COPING WITH REVENUE RECOGNITION IN THE LOYALTY REWARD PROGRAMS INDUSTRY: A STOCHASTIC MODELING APPROACH

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1 AMERICAN CONFERENCE ON APPLIED MATHEMATICS (MATH '08), Harvard, Massachuses, USA, March 24-26, 2008 COPING WITH REVENUE RECOGNITION IN THE LOYALTY REWARD PROGRAMS INDUSTRY A STOCHASTIC MODELING APPROACH MOUSTAPHA DIABY School of Business Adminisraion Universiy of Connecicu Sorrs, CT U.S.A mousapha.diaby@business.uconn.edu AARON L. NSAKANDA Spro School of Business Carleon Universiy 25 Colonel By drive, Oawa, Onario, Canada, KS 5B6 aaron_nsaanda@carleon.ca Absrac - In his paper, we propose a quaniaive mehodology for deermining he breaage rae in a Loyaly Reward Program (LRP). The proposed mehodology is a simulaion-based approach in which he accumulaion and redempion of poins is modeled as a sochasic process. An illusraive example is discussed. Key-Words Loyaly Reward Programs, Simulaion, Marovian Processes, Sysem Dynamics Inroducion Loyaly reward programs (LRPs) are mareing programs aimed a rewarding cusomers for using a produc or service. Consumers in hese programs are given incenives or rewards for repea business. These rewards in urn, serve as moivaions for consumers o coninue buying a produc or service []. Alhough differen ypes of LRPs exis in he lieraure, mos of he modern LRPs have heir roos in AAdvanage, he firs frequen flyer program inroduced by American Airlines in 98 [2]. Such programs involve a a minimum, a promoional currency (e.g., poins, or miles); he use of reward iers (eiher based on spending or accoun balance); a comprehensive cusomer daabase of individual consumer demographics, and deailed ransacion informaion. They also involve an exensive use of advanced echnology and sophisicaed sysems o operae he conac ceners, manage and analyze he member daabase, or redeem rewards (direcly or hrough he Inerne). Many such LRPs exis oday across a specrum of indusries (ravel, hoel, reail, elecommunicaion, baning, ec.). New LRPs coninue o be esablished worldwide, and exising ones coninue o be resrucured in order o increase heir conribuions o value growh. A number of LRP s have expanded in scope wih new parners, producs, or services over he years. This paper deals wih LRPs ha are profi ceners and offer one ype of reward from one main indusry (single produc srucure) raher han muliple ype of rewards from many indusries (muliple produc srucure). The currency used in such LRPs is generically referred o as poins. Based on some specified scheme, cusomers are awarded poins on heir purchases of producs or services. These poins, accumulaed in cusomer accouns, can be redeemed by cusomers based on a reward char pre-esablished by he firm ha owns he LRP. Basically, in his ype of LRP, cusomers become members, earn poins when hey buy a produc or service from one of he LRP firm s commercial parners, and are awarded a preesablished produc or service when hey decide o redeem hose poins. When a member decides o redeem poins, he LRP firm purchases he pre-deermined produc or service from is commercial parners in order o award i o he member. Hence, for a profi cener LRP, revenue is generaed a he ime a member earns poins, and cos is incurred a he ime a member redeems poins. One problem faced by a profi cener LRP firm is ha of revenue recogniion for accouning purposes and he esablishmen of ISSN ISBN

2 AMERICAN CONFERENCE ON APPLIED MATHEMATICS (MATH '08), Harvard, Massachuses, USA, March 24-26, 2008 financial saemens. The LRP company derives is revenue primarily from he sale of poins o commercial parners (gross billings) and incurs is main operaing coss when poins are redeemed. A ey characerisic of is business, herefore, is ha he gross proceeds received a he ime of sales of poins can be recognized as revenue for generally acceped accouning principles (GAAP) only when members redeem poins. In realiy, however, a percenage of he poins (called he breaage facor or breaage rae in he LRP indusry) accumulaed each year end up no being redeemed by members, and hese should, herefore, be recognized as revenue in he esablishmen of he periodical financial saemens. A higher breaage rae will conribue o increasing he ne income and profiabiliy on he financial saemens. This in urn, would offer a compeiive advanage o a firm in aracing and pricing new hird pary parners, developing company sraegic plans, and managing he overall yearly reward capaciy. Because of his, he breaage rae is a criical componen ha is exposed o inense scruiny from many sources (audiors, invesors, corporae finance, ec.). As far as we now, despie he criical imporance of he breaage rae for LRPs, he academic lieraure has no addressed he problem of how o assess i. The purpose of his sudy is o propose a quaniaive mehodology for deermining he breaage rae for LRPs. The proposed mehodology is a simulaion-based approach in which he accumulaion and redempion of poins in an LRP is modeled as a sochasic process. A numerical example is discussed. The plan of he paper is as follows. We presen a brief lieraure review in Secion 2. The overview of he modeling is discussed in secion 3. The proposed soluion mehodology is described in Secion 4. An illusraive example is discussed in Secion 5. Finally, conclusions are presened in Secion 6. 2 Lieraure Review Several papers have been published on various aspecs of LRPs. The majoriy of he exising papers are from he Mareing and he Economic lieraures, respecively. One se of papers are focused on offering insighs ino issues such as undersanding and designing LRPs [2-3], he effeciveness and profiabiliy of LRPs [4-5], he managemen of he LRP firm s excess capaciy [6], he impac of LRPs on repea-purchase paerns [7], and he fairness of LRPs for cusomers [8]. Anoher par of he lieraure focuses on he need o gain cusomer insighs hrough he analysis of he cliens purchases and personal informaion accumulaed in he LRP daabases, he argeing of seleced promising cusomers, he cusomizaion of mareing campaigns in erms of prices or promoions issues, ec. As far as we now, none of he publicaions found in he lieraure has addressed he problem of deermining he breaage rae, a criical componen for revenue recogniion in he loyaly programs indusry. 3 Overview of he Modeling As discussed in secion 2 of his paper, according o he generally-acceped accouning principles, for a profi cener LRP company, accumulaed poins ha will never be redeemed can be considered as revenue on financial shees. The raio of hese never-o-be-redeemed poins o he oal volume (in poins) of a company is referred o as he breaage rae or he breaage facor. Hence, he revenue recogniion issue in he LRP indusry is direcly lined o he assessmen of he breaage rae. In pracice, his rae is deermined based on Indusry sandards. Tha is, a company ypically compares wha oher companies are using and ses is own breaage rae based on some simple merics, such as he average, he minimum, or he maximum). The rae used has a significan impac on company financial saemens. A higher breaage rae will conribue o increasing he ne income and profiabiliy on he financial saemens. This, in urn, would offer a compeiive advanage o a firm in aracing and pricing new hird-pary parners, developing company sraegic plans, and managing he overall yearly reward capaciy. The main mehodology in his paper is o consider he LRP as a dynamic sysem. ISSN ISBN

3 AMERICAN CONFERENCE ON APPLIED MATHEMATICS (MATH '08), Harvard, Massachuses, USA, March 24-26, 2008 Members in he sysem are classified ino ransacion groups based on a combinaion of heir yearly average accumulaion levels and heir yearly average redempion levels. Table provides an example of a sysem wih four ransacion groups. A member in Transacion Group S 2 illusraed in he able would have a yearly average ( poin ) accumulaion ha falls in he range of [, 499] and a yearly average ( poin ) redempion in a range of [500, 999]. The classificaion of a member in he ransacion groups is based on he analysis of he member s pas yearly accumulaion aciviies and pas yearly redempion aciviies. The specific limis for he redempion ranges can be done using he reward chars pre-esablished by he LRP firm. The limis for he accumulaion ranges could be quaniaively se using a Pareo analysis in which hree or more classes can be used. Table Illusraion of Transacion Groups Accumulaion range [min, max] [, 499 ] [ 500, 4999 ] [ 5000, ] Redempion range [min, max] [ 500, 999 ] [ 000, 3000 ] S 2 S 3 S 4 S 5 S 6 S 7 Over ime, members in a given LRP sysem migrae o oher ransacion groups. The reasons for his are ha a person s socio- economic and demographic siuaions usually change over ime. For insance, a person enrolled in he program as a suden will have a differen economic siuaion afer graduaing and joining he worforce. Anoher example would be a person who is single a he ime of enrolmen and evenually becomes married wih children. Therefore, he iner-ransacion groups migraions are a funcion of socio-economic and demographic characerisics such as age, gender, marial saus, educaion, profession, annual earnings, senioriy in he program, for example. Hence, in pracice, saisical analyses can be conduced o obain esimaes of he probabiliies of hese migraions. A member of he LRP program can become an inacive member if his/her accoun has no aciviy (neiher accumulaion nor redempion) over a number of consecuive periods. Upon becoming inacive, all of he ousanding accumulaed poins become forfeied for he member. Furhermore, afer becoming inacive a member revers bac o a non-member saus, if he/she remains inacive for an addiional number of consecuive periods. In addiion o hese, any person in he populaion a large who has never joined he LRP can be considered as a non-member. Hence, for modeling purposes, we define wo addiional, special ransacion groups one is he ransacion group of non-members. The oher is he ransacion group of inacive members. Hence, he problem of deermining he breaage rae reduces essenially, o ha of modeling he mechanisms of how people migrae beween he differen ransacion groups (including he non-members and he inacive members ransacion groups). To illusrae our modeling of he migraions beween ransacion groups, consider he sysem shown in Figure wih four ransacion groups (S i, i = 0,,2,3), where S o is he ransacion group of non-members; S is he ransacion group of inacive members; and S 2 and S 3, are ransacion groups of acive members. Migraion from S o o S is no possible, since one mus firs become a member before one can become an inacive member. Liewise, migraions from S 2 and S 3 o S 0 respecively, are no possible since a member canno become a non-member wihou becoming an inacive member firs. However, migraions from S can occur o any oher ransacion groups (including iself). All of he possible migraions are shown on he diagram. Figure Members Movemen Diagram TRANSACTION GROUPS S 0 S S 2 S 3 Noe ha he oal number of poins ha will never be redeemed over a given planning horizon is equal o he oal number poins ha become forfeied by members who become inacive over he planning horizon. Hence, he breaage rae can be defined as he raio of he oal number of hese forfeied poins o he oal number of poins ha are acquired (i.e., ISSN ISBN

4 AMERICAN CONFERENCE ON APPLIED MATHEMATICS (MATH '08), Harvard, Massachuses, USA, March 24-26, 2008 accumulaed ) over he horizon. Hence, if he ransacion groups are hough of as saes of naure in a Marov chain, and he probabiliies associaed wih he arcs illusraed in Figure are assumed o be ime-invarian, hen he process of he iner-group migraions can be modeled as a saionary Marovian process. The approach we use in his paper however, is a simulaion-based approach, as described in he nex secion. 4 Simulaion Model In developing our proposed simulaion model, we assume ha he migraions beween ransacion groups occur a discree imes and ha every ransiion aes one uni of ime. In addiion, we assume ha he migraions from (Transacion) Group S 0 (i.e., he non-member group) o any acive members ransacion groups follow a Poisson disribuion. This amouns essenially, o assuming ha he arrivals process from populaion a large ino he LRP sysem is Poisson disribued. Hence, he oal number of people ha ener he LRP sysem can be deermined for any specified (migraion) probabiliy can be readily compued using he esimaed average for ha number (and herefore, wihou having o have nowledge of he size of he populaion a large). To simplify he presenaion, we will henceforh refer o a ransacion group simply as a group. The noaion we use is as follows. J n oi y i p ij a r o number of groups; number of members from Group S o who migrae ino Group S i a he end of period ; oal number of members in Group S i a he end of he period ; probabiliy of migraion from Group S i o Group S j ; number of poins accumulaed (acquired) by Member during period ; oal number of poins redeemed by Member during period ; number of ousanding poins (i.e., he poins balance) in he accoun of Member a he end of period ; O ousanding poins in he accoun of member a he ime of becoming inacive; T number of periods in he planning horizon; A oal number of poins acquired by Member over he planning horizon. se of members in Group S Y i () i a he end of period ; Q() se of members wih inacive accouns a he end of period ; F() se of acive members in he sysem a he end of period. Using he noaion above, he following relaions can be derived (a) The number of members in Group S i a he end of period J y i = y j p ji + n oi () j = Relaion () sipulaes ha he number of members in Group S i a he end of comprises he number of members from Groups oher han S o who have migraed o ha ransacion group plus he number of members from he populaion a large (S o ), ha is new members who have enered he sysem ino Group S i. (b) The number of ousanding poins in Member s accoun a he end of period - o = o + a - r (2) Relaion (2) sipulaes ha he number of ousanding poins in a member s accoun a he end of period is equal o he number of poins available a he beginning of he period plus he number of accumulaed by Member during period, minus he number of redeemed poins by Member during period. ISSN ISBN

5 AMERICAN CONFERENCE ON APPLIED MATHEMATICS (MATH '08), Harvard, Massachuses, USA, March 24-26, 2008 (c) The breaage rae (θ) θ = O Q(T) A { Q(T) F(T) } (3) Relaion (3) sipules ha he breaage rae is he raio of he oal number of forfeied poins (when members become inacive) o he oal number of accumulaed poins over he planning horizon by all he members. The main seps of our simulaion approach for deermining he breaage rae can be summarized as follows (a) Iniialisaion o Se =0. o F(0) = curren se of acive of members in he sysem. o Y i (0) = curren se of members in Group S i. 0 o y i = Yi (0). 0 o o = number of ousanding poins in he accoun of Member, Y (0). i o Go o (b). (b) Main Seps for = o T do o Generae n oi from appropriae Poisson disribuions. o Compue y i using relaions (). o Updae Se Y i (). o Generae a and r from appropriae uniform disribuions, Y (). i o Compue o using relaion (2). o Updae Ses Q() and F(). enddo (c) Compue O, Q(T ) and A, { Q(T) F(T}. (d) Compue θ (Using relaion (3)). The implemenaion of he above algorihm requires a procedure for assigning exising members o Se Y i (). To ha end, one may use a heurisic approach, a random approach, or a linear programming formulaion of he problem. 5 Illusraive Example For he sae of illusraion and wihou loss of generaliy, le s consider a problem wih four ransacion groups as illusraed earlier in Figure (S o, S, S 2, S 3 ). Table 2 provides he probabiliy of ransiion of a member beween wo ransacion groups. Table 3 provides he informaion abou he saus of each acive member in he sysem a he beginning of he firs period of he planning horizon (i.e., a ime =0). The able shows for each member, he curren number of ousanding poins in he member s accoun ( o 0 ), and he (ransacion) group, S i, o which he member belonged a ime =0. Table 2 Marix of Transiion Probabiliy From Transacion Group S 0 S S 2 S 3 To Transacion Group S 0 S S 2 S 3 Toal ISSN ISBN

6 AMERICAN CONFERENCE ON APPLIED MATHEMATICS (MATH '08), Harvard, Massachuses, USA, March 24-26, 2008 Table 3 Curren Acive Members Saus Informaion Member Curren Ousanding Poins Curren Sae of Naure () 0 o (S i ) Therefore, from period =0 o period =, he applicaion of he main seps of he algorihm yields he oucomes summarized in he ables discussed below. Columns of Table 4 indicae he numbers of members ha migrae o he corresponding groups, respecively. Rows indicae he numbers of members ha migrae ou of he corresponding groups, respecively, excep for he enries in he las column. These are obained by muliplying he curren numbers of members by he corresponding probabiliies of migraion (rounded o he closes ineger). The number of new members coming ino Group S i from he populaion a large (i.e., n oi ) was generaed from a Poisson disribuion. These numbers are shown in he firs row of Table 4. Table 4 Aggregae informaion of members migraion (=) S 0 S S 2 S 3 S y i S 3 3 S 2 3 S y i Table 5 provides he saus informaion of each member in he sysem a he end of period =. The able shows for each member, he curren ransacion group, he randomly generaed accumulaion and redempion levels based on Table, and he number of ousanding poins in he member s accoun ( o ) as defined by he relaion (2). In Table 5 he specific members ha migrae o a given group S j from a given group S i are randomly seleced from he se of members of Group S i ( Y i () ) who mee he requiremens for being included in Group S j. Members # 3 o 33 are new in he sysem. Table 6 provides informaion similar o ha in Table 4, excep ha i perains o period 2. Similarly, Table 7 provides he same informaion as in Table 5 for period =2. The new members ha ener he sysem a he end of period are Members # 34 o Conclusions We have proposed a simulaion-based approach for deermining he breaage rae in LRPs, and provided a brief numerical illusraion of he proposed approach. We are currenly in he process of esing he approach using real-life daa. The mehodology can be expanded o accommodae more complex siuaions, such as when here are muliple producs for example, or when poins can be ransferred beween members. We are currenly exploring such developmens, as well as he Marovian ISSN ISBN

7 AMERICAN CONFERENCE ON APPLIED MATHEMATICS (MATH '08), Harvard, Massachuses, USA, March 24-26, 2008 approach briefly described in Secion 3 of his paper. Table 7 Acive Members Saus Informaion a he end of period =2 Table 5 Members Saus Informaion a he end of period = Member New Sae of Naure Accumulaion level Redempion Level Curren Ousanding Poins Member New Sae of Naure Accumulaion level Redempion Level Curren Ousanding Poins () (S i ) a r o () (S i ) a 2 2 r o Table 6 Aggregae informaion of members migraion (=2) S 0 S S 2 S 3 S S 4 4 S S y i y i ISSN ISBN

8 AMERICAN CONFERENCE ON APPLIED MATHEMATICS (MATH '08), Harvard, Massachuses, USA, March 24-26, 2008 References [] Keh, H. T. and Lee, Y. H. [2006]. Do reward programs build loyaly for services? The moderaing effec of saisfacion on ype and iming of rewards, Journal of Reailing 82(2), pp [2] Berman, B. [2006]. Developing an effecive cusomer loyaly program. California Managemen Review 49() [3] Kadar, M. and Koano, B. [200]. Designing loyaly programs o enhance value growh, Mercer on Transpor & Travel 8(2) pp [4] Suzui, Y. [2003]. Airline frequen flyer programs equiy and araciveness. Transporaion Research, Par E 39 pp [5] Kim, B. D., Shi, M., and Srinivasan, K. [200]. Reward Programs and Taci Collusion, Mareing Science 20(4) pp [6] Kim, B.D., Shi, M., and Srinivasan, K. [2004]. Managing capaciy hrough reward programs, Managemen Science 50(4) pp [7] Sharp, B. and Sharp, A. [997]. Loyaly programs and heir impac on repeapurchase loyaly paerns. Inernaional Journal of Research in Mareing 4 pp [8] Lacey, R. and Sneah, J. Z. [2006]. Cusomer loyaly programs are hey fair o consumers? Journal of Consumer Mareing 23(7) pp [9] Terui, N. and Dahana, W. D. [2006]. Price cusomizaion using price hresholds esimaed from scanner panel daa. Journal of Ineracive Mareing 20(3-4) pp [0]Ziliani C. [2006] Price Targe promoions how o measure and improve promoional effeciveness hrough individual cusomer informaion. Journal of Targeing, Measuremen and Analysis for Mareing 4(3) pp ISSN ISBN