Internatonal Journal of Mathematcal, Engneerng and Management Scences Modelng Mult-generaton Innovaton Adopton based on Conjont effect of Awareness Process Mohn Agarwal 1, Deept Aggrawal 2*, Adarsh Anand 1#, Ompal Sngh 1! 1 Department of Operatonal Research 2 Keshav Mahavdyalaya Unversty of Delh, Delh 110007, Inda 1 mohn15oct@gmal.com, deept.aggrawal@gmal.com, # adarsh.anand86@gmal.com,! drompalsngh1@gmal.com * Correspondng author (Receved October 1, 2016; Accepted December 13, 2016) Abstract The pror models n the feld of mult-generaton dffuson modelng bascally concentrated on employng effects of substtuton and swtchng behavor. But lttle or no mportance has been gven to the manner n whch nformaton about the product s dffused n the marketplace for eventual determnaton of ntergeneratonal sales. Sales generally happen when users are nformed about the characterstc features of the product. Thus, the effect of nformaton flow on adopton of the product s mportant for evaluatng eventual sales. Wth the am of nculcatng awareness and adopton process as two dfferent factors mpactng the overall sales; n ths paper we have developed a systematc approach to model the sales for ntergeneratonal dffuson process. The results are verfed on sales data from Semconductor Industry DRAM shpments. Keywords: Cross-generaton shftng; Innovaton-dffuson models; Intergeneratonal dffuson 1. Introducton Today successful frms are recognzed for ther nnovatve strateges and recurrng launches n terms of new product ntroductons. Frms seek to adopt new product ntroducton strategy to gan long-term fnancal success and to ncrease demand of the products. The major work on new product sales model s based on nnovaton-dffuson theory (Kapur et al., 2010; Sngh et al., 2012; Aggrawal et al., 2015). The topc dffuson process has been wdely studed by researchers from dfferent dscplnes. Dffuson s the process through whch a new dea or new product s accepted n the market (Anand et al., 2014b) whereas nnovatveness defnes the dfference among ndvduals n ther response to new product or deas and s also a measure to defne the earlness of an ndvdual n adoptng a product (Anand et al., 2014b). Eventually the aggregate adopton of all ndvdual n partcular tme horzon determnes the dffuson of a product. The dffuson theory has ganed attenton from the poneerng work done by F. M. Bass n1969 whch s consdered to be the most wdely used and extended model to present date. Tll now there have been extensve work to extend sngle generaton model to account for more realstc scenaros that persst n the market. Some researchers have extended the frst purchase sales model to nclude marketng mx varable (Mahajan and Wnd, 1985; Kalsh and Sen, 1986; Bass et al., 1994) Stages n the adopton process (e.g., Kalsh, 1985; Mdgley, 1976), supply restrctons (e.g., Ho et al., 2002; Jan et al., 1991), repeat and replacement purchases (Llen et al., 1981; Wnd and Sharma, 1983), Retaler adopton (e.g., Bronnenberg and Mahajan, 2001) and spatal dffuson (Garber et al., 2004); processes for nterpersonal communcaton (e.g., cellular automata, Garber et al., 2004; Goldenberg et al., 2002); cross-market communcaton (Goldenberg et al., 2002). 74
Internatonal Journal of Mathematcal, Engneerng and Management Scences The recent polcy adopted by companes s to keep rollng out new versons one after another, wth newer versons beng acquanted wth some addtonal functonalty. Generally frms do not delver ther complete product n one go but keep launchng new verson frequently to mantan ther compettve edge n the market. Majorty of examples can be quoted such as: famly of Apple's Pod and Phone; also famly of Mcrosoft Wndows and Offces and many more (Jang and Jan, 2012; Aggrawal et al., 2015). Brngng successve generatons help the frms n mprovng the qualty of the product n latter development cycles. It also helps n attanng qucker returns on ther nvestments and the mpact of market uncertantes. Successful products n the market are generally substtuted by newer generatons wth advanced features and functonaltes whch can create new markets and can lead to ncreased sales. Frst- purchase sales models were not capable n explanng the dffuson process for mult-generatonal product. Thus, there was the towerng need for predctng the sales behavor for mult-generatonal products. Several models startng wth Norton and Bass model (1987) for predctng how multple generatons of a product compete have been proposed. Followng Norton and Bass (1987), other researchers developed extensons and varatons to the Norton and Bass model to examne how the entry of new generaton cannbalzes the sales of exstng generatons n the market (Mahajan and Muller, 1996; Islam and Meade, 1997; Meade and Islam, 2006, Jang, 2010). Understandng of what are customers atttudes toward the product or servce? s a key concern for marketers. For knowng the percepton of ndvduals, frms need to advertse and promote ther product whch may generate a group of prospectve buyers who wth passage of tme may adopt the product. Therefore, t s wse to artculate that advertsng and promoton may act as ntegral part of our socal and economc systems. Small retalers to large mult-natonal companes are ncreasngly gettng dependent on advertsng and promoton to help them market products and servces. On the other hand, consumers are also dependent on promoton and other sources for nformaton, whch they can use n makng purchase decson. Thus, the need for means of advertsement cannot be gnored n recent tmes for buldng thought process of ndvduals. Workng on smlar grounds of, ncreased demand of studyng the mpact of awareness process on adopton process; researchers have worked on extendng sngle stage models to mult- stage nnovaton dffuson models (Van den Bulte and Llen, 2007; De. Bruyn and Llen, 2008; Anand et al., 2014a). Consderng ths very mnd set, we have come wth a proposal to study the mpact of mult-stage nature of adopton on nter-generatonal sales of product. Emprcal verfcatons of prevous studes show that mult-generaton dffuson models are applcable not only to technologcal products such as IBM manframe computers and moble phones, but also to non-technologcal products such as mlk contaners (Speece and MacLachlan, 1995). But ths study s only concentrated on studyng the mpact of hgh technology product. Massve amount of work has been done n the feld of dffuson theory accountng from sngle generaton of a product (Bass, 1969) to ts successve generatons (Norton and Bass, 1987). Also, from sngle stage to mult-stage nature of adopton process based on theoretcal structure gven by Rogers (1962). Some of the glmpses are descrbed to smoothen the understandng of the present work. The remander of the paper s organzed as follows. In Secton 2, we brefly revew lterature of mult-generaton. The proposed model s presented n Secton 3. Emprcal analyss of proposed s reported n Secton 4. Fnally we dscuss the manageral mplcatons of ths study and concluson n Secton 5 and 6 respectvely. Further n Secton 7 comprses of Acknowledgement followed by references at last. 75
Internatonal Journal of Mathematcal, Engneerng and Management Scences 2. Bref Background Research for modelng the sales of mult-generaton s abundant stll more work s n ppelne. The frst ever model of mult-generatons of a product was proposed n the year 1987. Norton and Bass (1987) as beng the most parsmonous model n the feld of successve generatons, acknowledged the exstence of substtuton and skppers but do not dfferentate them. Even though Norton and Bass model has certan lmtatons, stll t remans the most appled and extended model n the feld of mult-generaton tll date. Speece and MacLachlan (1995) tested and appled the Norton and Bass model (1987) for forecastng the sales of successve generaton of packagng technology of mlk contaners. Mahajan and Muller (1996) extended the Norton and Bass model (1987) to account for more varablty n terms of skppng done by adopters,.e. an adopter of the frst generaton could replace t wth thrd generaton, etc. They appled ther model to sales of hgh-technology product.e. IBM Manframe computers. In the year 2010, Jang extended the Norton and Bass model (1987) that dfferentates the dfferent types of adopton. Kapur et al. (2010), proposed a multgeneratonal dffuson model consderng the mpact of repeat-adopton-substtuton dffuson n ther model. Based on smlar lnes Jang and Jan (2012) proposed Generalzed Norton and Bass model whch uses exactly the same set parameters as Norton and Bass model. A study to examne the number of product sold and number of product n use of two dfferent generatons s recently proposed by Aggrawal et al. (2015). In ths paper, we propose an nter-generatonal sales model under the jont mpact of two dfferent processes namely awareness process and adopton process. Usng a very realstc sayng that, Sales of the product can happen only after prospectve buyers have nformaton about the characterstc features of the product (Anand et al., 2014a). Awareness process can be defned as nformng the ndvduals by means of whch they may form an opnon (whch mght result nto adopton of the product) whereas n adopton process, nformed ndvduals wth postve percepton towards the product may turn up to be an adopter. 3. Modelng Framework 3.1. Assumptons () Intergeneratonal shftng s allowed and Substtuton and Swtchng are together consdered as shfters. () Repeat purchase n the same generaton s not allowed. () Adopton process s dependent on awareness process flowng n the market place. (v) Informed ndvduals havng only postve percepton (who actually turn up becomng adopters) are consdered. In lne wth all the aforesad assumpton and usng the concept proposed by Anand et al. (2014a) where a process can be understood usng the jont dstrbuton of the two nvolved processes (awareness and then adopton n our case); n ths artcle, we propose a framework that accounts for shft arsng from one generaton to successve generatons and the role of nformed ndvduals to adopter of the product. Consderng substtuton and swtchng as shftng (shfters), we assumed that 2 nd generaton was ntroduced at tme pont 2 ' ' 1 1 1 1 1 1 1 2 2 2. The smplfed equatons are: N t m. F G ( t) m. F G ( t). F G ( t ) (1) N ( t) m. F G ( t ) m. F G ( t). F G ( t ) (2) 2 2 2 2 2 1 1 1 2 2 2 76
Internatonal Journal of Mathematcal, Engneerng and Management Scences where N1 t and N2 t represents the cumulatve number of adopton for 1 st generaton and 2 nd m 1 m 2 generaton respectvely; and are the market potental for 1 st generaton and 2 nd generaton respectvely; also F 1 G 1 () t represents the jont dstrbuton functon for the adopton process of 1 st generaton whch comprses of two dfferent dstrbuton accountng for awareness and adopton process on smlar lnes F2 G2 ( t 2) represents the jont dstrbuton functon for the adopton process of 2 nd generaton attrbutng to awareness and adopton process. In equaton (1), the frst component represents the adopter s who are aware and would buy the same generaton; had there been no second generatonal avalable n the marketplace. The second component shows the connecton between awareness and adopton of the product when newer generaton comes n market and thereby ts reducton from the frst component shows the eventual sales that have happened for G1 of the product. On smlar grounds; equaton (2) can be explaned. The above framework can be extended for the case of dependent on ts predecessor generaton.e. on th 1 th generaton. As and when generaton beng 1 th generaton s ntroduced nto the market at tme ' 1 ', a porton of those prospectve buyers who would have adopted or have adopted generaton would shft to 1 th generaton. Hence cumulatve number of shfters (comprse of both swtchng and substtuton) from generaton to 1 th generaton (takng care of the two stages) can be modeled as follows: th th 1 1 1. 1 2 2 2. m 2 F 3 G 3 t 3. m... m F G t m F G t N t F G t.1 F 1 G 1 t 1 3 (3) where () N t be the cumulatve adoptons where 1,2..., n stands for generaton; F G t defnes the jont dstrbuton functon whch s defned usng Steltjes convoluton approach as used by Anand et al. (2014a). For analytcal reasons; we are now takng the case of two generaton and wll be presentng the sub cases accordngly: () When awareness s constant and adopton s logstc n nature. () When awareness and adopton both follows exponental pattern. () When awareness s exponental and adopton behaves n logstc pattern. (v) When awareness and adopton both follows logstc pattern. Above dscussed cases are presented mathematcally n tabular form n Table 1. On ncorporatng dfferent cases n equaton (1) and (2) dfferent successve model can be obtaned. 77
Internatonal Journal of Mathematcal, Engneerng and Management Scences 4. Data Analyss The model proposed n Secton 3 has been valdated on data collected from a Semconductor Industry whch ncludes data of world-wde dynamc random access memory (DRAM) shpments of sx generatons 4K, 16K, 64K, 256K,1M and 4M DRAM (Vctor and Ausubel, 2002) collected for a perod from 1974 to 1997. But we have used the frst two generatons (4K and 16K) n order to supplement our model. The parameters of proposed model were estmated usng smultaneously non lnear two stage least square by software package SAS (SAS/ETS User's Gude, 2004). Estmated values of dffuson parameters of the two technologes for proposed approach under dfferent cases (as explaned above) are gven n Table 2. # F t Case 1 ~ const Case 2 ~ exp b G t F G t ~ logstc b, ~ exp b Case 3 ~ exp b ~ logstc b, Case 4 ~ logstc b, ~ logstc b, 1 e 1 bt 1 e bt bt 1 1 bt e -b 1 t bt e (1- e )+(1+ ) e log 1 e bt 1- e 1 e 1- e e bt -b t 2 bt bt (1+ ) e 2 2 -bt + 2 bt log b 2 t -b t 1-1 e Table 1. Dfferent forms for jont adopton functon (Anand et al. (2014a)) Technology Cases Parameters m 1 m2 1 b b 2 1 2 Case 1 751.04 1332.5 0.5461 0.3653 35.908 16.552 DRAM Company Case 2 438.95 7745.8 0.323 0.0742 --- --- Case 3 817.21 1318.3 0.5406 0.372 14.825 5.3341 Case 4 821.17 1302 0.5759 0.3943 4.6916 2.1592 Table 2. Parameter estmaton results 78
Internatonal Journal of Mathematcal, Engneerng and Management Scences # Generaton SSE MSE RMSE R-Square Adj R-Sq Case 1 Case 2 Case 3 Case 4 G1 15914 1675.2 40.929 0.9004 0.8847 G2 60370 6354.7 79.716 0.9794 0.9762 G1 4260.4 405.8 20.143 0.9733 0.9721 G2 75190 7914.8 88.965 0.9743 0.9703 G1 10397 1094.4 33.082 0.9349 0.9246 G2 44136 4645.9 68.161 0.9849 0.9826 G1 10848 1141.9 33.792 0.9321 0.9214 G2 39592 4167.5 64.557 0.9865 0.9844 Table 3. Comparson crtera for all cases Fg. 1. Goodness of ft curve for case-1 79
Internatonal Journal of Mathematcal, Engneerng and Management Scences Fg. 2. Goodness of ft curve for case-2 Fg. 3. Goodness of ft curve for case-3 80
Internatonal Journal of Mathematcal, Engneerng and Management Scences Fg. 4. Goodness of ft curve for case-4 The actual and predcted values for the DRAM data set have been llustrated va graphs (Fg. 1 to 4). Clearly the graphs presents a good and close correspondance between actual and predcted values for proposed methodology. Table 3 and Fg. 5 shows the comparson crtera for all the cases. The MSE has mnmum value of 405.8 for frst generaton of case-2 whereas 4167.5 as the mnmum value for second generaton of case-4. The values R-Square are relatvely good for all cases wth a mnmum of 0.9004 for frst generaton (g1) and 0.9743 for second generaton (g2) correspondng to case-1 and 2 respectvely. Smlar s the case of other comparson attrbutes. Thus t s wse to say that the proposed modelng framework shows good valdaton results. On examnng the above table; t has been found that the case-1.e. when awareness s constant n the market and adopton s happenng s logstc manner; the results so obtaned s same as gven by Norton and Bass n 1987. From ths we can analyze and confrm that the model developed by Norton and Bass does not actually consder the behavor of nformaton avalable about the product n the market (as can be seen from the results obtaned from case-1). On scrutnzng the obtaned results, t further becomes clear that the pattern n whch the awareness prevals n the market does not mpact the sales behavor of the product (as obtaned n case - 2, 3, 4) and that s why case-1 (whch s nothng but Norton and Bass model (1987) that assume constant flow of nformaton/ constant awareness) s overpowered by all other scenaros n whch the awareness flow does follow some pattern. 81
Internatonal Journal of Mathematcal, Engneerng and Management Scences Fg. 5. Comparson crterons for all cases 5. Manageral Implcaton Crtcalty assocated wth the launch of multple versons of a product s somethng, whch cannot be gnored by the frms. Managng the recurrent generaton n the market, how the comng of a newer generaton mpact sales of exstng generaton and how people after beng nformed about avalable generatons make ther opnon about the purchase of ether of them or both; these are some questons whch are needed to be answered. Some of the exstng mult generaton models had a few capabltes to answer them. Knowng the mpact of how the penetraton of nformaton among prospectve buyers shapes the sale of successve generatons of the product was not answered n any of the earler work. Wth the am to provde more generc ntergeneratonal sales model whch also ncludes the mpact of nformaton suppled to consumers, the proposed model not only offers greater flexblty wth some added capabltes, but also delvers better overall performance both n terms of model ft and forecastng. Furthermore, the proposed model can ncorporate the dfferent functonal form to descrbe the nformaton and adopton flow. Hence, t s judcous to clam that the present model s well suted to help practtoner and frms n takng mportant decsons concernng towards marketng of successve generatons of a product. 6. Concluson The proposed framework captures the shftng from one generaton to successve generaton and how they behave under two stage modelng framework. Modelng nnovaton dffuson as a two step process s a generalzaton n whch the frms estmate the sales of a product from the aware consumers. Generally, the one who s not aware about the product does not go for ts adopton and aware consumers may have postve or a negatve thought for the product. The man focus s gven to the case of two generatons of a product under the assumpton that awareness and adopton process have dfferent functonal forms. The movement of adopters from one generaton to ts successve generaton has been termed as devaton; whch s able to account for both 82
Internatonal Journal of Mathematcal, Engneerng and Management Scences substtuton and swtchng effects. Based on SSE, MSE, Root MSE, and Adj., t s clear that the proposed model s able to provde a good ft to consdered sales data n contrast to tradtonal successve generaton models, whch assumed constant nformaton flow wth logstc dstrbuton representng the adopton process. Acknowledgement The research work presented n ths paper s supported by grants to the frst author from DST, va DST PURSE phase II, Inda. Reference Aggrawal, D., Anand, A., Sngh, O., & Kapur, P. K. (2015). Modellng successve generatons for products-n-use and number of products sold n the market. Internatonal Journal of Operatonal Research, 24(2), 228-244. Anand, A., Kapur, P. K., Agarwal, M., & Aggrawal, D. (2014a, October). Generalzed nnovaton dffuson modelng & weghted crtera based rankng. In Relablty, Infocom Technologes and Optmzaton (ICRITO) (Trends and Future Drectons), 2014 3rd Internatonal Conference on (pp. 1-6). IEEE. Anand, A., Sngh, O., Agarwal, M., & Aggarwal, R. (2014b, October). Modelng adopton process based on awareness and motvaton of consumers. In Relablty, Infocom Technologes and Optmzaton (ICRITO) (Trends and Future Drectons), 2014 3rd Internatonal Conference on (pp. 1-6). IEEE. Bass, F. M. (1969). A new product growth for model consumer durables. Management Scence, 15(5), 215-227. Bass, F. M., Krshnan, T. V., & Jan, D. C. (1994). Why the Bass model fts wthout decson varables. Marketng scence, 13(3), 203-223. Bronnenberg, B. J., & Mahajan, V. (2001). Unobserved retaler behavor n multmarket data: Jont spatal dependence n market shares and promoton varables. Marketng Scence, 20(3), 284-299. De Bruyn, A., & Llen, G. L. (2008). A mult-stage model of word-of-mouth nfluence through vral marketng. Internatonal Journal of Research n Marketng, 25(3), 151-163. Garber, T., Goldenberg, J., Lba, B., & Muller, E. (2004). From densty to destny: Usng spatal dmenson of sales data for early predcton of new product success. Marketng Scence, 23(3), 419-428. Goldenberg, J., Lba, B., & Muller, E. (2002). Rdng the saddle: How cross-market communcatons can create a major slump n sales. Journal of Marketng, 66(2), 1-16. Ho, T. H., Savn, S., & Terwesch, C. (2002). Managng demand and sales dynamcs n new product dffuson under supply constrant. Management Scence, 48(2), 187-206. Islam, T. & Meade, N. (1997). The dffuson of successve generatons of a technology: A more general model. Technologcal Forecastng and Socal Change, 56(1), 49-60. Jan, D., Mahajan, V., & Muller, E. (1991). Innovaton dffuson n the presence of supply restrctons. Marketng Scence, 10(1), 83-90. Jang, Z. (2010). How to gve away software wth successve versons. Decson Support Systems, 49(4), 430-441. Jang, Z., & Jan, D. C. (2012). A generalzed Norton Bass model for multgeneraton dffuson. Management Scence, 58(10), 1887-1897. Kalsh, S., & Sen, S. K. (1986). Dffuson models and the marketng mx for sngle products. Innovaton Dffuson Models of New Product Acceptance, 87-115. R 2 R 2 83
Internatonal Journal of Mathematcal, Engneerng and Management Scences Kalsh, S. (1985). A new product adopton model wth prce, advertsng, and uncertanty. Management Scence, 31(12), 1569-1585. Kapur, P. K., Chanda, U., Tandon, A., & Anand, S. (2010, December). Innovaton dffuson of successve generatons of hgh technology products. In Relablty, Safety and Hazard (ICRESH), 2010 2nd Internatonal Conference on (pp. 505-510). IEEE. Llen, G. L., Rao, A. G., & Kalsh, S. (1981). Bayesan estmaton and control of detalng effort n a repeat purchase dffuson envronment. Management Scence, 27(5), 493-506. Mahajan, V., & Muller, E. (1996). Tmng, dffuson, and substtuton of successve generatons of technologcal nnovatons: The IBM manframe case. Technologcal Forecastng and Socal Change, 51(2), 109-132. Mahajan, V., & Wnd, Y. (1985). Innovaton dffuson models of new product acceptance: A reexamnaton. Meade, N., & Islam, T. (2006). Modellng and forecastng the dffuson of nnovaton A 25-year revew. Internatonal Journal of Forecastng, 22(3), 519-545. Mdgley, D. F. (1976). A smple mathematcal theory of nnovatve behavor. Journal of Consumer Research, 31-41. Norton, J. A., & Bass, F. M. (1987). A dffuson theory model of adopton and substtuton for successve generatons of hgh-technology products. Management Scence, 33(9), 1069-1086. Rogers, E. M. (1962). Dffuson of Innovatons. The Free Press, New York. SAS Insttute Inc. (2004). SAS/ETS user's gude verson 9.1. Cary, NC: SAS Insttute Inc. Sngh, O., Anand, A., Kapur, P. K., & Aggrawal, D. (2012). Consumer behavour-based nnovaton dffuson modellng usng stochastc dfferental equaton ncorporatng change n adopton rate. Internatonal Journal of Technology Marketng, 7(4), 346-360. Speece, M. W., & Maclachlan, D. L. (1995). Applcaton of a mult-generaton dffuson model to mlk contaner technology. Technologcal Forecastng and Socal Change, 49(3), 281-295. Van den Bulte, C., & Llen, G. (2007). A two-stage model of nnovaton adopton wth partal observablty: Model development and applcaton. Mmeo, Unversty of Pennsylvana. Vctor, N. M., & Ausubel, J. H. (2002). DRAMs as model organsms for study of technologcal evoluton. Technologcal forecastng and Socal Change, 69(3), 243-262. Wnd, Y., & Sharma, S. (1983). An approach to repeat purchase dffuson models. In Proceedngs of the Amercan Marketng Educator's Conference. 84