hotelling line. Since, customers’ taste for the product is represented by their position on the line segment, the shift in a buyer’s position can be interpreted as his/her satisfaction level. However, in these studies, customers’ locations change randomly and independently from their location in the previous periods. As a result, the spatial distribution of customers in the market will not change in favor of a specific firm in a subsequent period. Thus, none of the firms realizes a change in the market share and profits that stem from the shift in preferences. In contrast, we incorporate the satisfaction level as a parameter in our model that can take on any value. In a Hotelling framework, this would imply that the customers’ distribution might become asymmetric, depending upon the firms’ relative performance in driving customer satisfaction in previous periods. In summary, we contribute to the existing literature on loyalty programs by incorporating a stochastic valuation and by analyzing the effects of customers’ satisfaction levels on the profitability of loyalty programs. A unique feature of our study is that the models are solved analytically. The objective of the model is to maximize the firm’s profit in term of its decision variables. Assuming a deterministic valuation, the optimization problem turns out to be linear programming. Stochastic valuation, on the other hand, results in nonlinear programming. The models consist of two parameters, and despite their complexities, the analytical optimal solutions are found in terms of the parameters. Structural properties of the optimal solutions yield valuable insight into the profitability of loyalty programs. The rest of this paper is structured as follows. The model formulation and its underlying assumptions are described in Section 2. Section 3 focuses on solving the model under three different valuation distributions. In Section 4, we extend the model to a case where customers’ anticipated change in their future valuation is taken into account. The obtained results are discussed in Section 5. We conclude in Section 6 with a summary of the findings and some directions for future research.

In this paper, we developed an analytical model to evaluate the effect of customers’ satisfaction on the loyalty programs’ profitability. The objective of the model is to maximize the profit of a firm selling a good or service through two periods in terms of its decision variables, that is, offered prices in each period and loyalty reward value. In fact, the firm pre-commits to the first and second period prices and loyalty reward. Customers who repeat their purchase in the second period earn the loyalty reward in the form of an absolute value. However, it can be seen that using a percent discount for reward will not affect our findings. One of the distinctive aspects of our model is that the satisfaction/dissatisfaction level is incorporated as a factor in the customers’ decision to buy. The satisfaction/dissatisfaction level is modeled as a parameter, δδ, which is added to/subtracted from customers’ valuation in the first period to form their valuation in the second period. Another factor in forming customers’ decision is their probability of repatronizing the firm in the second period. This is also modeled as a parameter, γγ. The conclusions are drawn based on how these two parameters affect optimal settings of the loyalty program. Optimal values of the firm’s decision variables were found under three different valuation settings: uniformly distributed, normally distributed and deterministic valuation. For the uniform and normal cases, we came up with nonlinear models. Despite the complexity of the models, especially for the normal valuation case, analytical solutions were derived in terms of the parameters. For deterministic valuation, a linear programming was obtained which was also solved in terms of γγ and δδ. It was observed that regardless of the valuation distribution, the optimal solutions follow the same structure. We also investigated the effect of customers’ anticipation of their future valuation on the results. It was observed that inclusion of foreseen future valuation would not affect the framework of results. Based on the obtained optimal solutions, we established the relationship between customers’ satisfaction level and profitability of loyalty programs. It was proved that if the firm manages to maintain satisfaction among customers, not offering a loyalty reward is optimal from the profitability perspective. However, if the firm decides not to implement loyalty program and customers experience dissatisfaction with their purchase in early periods, the firm will obtain suboptimal profits. It was also seen that by offering a loyalty reward, the firm must increase the first period price proportional to the reward value and to the degree to which customers intend to return in the second period. Here, we treated customers’ satisfaction level as an exogenous factor. One direction for future research is to endogenize the satisfaction level by making it a function of some endogenous variables. Such a model would provide a framework that enables a firm to balance the trade-off between investing in loyalty reward programs and implementing customer satisfaction programs. In this paper, by allowing a customer not to buy from the firm, we implicitly assumed that there are other sellers in the market that will meet the customer’s demand. However, the effect of other seller’s actions was not considered in the firm’s pricing decisions. Thus, the model can be extended by explicitly incorporating competition.