Multi-criteria media mix decision model for advertising a single product with segment specific and mass media

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October 2016, 12(4): 1367-1389. doi: 10.3934/jimo.2016.12.1367

Multi-criteria media mix decision model for advertising a single product with segment specific and mass media

P. C. Jha ^1, , Sugandha Aggarwal ^1, , Anshu Gupta ^2, and Ruhul Sarker ^3,

1.	Department of Operational Research, University of Delhi, Delhi-110007, India, India
2.	School of Business, Public Policy and Social Entrepreneurship, Ambedkar University Delhi, Delhi-110006, India
3.	School of Engineering and Information Technology, University of New South Wales @ ADFA, Canberra 2600, Australia

Received December 2014 Revised October 2015 Published January 2016

Abstract
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The effectiveness of any advertisement campaign relies heavily on the combination of media vehicles chosen for communicating the messages and the amount of advertisements placed in them. This paper presents a media planning model that assists a firm in determining the optimal media mix for a product advertised in a segmented market. The model determines the number of advertisements to be placed in different segment specific media as well as mass media. The objective is to maximize the reach of the product in the potential market by placement of the advertisements. A case study is presented to illustrate the application of the model in which the market considered is geographically segmented on the basis of cultural and lingual diversity. The segments respond to regional advertising (segment specific) and to national advertising which reaches segments with a fixed spectrum. Interactive weighted sum goal programming technique is discussed to solve the problem.

Keywords: spectrum effect, multi-objective decision making, Media planning, interactive weighted sum goal programming., mass advertising, segment specific advertising.

Mathematics Subject Classification: 90B60, 90C10, 90C2.

Citation: P. C. Jha, Sugandha Aggarwal, Anshu Gupta, Ruhul Sarker. Multi-criteria media mix decision model for advertising a single product with segment specific and mass media. Journal of Industrial and Management Optimization, 2016, 12 (4) : 1367-1389. doi: 10.3934/jimo.2016.12.1367

References:

[1]	D. A. Aaker, A probabilistic approach to industrial media selection, Lecture Notes in Economics and Mathematical Systems, 132 (1976), 144-145. doi: 10.1007/978-3-642-51565-1_48.
[2]	S. Aggarwal, K. Govindan, P. C. Jha and I. Meidute, Effect of repeat purchase and dynamic market size on diffusion of an innovative technological consumer product in a segmented market, Technological and Economic Development of Economy, 20 (2014), 97-115. doi: 10.3846/20294913.2014.885914.
[3]	B. D. Aouni, C. Calapinto and D. L. Torre, Stochastic goal programming model and satisfaction functions for media selection and planning problem, International Journal of Multicriteria Decision Making, 2 (2012), 391-407. doi: 10.1504/IJMCDM.2012.050678.
[4]	P. V. Balakrishnan and N. G. Hall, A maximin procedure for the optimal insertion timing of ad executions, European Journal of Operational Research, 85 (1995), 368-382.
[5]	F. M. Bass and R. T. Lonsdale, An exploration of linear programming in media selection, Lecture Notes in Economics and Mathematical Systems, 132 (1976), 137-139. doi: 10.1007/978-3-642-51565-1_46.
[6]	F. M. Bass, A. Krishnamoorthy, A. Prasad and S. P. Sethi, Advertising competition with market expansion for finite horizon firms, Journal of Industrial and Management Optimization, 1 (2005), 1-19. doi: 10.3934/jimo.2005.1.1.
[7]	D. Berkowitz, A. Alaway and G. D. Souza, The impact of differential lag effects on the allocation of advertising budgets across media, Journal of Advertising Research, 41 (2001), 27-37.
[8]	U. K. Bhattacharya, A chance constraints goal programming model for the advertising planning problem, European Journal of Operational Research, 192 (2009), 382-395. doi: 10.1016/j.ejor.2007.09.039.
[9]	A. Buratto, L. Grosset and B. Viscolani, Advertising channel selection in a segmented market, Automatica, 42 (2006), 1343-1347. doi: 10.1016/j.automatica.2006.03.015.
[10]	A. Buratto, L. Grosset and B. Viscolani, Advertising a new product in a segmented market, European Journal of Operational Research, 175 (2006), 1262-1267. doi: 10.1016/j.ejor.2005.06.035.
[11]	E. Cetin and S. T. Esen, A weapon-target assignment approach to media allocation, Applied Mathematics and Computation, 175 (2006), 1266-1275.
[12]	A. Charnes, W. W. Cooper, J. K. DeVoe, D. B. Learner and W. Reinecke, A goal programming model for media planning, Lecture Notes in Economics and Mathematical Systems, 132 (1976), 140-143. doi: 10.1007/978-3-642-51565-1_47.
[13]	K. Coulter and J. Sarkis, An application of the analytic network process to the advertising media budget allocation decision, The International Journal on Media Management, 8 (2006), 164-172. doi: 10.1207/s14241250ijmm0804_2.
[14]	P. J. Danaher and R. T. Rust, Determining the optimal return on investment for an advertising campaign, European Journal of Operational Research, 95 (1996), 511-521. doi: 10.1016/0377-2217(95)00319-3.
[15]	C. A. De Kluyver, Hard and soft constraints in media scheduling., Journal of Advertisement Research, 18 (1978), 27-31.
[16]	G. E. Fructhter and S. Kalish, Dynamic promotional budgeting and media allocation, European Journal of Operational Research, 111 (1998), 15-27.
[17]	D. H. Gensch and U. P. Welam, An optimum budget allocation model for dynamic, interacting market segments, Management Science, 20 (1973), 179-190. doi: 10.1287/mnsc.20.2.179.
[18]	A. M. Geoffrion, Proper efficiency and the theory of vector maximization, Journal of Mathematical Analysis and Applications, 22 (1968), 618-630. doi: 10.1016/0022-247X(68)90201-1.
[19]	L. Grosset and B. Viscolani, Advertising in a segmented market: Comparison of media choices, IMA Journal of Management Mathematics, 19 (2008), 219-226. doi: 10.1093/imaman/dpm040.
[20]	L. Grosset and B. Viscolani, Advertising and exogenous interference in a segmented market, Journal of Interdisciplinary Mathematics, 14 (2011), 29-38. doi: 10.1080/09720502.2011.10700733.
[21]	M. P. Haydock, Media allocation optimization, The International Journal of Applied Management and Technology, (2007), 146-164.
[22]	R. H. Huang and C. L. Yang, Optimal planning of advertising scheduling, Journal of Statistics and Management Systems, 16 (2013), 363-380. doi: 10.1080/09720510.2013.842057.
[23]	J. P. Ignizio, Goal Programming and Extensions, Health Lexington Books, Lexington, Massachusetts, 1976.
[24]	P. C. Jha, R. Aggarwal and A. Gupta, Optimal media planning for multi-product in segmented market, Applied Mathematics and Computation,217 (2011), 6802-6818. doi: 10.1016/j.amc.2010.12.111.
[25]	A. J. Keown and C. P. Duncan, Integer goal programming in advertising media selection, Decision Sciences,10 (1979), 577-592. doi: 10.1111/j.1540-5915.1979.tb00048.x.
[26]	N. K. Kwak, C. W. Lee and J. H. Kim, An MCDM model for media selection in the dual consumer/industrial market, European Journal of Operational Research,166 (2005), 255-265. doi: 10.1016/j.ejor.2004.02.016.
[27]	J. D. C. Little and L. M. Lodish, A media selection model and its optimization by dynamic programming, Industrial Management Review, 8 (1966), 15-23.
[28]	J. D. Leckenby and K. H. Ju, Advances in media decision models, Current Issues and research in Advertising,12 (1990), 311-357.
[29]	W. B. Locander, R. W. Scamell, R. M. Sparkman and J. P. Burton, Media allocation model using nonlinear benefit curves, Journal of Business Research, 6 (1978), 273-293.
[30]	R. B. Maffei, Planning advertising expenditures by dynamic programming methods, Management Technology, 1 (1960), 94-100. doi: 10.1287/mantech.1.2.94.
[31]	E. C. Malthouse, D. Qiu and J. Xu, Optimal selection of media vehicles using customer databases, Expert Systems with Applications, 39 (2012), 13035-13045. doi: 10.1016/j.eswa.2012.05.095.
[32]	A. Mihiotis and I. Tsakiris, A mathematical programming study of advertising allocation problem, Applied Mathematics and Computation, 148 (2004), 373-379. doi: 10.1016/S0096-3003(02)00853-6.
[33]	G. P. Moynihan, A. Kumar, G. D'Souza and W. G. Nockols, A decision support system for media planning, , 29(1), Computer and Industrial Engineering, 29 (1995), 383-386.
[34]	P. A. Naik, M. K. Mantrala and A. G. Sawyer, Planning media schedules in the presence of dynamic advertising quality, Marketing Science,17 (1998), 214-235. doi: 10.1287/mksc.17.3.214.
[35]	V. S. Ramaswamy and S. Namakumari, Marketing Management: Global Perspective - Indian Context, $5^{th}$ edition, McGraw Hill Education (India) P. Ltd., New Delhi, 2013.
[36]	B. C. Royo, H. Zhang, L. A. Blanco and J. Almagro, Multistage multiproduct advertising budgeting, European Journal of Operational Research, 225 (2013), 179-188. doi: 10.1016/j.ejor.2012.09.022.
[37]	R. E. Steuer, Multiple Criteria Optimization: Theory, Computation and Application, John Wiley, New York, 546, 1986.
[38]	H. Thiriez, OR software LINGO, European Journal of Operational Research, 12 (2000), 655-656.
[39]	B. Viscolani, Advertising decisions for a segmented market, Optimization, 58 (2009), 469-477. doi: 10.1080/02331930701763355.
[40]	B. Viscolani, Advertising decisions in a vertical distribution channel, International Game Theory Review, 11 (2009), 273-284. doi: 10.1142/S0219198909002315.
[41]	D. Wang and J. Xu, A fuzzy multi-objective decision making model of the advertising budgeting allocation and its application to an IT Company, Proceedings of the 2008 IEEE ICMIT, (2008), 740-745. doi: 10.1109/ICMIT.2008.4654457.
[42]	F. S. Zufryden, Media scheduling, a stochastic dynamic model approach, Management Science, 19 (1973), 1395-1406. doi: 10.1287/mnsc.19.12.1395.
[43]	F. S. Zufryden, Media scheduling and solution approaches, Operational Research Quarterly, 26 (1975), 283-295.
[44]	F. S. Zufryden, On the dual optimization of media reach and frequency, Journal of Business, 48 (1975), 558-570. doi: 10.1086/295782.
[45]	F. S. Zufryden, Optimal multi-period advertising budget allocation within a competitive environment, Journal of the Operational Research Society, 26 (1975), 743-754.

show all references

References:

[1]	D. A. Aaker, A probabilistic approach to industrial media selection, Lecture Notes in Economics and Mathematical Systems, 132 (1976), 144-145. doi: 10.1007/978-3-642-51565-1_48.
[2]	S. Aggarwal, K. Govindan, P. C. Jha and I. Meidute, Effect of repeat purchase and dynamic market size on diffusion of an innovative technological consumer product in a segmented market, Technological and Economic Development of Economy, 20 (2014), 97-115. doi: 10.3846/20294913.2014.885914.
[3]	B. D. Aouni, C. Calapinto and D. L. Torre, Stochastic goal programming model and satisfaction functions for media selection and planning problem, International Journal of Multicriteria Decision Making, 2 (2012), 391-407. doi: 10.1504/IJMCDM.2012.050678.
[4]	P. V. Balakrishnan and N. G. Hall, A maximin procedure for the optimal insertion timing of ad executions, European Journal of Operational Research, 85 (1995), 368-382.
[5]	F. M. Bass and R. T. Lonsdale, An exploration of linear programming in media selection, Lecture Notes in Economics and Mathematical Systems, 132 (1976), 137-139. doi: 10.1007/978-3-642-51565-1_46.
[6]	F. M. Bass, A. Krishnamoorthy, A. Prasad and S. P. Sethi, Advertising competition with market expansion for finite horizon firms, Journal of Industrial and Management Optimization, 1 (2005), 1-19. doi: 10.3934/jimo.2005.1.1.
[7]	D. Berkowitz, A. Alaway and G. D. Souza, The impact of differential lag effects on the allocation of advertising budgets across media, Journal of Advertising Research, 41 (2001), 27-37.
[8]	U. K. Bhattacharya, A chance constraints goal programming model for the advertising planning problem, European Journal of Operational Research, 192 (2009), 382-395. doi: 10.1016/j.ejor.2007.09.039.
[9]	A. Buratto, L. Grosset and B. Viscolani, Advertising channel selection in a segmented market, Automatica, 42 (2006), 1343-1347. doi: 10.1016/j.automatica.2006.03.015.
[10]	A. Buratto, L. Grosset and B. Viscolani, Advertising a new product in a segmented market, European Journal of Operational Research, 175 (2006), 1262-1267. doi: 10.1016/j.ejor.2005.06.035.
[11]	E. Cetin and S. T. Esen, A weapon-target assignment approach to media allocation, Applied Mathematics and Computation, 175 (2006), 1266-1275.
[12]	A. Charnes, W. W. Cooper, J. K. DeVoe, D. B. Learner and W. Reinecke, A goal programming model for media planning, Lecture Notes in Economics and Mathematical Systems, 132 (1976), 140-143. doi: 10.1007/978-3-642-51565-1_47.
[13]	K. Coulter and J. Sarkis, An application of the analytic network process to the advertising media budget allocation decision, The International Journal on Media Management, 8 (2006), 164-172. doi: 10.1207/s14241250ijmm0804_2.
[14]	P. J. Danaher and R. T. Rust, Determining the optimal return on investment for an advertising campaign, European Journal of Operational Research, 95 (1996), 511-521. doi: 10.1016/0377-2217(95)00319-3.
[15]	C. A. De Kluyver, Hard and soft constraints in media scheduling., Journal of Advertisement Research, 18 (1978), 27-31.
[16]	G. E. Fructhter and S. Kalish, Dynamic promotional budgeting and media allocation, European Journal of Operational Research, 111 (1998), 15-27.
[17]	D. H. Gensch and U. P. Welam, An optimum budget allocation model for dynamic, interacting market segments, Management Science, 20 (1973), 179-190. doi: 10.1287/mnsc.20.2.179.
[18]	A. M. Geoffrion, Proper efficiency and the theory of vector maximization, Journal of Mathematical Analysis and Applications, 22 (1968), 618-630. doi: 10.1016/0022-247X(68)90201-1.
[19]	L. Grosset and B. Viscolani, Advertising in a segmented market: Comparison of media choices, IMA Journal of Management Mathematics, 19 (2008), 219-226. doi: 10.1093/imaman/dpm040.
[20]	L. Grosset and B. Viscolani, Advertising and exogenous interference in a segmented market, Journal of Interdisciplinary Mathematics, 14 (2011), 29-38. doi: 10.1080/09720502.2011.10700733.
[21]	M. P. Haydock, Media allocation optimization, The International Journal of Applied Management and Technology, (2007), 146-164.
[22]	R. H. Huang and C. L. Yang, Optimal planning of advertising scheduling, Journal of Statistics and Management Systems, 16 (2013), 363-380. doi: 10.1080/09720510.2013.842057.
[23]	J. P. Ignizio, Goal Programming and Extensions, Health Lexington Books, Lexington, Massachusetts, 1976.
[24]	P. C. Jha, R. Aggarwal and A. Gupta, Optimal media planning for multi-product in segmented market, Applied Mathematics and Computation,217 (2011), 6802-6818. doi: 10.1016/j.amc.2010.12.111.
[25]	A. J. Keown and C. P. Duncan, Integer goal programming in advertising media selection, Decision Sciences,10 (1979), 577-592. doi: 10.1111/j.1540-5915.1979.tb00048.x.
[26]	N. K. Kwak, C. W. Lee and J. H. Kim, An MCDM model for media selection in the dual consumer/industrial market, European Journal of Operational Research,166 (2005), 255-265. doi: 10.1016/j.ejor.2004.02.016.
[27]	J. D. C. Little and L. M. Lodish, A media selection model and its optimization by dynamic programming, Industrial Management Review, 8 (1966), 15-23.
[28]	J. D. Leckenby and K. H. Ju, Advances in media decision models, Current Issues and research in Advertising,12 (1990), 311-357.
[29]	W. B. Locander, R. W. Scamell, R. M. Sparkman and J. P. Burton, Media allocation model using nonlinear benefit curves, Journal of Business Research, 6 (1978), 273-293.
[30]	R. B. Maffei, Planning advertising expenditures by dynamic programming methods, Management Technology, 1 (1960), 94-100. doi: 10.1287/mantech.1.2.94.
[31]	E. C. Malthouse, D. Qiu and J. Xu, Optimal selection of media vehicles using customer databases, Expert Systems with Applications, 39 (2012), 13035-13045. doi: 10.1016/j.eswa.2012.05.095.
[32]	A. Mihiotis and I. Tsakiris, A mathematical programming study of advertising allocation problem, Applied Mathematics and Computation, 148 (2004), 373-379. doi: 10.1016/S0096-3003(02)00853-6.
[33]	G. P. Moynihan, A. Kumar, G. D'Souza and W. G. Nockols, A decision support system for media planning, , 29(1), Computer and Industrial Engineering, 29 (1995), 383-386.
[34]	P. A. Naik, M. K. Mantrala and A. G. Sawyer, Planning media schedules in the presence of dynamic advertising quality, Marketing Science,17 (1998), 214-235. doi: 10.1287/mksc.17.3.214.
[35]	V. S. Ramaswamy and S. Namakumari, Marketing Management: Global Perspective - Indian Context, $5^{th}$ edition, McGraw Hill Education (India) P. Ltd., New Delhi, 2013.
[36]	B. C. Royo, H. Zhang, L. A. Blanco and J. Almagro, Multistage multiproduct advertising budgeting, European Journal of Operational Research, 225 (2013), 179-188. doi: 10.1016/j.ejor.2012.09.022.
[37]	R. E. Steuer, Multiple Criteria Optimization: Theory, Computation and Application, John Wiley, New York, 546, 1986.
[38]	H. Thiriez, OR software LINGO, European Journal of Operational Research, 12 (2000), 655-656.
[39]	B. Viscolani, Advertising decisions for a segmented market, Optimization, 58 (2009), 469-477. doi: 10.1080/02331930701763355.
[40]	B. Viscolani, Advertising decisions in a vertical distribution channel, International Game Theory Review, 11 (2009), 273-284. doi: 10.1142/S0219198909002315.
[41]	D. Wang and J. Xu, A fuzzy multi-objective decision making model of the advertising budgeting allocation and its application to an IT Company, Proceedings of the 2008 IEEE ICMIT, (2008), 740-745. doi: 10.1109/ICMIT.2008.4654457.
[42]	F. S. Zufryden, Media scheduling, a stochastic dynamic model approach, Management Science, 19 (1973), 1395-1406. doi: 10.1287/mnsc.19.12.1395.
[43]	F. S. Zufryden, Media scheduling and solution approaches, Operational Research Quarterly, 26 (1975), 283-295.
[44]	F. S. Zufryden, On the dual optimization of media reach and frequency, Journal of Business, 48 (1975), 558-570. doi: 10.1086/295782.
[45]	F. S. Zufryden, Optimal multi-period advertising budget allocation within a competitive environment, Journal of the Operational Research Society, 26 (1975), 743-754.

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