# 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

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:
 [1] D. A. Aaker, A probabilistic approach to industrial media selection,, Lecture Notes in Economics and Mathematical Systems, 132 (1976), 144. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Google Scholar [16] G. E. Fructhter and S. Kalish, Dynamic promotional budgeting and media allocation,, European Journal of Operational Research, 111 (1998), 15. 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. 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. 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. 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. 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. Google Scholar [22] R. H. Huang and C. L. Yang, Optimal planning of advertising scheduling,, Journal of Statistics and Management Systems, 16 (2013), 363. doi: 10.1080/09720510.2013.842057. Google Scholar [23] J. P. Ignizio, Goal Programming and Extensions,, Health Lexington Books, (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. 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. 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. 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. Google Scholar [28] J. D. Leckenby and K. H. Ju, Advances in media decision models,, Current Issues and research in Advertising, 12 (1990), 311. 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. Google Scholar [30] R. B. Maffei, Planning advertising expenditures by dynamic programming methods,, Management Technology, 1 (1960), 94. 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. 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. 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. 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. 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, (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. doi: 10.1016/j.ejor.2012.09.022. Google Scholar [37] R. E. Steuer, Multiple Criteria Optimization: Theory, Computation and Application,, John Wiley, (1986). Google Scholar [38] H. Thiriez, OR software LINGO,, European Journal of Operational Research, 12 (2000), 655. Google Scholar [39] B. Viscolani, Advertising decisions for a segmented market,, Optimization, 58 (2009), 469. doi: 10.1080/02331930701763355. Google Scholar [40] B. Viscolani, Advertising decisions in a vertical distribution channel,, International Game Theory Review, 11 (2009), 273. 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. doi: 10.1109/ICMIT.2008.4654457. Google Scholar [42] F. S. Zufryden, Media scheduling, a stochastic dynamic model approach,, Management Science, 19 (1973), 1395. doi: 10.1287/mnsc.19.12.1395. Google Scholar [43] F. S. Zufryden, Media scheduling and solution approaches,, Operational Research Quarterly, 26 (1975), 283. Google Scholar [44] F. S. Zufryden, On the dual optimization of media reach and frequency,, Journal of Business, 48 (1975), 558. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. Google Scholar [16] G. E. Fructhter and S. Kalish, Dynamic promotional budgeting and media allocation,, European Journal of Operational Research, 111 (1998), 15. 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. 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. 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. 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. 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. Google Scholar [22] R. H. Huang and C. L. Yang, Optimal planning of advertising scheduling,, Journal of Statistics and Management Systems, 16 (2013), 363. doi: 10.1080/09720510.2013.842057. Google Scholar [23] J. P. Ignizio, Goal Programming and Extensions,, Health Lexington Books, (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. 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. 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. 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. Google Scholar [28] J. D. Leckenby and K. H. Ju, Advances in media decision models,, Current Issues and research in Advertising, 12 (1990), 311. 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. Google Scholar [30] R. B. Maffei, Planning advertising expenditures by dynamic programming methods,, Management Technology, 1 (1960), 94. 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. 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. 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. 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. 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, (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. doi: 10.1016/j.ejor.2012.09.022. Google Scholar [37] R. E. Steuer, Multiple Criteria Optimization: Theory, Computation and Application,, John Wiley, (1986). Google Scholar [38] H. Thiriez, OR software LINGO,, European Journal of Operational Research, 12 (2000), 655. Google Scholar [39] B. Viscolani, Advertising decisions for a segmented market,, Optimization, 58 (2009), 469. doi: 10.1080/02331930701763355. Google Scholar [40] B. Viscolani, Advertising decisions in a vertical distribution channel,, International Game Theory Review, 11 (2009), 273. 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. doi: 10.1109/ICMIT.2008.4654457. Google Scholar [42] F. S. Zufryden, Media scheduling, a stochastic dynamic model approach,, Management Science, 19 (1973), 1395. doi: 10.1287/mnsc.19.12.1395. Google Scholar [43] F. S. Zufryden, Media scheduling and solution approaches,, Operational Research Quarterly, 26 (1975), 283. Google Scholar [44] F. S. Zufryden, On the dual optimization of media reach and frequency,, Journal of Business, 48 (1975), 558. 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. Google Scholar

2018 Impact Factor: 1.025