# American Institute of Mathematical Sciences

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

 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

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.
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 & Management Optimization, 2016, 12 (4) : 1367-1389. doi: 10.3934/jimo.2016.12.1367
##### References:
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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.  Google Scholar [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.  Google Scholar [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. Google Scholar [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.  Google Scholar [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.  Google Scholar [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.  Google Scholar [11] E. Cetin and S. T. Esen, A weapon-target assignment approach to media allocation, Applied Mathematics and Computation, 175 (2006), 1266-1275. Google Scholar [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.  Google Scholar [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.  Google Scholar [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.  Google Scholar [15] C. A. De Kluyver, Hard and soft constraints in media scheduling., Journal of Advertisement Research, 18 (1978), 27-31. Google Scholar [16] G. E. Fructhter and S. Kalish, Dynamic promotional budgeting and media allocation, European Journal of Operational Research, 111 (1998), 15-27. Google Scholar [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.  Google Scholar [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.  Google Scholar [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.  Google Scholar [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.  Google Scholar [21] M. P. Haydock, Media allocation optimization, The International Journal of Applied Management and Technology, (2007), 146-164. Google Scholar [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.  Google Scholar [23] J. P. Ignizio, Goal Programming and Extensions, Health Lexington Books, Lexington, Massachusetts, 1976. Google Scholar [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.  Google Scholar [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.  Google Scholar [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.  Google Scholar [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. Google Scholar [28] J. D. Leckenby and K. H. Ju, Advances in media decision models, Current Issues and research in Advertising,12 (1990), 311-357. Google Scholar [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. Google Scholar [30] R. B. Maffei, Planning advertising expenditures by dynamic programming methods, Management Technology, 1 (1960), 94-100. doi: 10.1287/mantech.1.2.94.  Google Scholar [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.  Google Scholar [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.  Google Scholar [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. Google Scholar [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.  Google Scholar [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. Google Scholar [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.  Google Scholar [37] R. E. Steuer, Multiple Criteria Optimization: Theory, Computation and Application, John Wiley, New York, 546, 1986.  Google Scholar [38] H. Thiriez, OR software LINGO, European Journal of Operational Research, 12 (2000), 655-656. Google Scholar [39] B. Viscolani, Advertising decisions for a segmented market, Optimization, 58 (2009), 469-477. doi: 10.1080/02331930701763355.  Google Scholar [40] B. Viscolani, Advertising decisions in a vertical distribution channel, International Game Theory Review, 11 (2009), 273-284. doi: 10.1142/S0219198909002315.  Google Scholar [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.  Google Scholar [42] F. S. Zufryden, Media scheduling, a stochastic dynamic model approach, Management Science, 19 (1973), 1395-1406. doi: 10.1287/mnsc.19.12.1395.  Google Scholar [43] F. S. Zufryden, Media scheduling and solution approaches, Operational Research Quarterly, 26 (1975), 283-295.  Google Scholar [44] F. S. Zufryden, On the dual optimization of media reach and frequency, Journal of Business, 48 (1975), 558-570. doi: 10.1086/295782.  Google Scholar [45] F. S. Zufryden, Optimal multi-period advertising budget allocation within a competitive environment, Journal of the Operational Research Society, 26 (1975), 743-754. Google Scholar

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.  Google Scholar [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.  Google Scholar [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.  Google Scholar [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. Google Scholar [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.  Google Scholar [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.  Google Scholar [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. Google Scholar [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.  Google Scholar [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.  Google Scholar [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.  Google Scholar [11] E. Cetin and S. T. Esen, A weapon-target assignment approach to media allocation, Applied Mathematics and Computation, 175 (2006), 1266-1275. Google Scholar [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.  Google Scholar [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.  Google Scholar [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.  Google Scholar [15] C. A. De Kluyver, Hard and soft constraints in media scheduling., Journal of Advertisement Research, 18 (1978), 27-31. Google Scholar [16] G. E. Fructhter and S. Kalish, Dynamic promotional budgeting and media allocation, European Journal of Operational Research, 111 (1998), 15-27. Google Scholar [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.  Google Scholar [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.  Google Scholar [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.  Google Scholar [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.  Google Scholar [21] M. P. Haydock, Media allocation optimization, The International Journal of Applied Management and Technology, (2007), 146-164. Google Scholar [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.  Google Scholar [23] J. P. Ignizio, Goal Programming and Extensions, Health Lexington Books, Lexington, Massachusetts, 1976. Google Scholar [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.  Google Scholar [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.  Google Scholar [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.  Google Scholar [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. Google Scholar [28] J. D. Leckenby and K. H. Ju, Advances in media decision models, Current Issues and research in Advertising,12 (1990), 311-357. Google Scholar [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. Google Scholar [30] R. B. Maffei, Planning advertising expenditures by dynamic programming methods, Management Technology, 1 (1960), 94-100. doi: 10.1287/mantech.1.2.94.  Google Scholar [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.  Google Scholar [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.  Google Scholar [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. Google Scholar [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.  Google Scholar [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. Google Scholar [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.  Google Scholar [37] R. E. Steuer, Multiple Criteria Optimization: Theory, Computation and Application, John Wiley, New York, 546, 1986.  Google Scholar [38] H. Thiriez, OR software LINGO, European Journal of Operational Research, 12 (2000), 655-656. Google Scholar [39] B. Viscolani, Advertising decisions for a segmented market, Optimization, 58 (2009), 469-477. doi: 10.1080/02331930701763355.  Google Scholar [40] B. Viscolani, Advertising decisions in a vertical distribution channel, International Game Theory Review, 11 (2009), 273-284. doi: 10.1142/S0219198909002315.  Google Scholar [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.  Google Scholar [42] F. S. Zufryden, Media scheduling, a stochastic dynamic model approach, Management Science, 19 (1973), 1395-1406. doi: 10.1287/mnsc.19.12.1395.  Google Scholar [43] F. S. Zufryden, Media scheduling and solution approaches, Operational Research Quarterly, 26 (1975), 283-295.  Google Scholar [44] F. S. Zufryden, On the dual optimization of media reach and frequency, Journal of Business, 48 (1975), 558-570. doi: 10.1086/295782.  Google Scholar [45] F. S. Zufryden, Optimal multi-period advertising budget allocation within a competitive environment, Journal of the Operational Research Society, 26 (1975), 743-754. Google Scholar
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