Multi Period Advertising Media Selection in a Segmented Market

Abstract

A product passes through different life cycle phases once it comes in the market. During the launch phase it is promoted on mass level, second phase stresses on capturing maximum potential, and in later phases company emphasizes on retention of the product in the minds of the customers until its continuation in the market. The advertising budget and media mix used to advertise the product must be planned according to the current phase of the product. Thus it becomes imperative for a company to look at media planning problems in a dynamic manner over a planning period as the market conditions change and the product moves through its cycle with time. In this paper we have formulated a multi-period mathematical programming problem that dynamically computes the optimal number of insertions and allocates advertising budget in various media channels of a segmented market. The aim is to maximize the reach obtained through each media from all the segments in each time period under budgetary constraints and bounds on the decision variables. The reach in any period for a media is taken as a sum of current period reach and retention of the previous periods reach. Goal programming technique is used to solve the problem. A case study is presented to show the real life application of the model.

Appendices

Appendix A

Let f (X) and b be the function and its goal respectively and η and ρ be the over and under achievement (negative and positive deviational) variables then the choice of deviational variable in the goal objective functions which has to be minimized depend upon the following rule:

• if f (X) <= b, ρ is minimize under the constraints f (X) + η − ρ = b

• if f (X) >= b, η is minimized under the constraints f (X) + η − ρ = b and

• if f (X) = b, η + ρ is minimized under the constraints f (X) + η − ρ = b

Appendix B

Definition 1

[4]: A solution x ⁰ is said to be efficient solution if x ⁰∈S and there exist no other feasible point x such that F(x) ≥ F(x ⁰ ) and F(x) ≠ F(x ⁰ ).

Definition 2

[4]: A solution x ⁰ is said to be a properly efficient solution if it is efficient and if there exist a scalar M > 0 such that, for each i, we have $\frac{{f_{i} (x) - f_{i} (x^{0} )}}{{f_{j} (x^{0} ) - f_{j} (x)}} \le M$. For some j such that f _j (x) < f _j (x ⁰) whenever x∈X and f _i (x) > f _i (x ⁰)

Lemma 1:

Through definition 1 and 2, optimal solution of the problem (P5) will be properly efficient solution to the problem (P3).

Appendix C

Table 3.1 Circulation in Newspapers (‘0000)

Table 3.2 Advertisement Cost in Newspapers(‘000)

Table 3.3 Retention Factor in Newspapers (%)

Table 3.4 Upper and Lower Bounds on Advertisement in Newspapers

Table 3.5 Readership Profile Matrix for Newspapers

Table 4.1 Average Viewership in Television (‘0000)

Table 4.2 Advertisement Cost in Television(‘000)

Table 4.3 Upper and Lower bounds on advertisement in Television

Table 4.4 Retention Factor in Television (%)

Table 4.5 Viewership Profile Matrix for Television

Table 5.1 Average no. of listeners in Radio (‘0000)

Table 5.2 Advertisement cost in Radio(‘00)

Table 5.3 Upper and Lower Bounds on Advertisement in Radio

Table 5.4 Retention Factor in Radio (%)

Table 5.5 Listenership Profile Matrix for Radio

Table 6 Weights assigned for customer profile criteria

Table 7 Weights assigned to media in stage 2 of Goal Programming in different time periods