Omega 38 (2010) 84--94 Contents lists available at ScienceDirect Omega journal homepage: www.elsevier.com/locate/omega Planning a TV advertising campaign: A crisp multiobjective programming model from fuzzy basic data  B. Pérez-Gladish a, * , I. Gonzalez b , A. Bilbao-Terol a , M. Arenas-Parra a a Departamento de Economía Cuantitativa, Facultad de Ciencias Económicas de la Universidad de Oviedo, Avda. del Cristo s/n, 33006, Oviedo (Asturias), Spain b Technical University of Valencia (Alcoy School), Spain ARTICLE INFO ABSTRACT Article history: Received 12 January 2007 Accepted 30 April 2009 Available online 8 May 2009 Keywords: Ad impact Weber and Fechner's logarithmic law Audience expectation Budgeting Multiobjective programming Fuzzy techniques This paper proposes a crisp two-objective logarithmic programming model to help companies decide their advertising campaigns on TV networks for mature products. Both objectives are: (a) to achieve the highest audience impact and (b) to reduce advertising costs as much as possible. Information input is fuzzily elaborated from statistical data, the fuzzy variables being defuzzified to introduce them into the crisp model. This fuzzy information is elicited by TV experts (often independent consultants). Although these experts know statistical information on audience in the past, they do not fully trust its predictive ability. The approach leads to the strategic advertisement (ad) placement among different broadcasts. Users (often managers of big companies) should inform the analyst about their advertising campaign budget. From Weber and Fechner-based psychological research, the ad impact during the advertising campaign is measured depending on the logarithm of ad repetitions. The crisp two-objective problem is solved by a tradeoff method subject to TV technical constraints. A case study with real world data is developed. © 2009 Elsevier Ltd. All rights reserved. 1. Introduction Decision making supported by mathematical tools can be achieved either using an existing approach or building a specific model tailored to the problem to be solved. This last option is appropriate when no existing approach can be directly applied or accommodated to our environment. Constructing a specific model does not mean overlooking previous methods, theories and results, but articulating them in a coherent structure with new elements and perspectives. In short, such a task is worth it under two condi- tions, relevance of the environment and serious difficulties to use an existing model adequately. In the TV advertising case addressed in this paper, both conditions hold. Indeed, advertising is a rele- vant ongoing issue concerning both new and mature products (see [1,2]). In particular, mature products need advertising to keep fit for a long time. Advertising is today a significant policy within the marketing structure of the five “Ps” (product, price, place, position- ing and promotion), even adding new “P” strategies, e.g., “purple” (innovation) as suggested by Godin [3]. As to the second condition  This article was processed by Associate Editor Stewart. * Corresponding author. Tel.: +34 985106292. E-mail addresses: bperez@uniovi.es (B. Pérez-Gladish), eballe@esp.upv.es (I. Gonzalez), ameliab@uniovi.es (A. Bilbao-Terol), mariamar@uniovi.es (M. Arenas-Parra). 0305-0483/$ - see front matter © 2009 Elsevier Ltd. All rights reserved. doi:10.1016/j.omega.2009.04.004 to justify research on specific models for advertising decision mak- ing, our literature search shows that TV commercial advertising is not treated from the Weber and Fechner's law of perception (see Section 2 below), whose articulation requires a new model of loga- rithmic structure. This paper pursues the following aims. (i) To estimate an index of audience expectation based on experts' predictions. Although ex- perts know statistical data, they prefer to handle them by fuzzy techniques because the future is not expected to resemble the past mechanically. (ii) To propose a crisp multiobjective logarithmic pro- gramming model to allocate companies' advertising budgets among an opportunity set of TV broadcasts. This model is established from the audience expectation fuzzy index above estimated, which will be defuzzified to use it in the crisp multiobjective approach. (iii) To develop a case study in which our theoretical contribution is applied to a real world problem with genuine information on broadcast au- dience and advertising fees for the three main TV networks currently operating in Spain. To gain insight into our proposal, let us cite Paurcar-Caceres [4], who maps the management science discourse over the last 35 years in four paradigms: (1) optimisation/normative; (2) interpreta- tive/learning; (3) critical and (4) a post-modern management science approach. Our proposal could be encompassed between the two first paradigms in the middle of the so called “hard” and “soft” OR/MS methods.