THE OPTIMAL REWARD PROGRAMS STRUCTURAL Elements: DESIGNING and ANALYSIS

THE OPTIMAL REWARD PROGRAMS STRUCTURAL elements: DESIGNING AND ANALYSIS

Abstract

In this paper, a method is employed for designing and analyzing the optimal reward programs structural elements in a dynamic environment where customers maximize utility and the firm maximizes CLV, and the model is applied to customer data from a supermarket, it summarizes the results of the model that it is valid and feasible for these types of customers. The method gives the optimal mixed marketing strategies according to the customer’s states. It is presented that appropriate reward program is good at improving firm’s profits and relaxing the price competition. The reward threshold should be higher than the customer’s average purchase. Reward rate should be adjusted in the same way as reward threshold. The right program time horizon is about one year. It’s better not to mail to customers with higher frequency and save the money to the customers who don’t buy frequently. It is not necessary to discount either at the beginning or ending of the reward programs. However, It is necessary to depreciate to low purchasing frequency customers in the mid of program time horizon.

Keywords:optimal reward programs, dynamic customer relationship management, customer utility; customer lifetime value

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1. Introduction

Reward programs, also known as “loyalty programs” or “loyalty schemes”, offer are incentives to consumers on the basis of cumulative purchases of a given product or service from a firm (Kim, et al. 2001), which have become significantcomponents of marketing strategy for many organizations (Kopalle Praveen and Scott Neslin, 2003) and increasingly common tools in the marketing arsenal (Lewis Michael V., 2001). While the specifics of the programs differ, the common theme is that frequency reward programs provide the customer with benefit for repeat purchasing the brand (Kopalle Praveen and Scott Neslin, 2003). Reward programs have been established elements of customer relationship management for firms in industries such as airlines, hotels, and rental cars for many years and are now growing in popularity in non-travel related industries such as gaming, financial services, and retailing (Deighton 2000,Barlow 1999).

The critical problem of implementing reward programs is how to design the structural elements of reward programs in a dynamic environment where customers maximize the utility and the firm maximizes the CLV over an extended time period. The academic literature focusing on customer response to loyalty programs, while limited, has begun to grow over the last few years (Kim 2001, Kopalle 2003, Lewis 2001, Deighton 2000,Barlow 1999, Klemperer 1987, O’Brien 1995). O’Brien and Jones (1995) suggest that two of the major factors that customers consider when evaluating programs are the relative value of redemption rewards and the likelihood of achieving a reward. Kim, Shi and Srinivasan (2001) use a game theoretic model to study what type of reward programs, i.e., reward type (what to offer)and reward amount (how much to offer), firms should select. They found thatin most cases, firms andthe heavy users often stand to gainmore from the reward programand are better off at the expense of light users. Sharp and Sharp (1997) analyze individual level data from an Australian program called fly buys using a one period switching model of repeat purchasing to examine the program’s ability to alter normal market repeat purchase behavior. Unfortunately, the study results are relatively inconclusive. In contrast, Dreze and Hoch (1998) report the results of a live test of a category specific loyalty program that produced a positive result. They find that the use of a category specific program resulted in increase for both the specific category and for total store traffic.

Research that employs models that more accurately replicate the dynamics of consumer response is needed to accurately judge the effectiveness of loyalty programs. Lewis Michael V.suggests structural elements that determine the expected value of participation are the value of rewards, reward thresholds and program time horizon. The relative value of the reward involves the cash value of the rewards. Reward thresholds are the levels of cumulative purchasing or other requirements that must be met to earn an award. The program time horizon is any time constraint that defines the period in which cumulative purchases are counted.

There are relative few scholars concentrating their attention on designing the three structure elements of the reward programs. The purpose of this paper is to develop a DCRM model with reward programs by modifying the loyalty programs model and taking the reward rate, reward threshold, program time horizon and mixed marketing strategies as the main variables into the model. Moreover, maximizing the customer utility and the CLV are also considered into the model. The optimal structural elements of reward programs and the effective mixed marketing strategies can be calculated from the model according to different customer data sets.

The empirical section uses individual level customer data from a supermarket. The analysis utilizes a research methodology known as estimable structural dynamic programming or discrete choice dynamic programming. It is presented that appropriate reward program is good at improving firm’s profits and relax the price competition. The reward threshold should be higher than the customer’s average purchase. Reward rate should be adjusted same direction as reward threshold. The right program time horizon is about one year. It’s better not mail to customers with higher frequent and save the money to the customers who don’t buy frequently. It is not necessary to discount either at the beginning or ending of the reward programs. However, It is necessary to depreciate to low purchasing frequency customers in the mid of program time horizon.

In the rest of the paper, Section 2 present the dynamic customer relationship management model. Section 3 describes the data used in this paper and presents the results of estimation andempirical application. Section 4 concluded with a summary.

1. The Dynamic Customer Relation- ship Management model

2.1Qualitative Description of Key Components of the Model

What we consider is a monopoly market where there is only one seller. In each time period the seller decides whether to implement mixed marketing strategies (for example mail information on goods, pricing and reward programs et al.) to each of its customers on the long-term customer list. In each time period a customer decides whether to respond in the form of a purchase. The mixed marketing strategies and the customer response interaction are repeated every period in this manner, and form one multiple repeat game scheme. Under the hypothesis of purchase decision is the function of current customer states and firm’s policies, the customer’s states sequence forms Markov chain, the customer’s decision named as the system’s transport probability is a stochastic variable, The firm can control the Markov chain’s evolvement, so we can model customer relationship management (CRM)as a Markov Decision Process (MDP) (Lewis Michael V., 2001).

In this modeling approach, customers areclassified into states based upon observed transaction histories and marketing policiesare selected in order to optimallycontrol transitions between customer classifications orstates.Assuming that the firm can affect the transition ratesbetween states through the mixed marketing strategies, a combination of stochastic game theory and estimable structural dynamic programming maybeused to optimize the firm's customer managementpolicies and reward programs’ structure.

2.2Customer’s Utility Model and Value Function

2.2.1 Customer’s Utility Model

The main challenge of modeling customer utility with reward programs is how to consider the three structural elements such as R, TH and T. We can use the suggestion of O’Brienes and Jones (1995)，that takes two of the major factors which are the relative value of redemption rewards and the likelihood of achieving a reward as the criterion customer whether participate in the programs. We hypothesize that the reward programs begin on 1st Jan. and end on 31st Dec. Time period is a month to suit the nature of reward programs. So the customer’s utility model is:

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（1）

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Where pit is the change rate of the customer i’s price at period t (Pt) comparing to the primary price (P0). The pit can be formulated as:

（2）

Fit=R*Msit is the total effect of R and cumulative purchase to customer utility when the customer gets the reward, where Msit is the discrete level of customer ’s cumulative purchase till period t, the level’s number of the Msit can determine by the character of the database. Ritis the likelihood of achieving a reward, which can be formulated as Equation (3),

Where A is the discrete level of customer’s average monetary value (Av) per year, the definition and scheme

（3）

of state transfer of r and f can be seen in the study of LI Chunqing et al. (2003), Mit’s definition can be formulated as Equation (4).

In Equation (1), we normalize the utility of not buying from the firm in a single period to zero, as the first part in the equation. In the range of the program time horizon, the utility is expressed as the second part. If the customer makes a purchase after the ended program time horizon but in one year, the utility is expressed as the third part, it is the same as the utility of without reward programs. εitk1 andεitk2 are the

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（4）

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unobserved random terms. The relation of customer’s utility and recency r or frequency f can see the study of LI Chunqing et al. (2003).

2.2.2 Customer’s Value Function

The value function of customer iat time t is:

(5)

(6)

Where,

is Euler’s constant (its value is 0.57721, see Rust John(1987), p1012), and where an upper bar indicates the deterministic part of the value functions. The choice probabilities achieve the following convenient formulation:

(7)

The evolution of Equations (5) to (7) can be seen in the study of Gonul et al. (1998).

2.3 The Firm’s Profit Function and the Optimal Reward Structural Elements and Mixed Marketing Strategies

In this section, we model the firm’s profit maximization problem. The current period profit of customer i at time t is:

（8）

Where Akis the average amount of buying corresponding to the customer’s monetary value at level k, and Csis service cost per purchase, Cmis the mail cost to customer, Cris the reward cost of the firm, Dit(mit,pit,TH,R,T) is the firm’s decision space, and where mitis the firm’s mailing decision to customer i at time t, that is,

(9)

and r1 is gross profit rate when the firm adopts the marked price , it can be formulated as,

（10）

Wherer0 is gross profit rate when the firm adopts the original price P0, C is the cost price. So the maximum profit which is contributedfrom customer i during time t to the future is:

（11）

We can determine the optimal structural elements of the reward programs and mixed marketing strategies by combination of the stochastic game theory and estimable structural dynamic programming.

1. Model Estimation and Empirical Application

3.1 Data Description

Our data set consists of the purchase histories of 3000 long-term customers who take part in the reward programs of one supermarket. The reward programs are implemented in January 2002, the detailis as follows: a customer can participate in the reward programs as long as his/her once purchase value is beyond the limit of RMB 100 Yuan; if his/her cumulative purchase level is beyond RMB 4000 Yuan by the end of 2002, he/she can achieve a reward of coupon which value is 1% of the total purchasing value, the customer acquires the coupon by reward programs card during 25th to 31st December, then the record of the card is reset to zero and a new reward program will begin at the next January. The sample characteristics aresummarized in Table 1.

3.2 Likelihood Function and Estimation Issues

The log-likelihood function for customer iin period t is:

(15)

The sample log-likelihood function is,

(16)

Wherei is the number of customers and the period [bi,Bi] is the interval during which individual i is observed. The maximum likelihood estimation routine searches for the optimum over the parameter space by changing parameter values, the detail algorithm is similar to LI Chunqing et al. (2003), in this example, we can obtain the solution after the program runs 4053 steps.

To compare with the dynamic model, we estimate a single period model (δc=0). Akaike information

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Table 1 Summary Statistics

Note: Number of customers in the sample is 3 000.Total number of records observed is 36 000.

Table 2 Estimate Result from Single-Period and Dynamic Models

Note: Significance at 0.01 level is denoted by (***), at 0.05 level (**) and at 0.1 level by (*).The asymptotic normal statistics are placed in parentheses.

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Criterion (AIC) and Bayesian information Criterion (BIC) are used to estimate the statistical fit of the model. In addition, the discount factor is adjusted as a parameter, which can ensure the value of discount factor corresponding to the characteristics of the database, the value is 0.64 so that customers discount the future utility at 56% per month. The results of the model are presented in Table 2.

It can be concluded from the Table 2 that the dynamic models perform better than the single-period models according to AIC and BIC index.

3.3 The Optimal Structural Elements of Reward Programs and Marketing Mixed Strategies

The optimal structural elements of reward programs, mailing and pricing policies in every period during the time horizon can be got by maximizing the CLV function. The optimal structural elements of reward programs are: TH=5500，R=0.08，T=12. Among the mixed marketing strategies, the optimal mailing policy mit* and pricing policy pit* corresponding to different customer state are presented in Table 3.(Only some examples are given because there are too many to list all (the total state are 2005).).

The comparison of the profit of firm at different mixed marketing strategies is presented in Table 4.

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Table 3 The optimal mailing and pricing policy with reward programs at different customer state

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Table 4 The comparison of the profit of firm at different mixed marketing strategies

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It can be concluded from Table 4 that the reward programs the supermarket adopts are not ideal ones. Because its reward rate is only 1%, the reward programs do not promote the customers’ more purchasing obviously. Moreover, the reward threshold is too low which is exactly equal to the customer average purchasing amount per year, the customers can get the reward if he/she purchase as usual, so the reward program does not work as it is expected but add the cost and reduce the profit of the firm.

1. Conclusions

It is presented that appropriate reward program is good at improving firm’s profits and relax the price competition. The reward threshold should be higher than the customer’s average purchase. Reward rate should be adjusted same direction as reward threshold. The right program time horizon is about one year. It’s better not mail to customers with higher frequent and save the money to the customers who don’t buy frequently. It is not necessary to discount either at the beginning or ending of the reward programs. However, It is necessary to depreciate to low purchasing frequency customers in the mid of program time horizon.

aCkNOWLEDGeMENTS：

This research is supported by NSFC(70121001, 10371094) , the Scientific and Technology Department of Shaanxi Province (02G11,03G07)and the Education Department (02JK009, 03JK176) of Shaanxi Province.

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