Multi-period media planning for multi-products incorporating segment specific and mass media

Abstract

Efficient budget allocation between different communication channels is one of the fundamental activities of any media planner. In this paper, we attempt to develop a multi-objective integer linear programming model to determine the optimal schedule of advertisements for a set of multiple products of a firm in a segmented market (influenced by both mass and segment-specific media) over a planning horizon. The objectives are to maximize the gross impressions of advertisements and simultaneously minimize the advertising expenditure. To incorporate continuous changes that occur in the market, the total planning horizon is divided into shorter time periods and decisions for each of the subsequent time periods are taken, bearing in mind the changes that have occurred in the preceding time periods. Based on the gap that exists in the extant literature, we also jointly consider, in our model, the notions of (a) carry-over effect of gross impressions, (b) spectrum effect of mass media on segments, and (c) cross-product effect. The model is solved through a goal programming approach to achieve the best trade-off between the conflicting objectives. Further, the model could be adapted to provide solutions in a wide variety of real-life situations. This is substantiated via a numerical analysis for a firm that advertises products in the Indian market through mass and segment-specific media.

Appendices

Appendix A

Consider a multi-objective programming problem as follows (Steuer 1986)

$$\begin{aligned}&Max\;F(x)=(f_1 (x),f_2 (x),\ldots ,f_m (x)) \\&\hbox { subject to }x\in S=\left\{ {h_i (x)\ge 0\hbox { };\hbox { }i=1,2,\ldots ,n} \right\} \; \\ \end{aligned}$$

Definition 1

(Geoffrion 1968) $x^{0}\in S$ is said to be an efficient solution of the multi-objective problem if there does not exist any $x \in S$such that

$$\begin{aligned} f_j (x)\ge & {} f_j (x^{0})\;\;\forall j=1,2,\ldots ,m\;\hbox { and }\\ f_j(x)> & {} f_j (x^{0})\; \hbox { for some}\;j\in \left\{ {1,2,\ldots ,m} \right\} \hbox { and } f_j (x)\ne f_j (x^{0})\; \end{aligned}$$

Definition 2

(Geoffrion 1968) An efficient solution $x^{0}\in S$ is said to be properly efficient solution of the multi-objective problem if there exists a scalar $\theta >0$ such that, for each j and $x\in S$

$$\begin{aligned}&f_j (x)-f_j (x^{0})\le \theta (f_k (x^{0})-f_k (x))\;\;\hbox {for}\;\hbox {some}\;k\;\hbox {with}\;f_k (x)<f_k(x^{0})\; \\&\quad \hbox { where }x\in S \hbox { and }\;\;f_j (x)>f_j (x^{0})\; \end{aligned}$$

Lemma 1

(Geoffrion 1968) Optimal solution of problem (P4) is a properly efficient solution of the problem (P3).

Since the problem (P3) is a vector minimization goal programming problem, the optimal solution of the problem (P4)is goal properly efficient solution to the problem (P3).

Appendix B

See Tables 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20 and 21.

Table 8 Circulation of newspaper

Table 9 Viewership of television

Table 10 Weights

Table 11 Percentage profile matrix of newspaper for product 1

Table 12 Percentage profile matrix of television for product 1

Table 13 Spectrum effect for newspaper for product 1

Table 14 Spectrum effect for television for product 1

Table 15 Proportion of carryover for newspaper for product 1

Table 16 Proportion of carryover for television for product 1

Table 17 Cross product effect

Table 18 Cost of newspaper for a 4 cm $\times$ 4 cm advertisement (in INR)

Table 19 Cost of television for 30 s spot (in INR)

Table 20 Maximum, minimum frequency for newspaper for product 1

Table 21 Maximum, minimum frequency for television for product 1