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Bi-level decision making models for advertising allocation problem under fuzzy environment

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Abstract

This paper presents bi-level decision making models for advertising planning problem. Advertising planning process consists of multiple objectives and is generally decentralised involving various hierarchical levels of decision making. Considering the cost and impact related factors, long and short duration ads for a single product are made for telecasting. The models presented in the paper are designed so as to allocate the number of advertisements of each kind to different channels under different time zones of a day with the objectives of maximization of ads impact and minimization of net cost at two different levels. We present two models based on minimum impact value to be achieved by advertisement as a constraint considering that the budget available for advertising is uncertain. We extend and present a solution approach developed for fuzzy bi-level integer decision making model with fuzzy constraints. Finally, we provide a numerical illustration to discuss the applicability of the proposed models.

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References

  • Adhami AY, Muneeb SM, Nomani MA (2017) A multi-level decision making model for the supplier selection problem in a fuzzy situation. Oper Res Decis 27(4):5–26

    Google Scholar 

  • Aggarwal R, Chanda U (2017) Optimal duration of advertising campaigns for successive technology generations using innovation diffusion theory. Int J Oper Res 28(3):415–428

    Article  MathSciNet  MATH  Google Scholar 

  • Baky IA (2009) Fuzzy goal programming algorithm for solving decentralized bi-level multi-objective programming problems. Fuzzy Sets Syst 160:2701–2713

    Article  MathSciNet  MATH  Google Scholar 

  • Belenky AS, Belenkii I (2002) Optimization of planning an advertising campaign of goods and services. Math Comput Model 35(13):1391–1403

    Article  MathSciNet  MATH  Google Scholar 

  • Beltran-Royo C, Escudero LF, Zhang H (2016) Multiperiod multiproduct advertising budgeting: stochastic optimization modeling. Omega 59:26–39

    Article  Google Scholar 

  • Bhattacharya UK (2009) A chance constraints goal programming model for the advertising planning problem. Eur J Oper Res 192(2):382–395

    Article  MathSciNet  MATH  Google Scholar 

  • Bialas WF, Karwan MH (1984) Two-level linear programming. Manag Sci 30(8):1004–1020

    Article  MathSciNet  MATH  Google Scholar 

  • Colapinto C, Torre DL (2015) Media planning and preferences: a fuzzy goal programming model. Int J Multicriteria Decis Mak 5(3):167–181

    Google Scholar 

  • Emam OE (2006) A fuzzy approach for bi-level integer non-linear programming problem. Appl Math Comput 172(1):62–71

    MathSciNet  MATH  Google Scholar 

  • Emam OE (2013) Interactive approach to bi-level integer multi-objective fractional programming problem. Appl Math Comput 223:17–24

    MathSciNet  MATH  Google Scholar 

  • Gao Jinwu, Liu Baoding (2005) Fuzzy multilevel programming with a hybrid intelligent algorithm. Comput Math Appl 49(9):1539–1548

    Article  MathSciNet  MATH  Google Scholar 

  • Horen JH (1980) Scheduling of network television programs. Manag Sci 26(4):354–370

    Article  Google Scholar 

  • Jalil SA, Sadia S, Javaid S, Ali QM (2017) A solution approach for solving fully fuzzy multiobjective solid transportation problem. Int J Agric Stat Sci 13(1):75–84

    Google Scholar 

  • Jan RH, Chern MS (1994) Nonlinear integer bilevel programming. Eur J Oper Res 72(3):574–587

    Article  MATH  Google Scholar 

  • Javan HT, Khanlari A, Motamedi O, Mokhtari H (2018) A hybrid advertising media selection model using AHP and fuzzy-based GA decision making. Neural Comput Applic 29(4):1153–1167

    Article  Google Scholar 

  • Jha PC, Aggarwal R, Gupta A (2011) Optimal media planning for multi-products in segmented market. Appl Math Comput 217(16):6802–6818

    MATH  Google Scholar 

  • Jha PC, Aggarwal S, Gupta A, Sarker R (2016) Multi-criteria media mix decision model for advertising a single product with segment specific and mass media. J Ind Manag Optim 12(4):1367–1389

    Article  MathSciNet  MATH  Google Scholar 

  • Keown AJ, Duncan CP (1979) Integer goal programming in advertising media selection. Decis Sci 10(4):577–592

    Article  Google Scholar 

  • Liu Baoding, Yao Kai (2015) Uncertain multilevel programming: algorithm and applications. Comput Ind Eng 89:235–240

    Article  Google Scholar 

  • Mihiotis A, Tsakiris I (2004) A mathematical programming study of advertising allocation problem. Appl Math Comput 148(2):373–379

    MathSciNet  MATH  Google Scholar 

  • Mondal SP (2016) Differential equation with interval valued fuzzy number and its applications. Int J Syst Assur Eng Manag 7(3):370–386

    Article  Google Scholar 

  • Moynihan GP, Kumar AN, D’Souza G, Nichols WG (1995) A decision support system for media planning. Comput Ind Eng 29(1–4):383–386

    Article  Google Scholar 

  • Osman MS, Abo-Sinna MA, Amer AH (2004) A multi-level non-linear multi-objective decision-making under fuzziness. Appl Math Comput 153:239–252

    MathSciNet  MATH  Google Scholar 

  • Paul S, Mondal SP, Bhattacharya P (2016) Discussion on fuzzy quota harvesting model in fuzzy environment: fuzzy differential equation approach. Model Earth Syst Environ 2(2):70

    Article  Google Scholar 

  • Paul S, Jana D, Mondal SP, Bhattacharya P (2017) Optimal harvesting of two species mutualism model with interval parameters. J Intell Fuzzy Syst 33(4):1991–2005

    Article  MATH  Google Scholar 

  • Pérez-Gladish B, González I, Bilbao-Terol A, Arenas-Parra M (2010) Planning a TV advertising campaign: a crisp multiobjective programming model from fuzzy basic data. Omega 38(1):84–94

    Article  Google Scholar 

  • Pieters R, Warlop L, Wedel M (2002) Breaking through the clutter: benefits of advertisement originality and familiarity for brand attention and memory. Manag Sci 48(6):765–781

    Article  Google Scholar 

  • Pramanik S, Banerjee D (2012) Chance constrained quadratic bi-level programming problem. Int J Mod Eng Res 2(4):2417–2424

    Google Scholar 

  • Saad OM, Emam OE (2011) Taylor series approach for solving chance-constrained bi-level integer linear fractional programming problem. Int J Math Arch (IJMA) 2(5):1–6

    Google Scholar 

  • Sakawa M, Nishizaki I (2002) Interactive fuzzy programming for decentralized two-level linear programming problems. Fuzzy Sets Syst 125:301–315

    Article  MathSciNet  MATH  Google Scholar 

  • Shih HS, Lai YJ, Lee ES (1996) Fuzzy approach for multi-level programming problems. Comput Oper Res 23(1):73–91

    Article  MathSciNet  MATH  Google Scholar 

  • Sinha S, Sinha SB (2002) KKT transformation approach for multi-objective multi-level linear programming problems. Eur J Oper Res 143:19–31

    Article  MathSciNet  MATH  Google Scholar 

  • Tafreshi PF, Aghdaie MH, Behzadian M, Abadi MG (2016) Developing a group decision support system for advertising media evaluation: a case in the middle east. Group Decis Negot 25(5):1021–1048

    Article  Google Scholar 

  • Toksarı MD, Bilim Y (2015) Interactive fuzzy goal programming based on Jacobian matrix to solve decentralized bi-level multi-objective fractional programming problems. Int J Fuzzy Syst 17(4):499–508

    Article  MathSciNet  Google Scholar 

  • Yager RR (1997) Intelligent agents for World Wide Web advertising decisions. Int J Intell Syst 12(5):379–390

    Article  Google Scholar 

  • Youness EA, Emam OE, Hafez MS (2014) Fuzzy bi-level multi-objective fractional integer programming. Appl Math 8(6):2857–2863

    MathSciNet  Google Scholar 

  • Zhang T, Hu T, Zheng Y, Guo X (2012) An improved particle swarm optimization for solving bilevel multiobjective programming problem. J Appl Math. https://doi.org/10.1155/2012/626717

    MathSciNet  MATH  Google Scholar 

Download references

Acknowledgements

Authors are thankful to the reviewers and the editor for the insightful revision suggestions. The second author gratefully acknowledges the financial support of UGC-New Delhi (UGC-BSR Start-up Grant No. F.30-62/2014(BSR)).

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Authors and Affiliations

  1. Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh, India

    Syed Mohd Muneeb, Ahmad Yusuf Adhami, Zainab Asim & Syed Aqib Jalil

Authors
  1. Syed Mohd Muneeb
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  2. Ahmad Yusuf Adhami
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  3. Zainab Asim
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  4. Syed Aqib Jalil
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Corresponding author

Correspondence to Syed Mohd Muneeb.

Appendix 1

Appendix 1

The model 2 obtained by using the data set provided under Sect. 4.1 is represented as:

I Level

Minimize Z1 = 0.012 n111 + 0.024n112 + 0.048n113 + 0.036n114 + 0.018n121 + 0.036n122 + 0.072n123 + 0.054n124 + 0.024n131 + 0.048n132 + 0.096n133 + 0.072n134 + 0.006n141 + 0.012n142 + 0.024n143 + 0.018n144 + 0.008n211 + 0.016n212 + 0.032n213 + 0.024n214 + 0.012n221 + 0.024n222 + 0.048n223 + 0.036n224 + 0.016n231 + 0.032n232 + 0.064n233 + 0.048n234 + 0.004n241 + 0.008n242 + 0.016n243 + 0.012n244

Where n111,n112,n113,n114,n121,n122,n123,n124,n141,n142,n143,n144,n211,n212,n213,n214,n221,n222,n223,n224,n241,n242,n243,n244 solve

Maximize Z2 = 3000 n111 + 3500n112 + 4500n113 + 4000n114 + 3500n121 + 4000n122 + 5000n123 + 4500n124 + 4000n131 + 5000n132 + 6000n133 + 5500n134 + 2000n141 + 2500n142 + 3500n143 + 3000n144 + 4500n211 + 5000n212 + 7000n213 + 5500n214 + 5000n221 + 5500n222 + 6500n223 + 6000n224 + 5500n231 + 6500n232 + 7500n233 + 7000n234 + 3000n241 + 3500n242 + 4500n243 + 4000n244

Subject to constraints

3000 n111 + 3500n112 + 4500n113 + 4000n114 + 3500n121 + 4000n122 + 5000n123 + 4500n124 + 4000n131 + 5000n132 + 6000n133 + 5500n134 + 2000n141 + 2500n142 + 3500n143 + 3000n144 + 4500n211 + 5000n212 + 7000n213 + 5500n214 + 5000n221 + 5500n222 + 6500n223 + 6000n224 + 5500n231 + 6500n232 + 7500n233 + 7000n234 + 3000n241 + 3500n242 + 4500n243 + 4000n244\(\tilde{ < }\) 450,000.

n111 + n112 + n113 + n114 + n121 + n122 + n123 + n124 + n131 + n132 + n133 + n134 + n141 + n142 + n143 + n144 + n211 + n212 + n213 + n214 + n221 + n222 + n223 + n224 + n231 + n232 + n233 + 7000n234 + n241 + n242 + n243 + n244 ≤  70.

n111,n112, n113, n114, n121, n122, n123, n124, n141, n142, n143, n144, n211, n212, n213, n214, n221, n222, n223, n224, n241, n242, n243, n244 ≥ 1.

n111, n112, n113, n114, n121, n122, n123, n124, n141, n142, n143, n144, n211, n212, n213, n214, n221, n222, n223, n224, n241, n242, n243, n244 ≤ 3.

n131, n132, n133, n134, n231, n232, n233, n234 ≥ 2.

n131, n132, n133, n134, n231, n232, n233, n234 ≤  4.

0.012 n111 + 0.024n112 + 0.048n113 + 0.036n114 + 0.008n211 + 0.016n212 + 0.032n213 + 0.024n214 ≥  0.20.

0.018n121 + 0.036n122 + 0.072n123 + 0.054n124 + 0.012n221 + 0.024n222 + 0.048n223 + 0.036n224 ≥ 0.19.

0.024n131 + 0.048n132 + 0.096n133 + 0.072n134 + 0.016n231 + 0.032n232 + 0.064n233 + 0.048n234 ≥ 0.22.

0.006n141 + 0.012n142 + 0.024n143 + 0.018n144 + 0.004n241 + 0.008n242 + 0.016n243 + 0.012n244 ≥ 0.17.

n111, n112, n113, n114, n121, n122, n123, n124, n141, n142, n143, n144, n211, n212, n213, n214, n221, n222, n223, n224, n241, n242, n243, n244, n131, n132, n133, n134, n231, n232, n233, n234 ≥ 0 and Integers

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Muneeb, S.M., Adhami, A.Y., Asim, Z. et al. Bi-level decision making models for advertising allocation problem under fuzzy environment. Int J Syst Assur Eng Manag 10, 160–172 (2019). https://doi.org/10.1007/s13198-018-0723-z

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