برنامه ریزی تبلیغاتی تلویزیونی مبارزات انتخاباتی : مدل برنامه ریزی چندمنظوره واضح از داده های فازی اولیه

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.

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 conditions, 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 relevant ongoing issue concerning both new and mature products (see [1] and [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, positioning and promotion), even adding new “P” strategies, e.g., “purple” (innovation) as suggested by Godin [3]. As to the second condition to justify research on specific models for advertising decision making, 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 logarithmic structure. This paper pursues the following aims. (i) To estimate an index of audience expectation based on experts’ predictions. Although experts 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 programming 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 audience and advertising fees for the three main TV networks currently operating in Spain.

For big companies and independent consultants, the crisp two-objective logarithmic programming model (10) and (11) with fuzzy information and technical constraints has proven sound to determine efficient solutions to the ad placement problem. It has also proven easy to implement. This approach is new and relevant as it allows us to take advantage of psychological research on the audience impact. Indeed, according to Weber and Fechner's law, this impact has been described by a logarithmic function, which rules out linear models. A remarkable issue is that estimating audience expectation (8) for each broadcast relies on subjective judgments, namely, the available statistical data have been handled by fuzzy logic. We acknowledge that statistical data based on historical series are appealing to analysts who believe that past results have at least some predictive ability; however, fuzzy data are preferable for analysts who distrust past information as a tool to predict future audience. In this sense, the paper harmonizes both ways of prediction. Indeed, we have shown how fuzzy logic can be appealing to the analyst without overlooking statistical data. In the paper, statistical data have been useful as an auxiliary source helping experts to state their own opinions and beliefs. From the efficient frontier of solutions (see Section 4.8), we have proposed two standard procedures to determine the final solution. One of them is to discuss with the user as Section 4.9 shows. An alternative procedure is to approximate the utility optimum on the efficient frontier, as Appendix A, case 1, shows. Results are consistent as discussed in Appendix A. Nowadays, company managers and consultants can find broad information on different aspects related to TV advertising. These aspects include audience ratings, advertising fees, ad design and psychological issues such as visual attention, viewers’ memory and others. However, this paper provides a value added to the client, who can use the proposed model to decide its advertising budget and advertisement allocation on TV networks in an optimal way.