21.19 Marketing Resource Allocation Models

This section is based on (Mantrala, Sinha, and Zoltners 1992)

21.19.1 Case study 1

Concave sales response function

• Optimal vs. proportional at different investment levels
• Profit maximization perspective of aggregate function

$$s_i = k_i (1- e^{-b_i x_i})$$

where

• $s_i$ = current-period sales response (dollars / period)
• $x_i$ = amount of resource allocated to submarket i
• $b_i$ = rate at which sales approach saturation
• $k_i$ = sales potential

Allocation functions

• Fixed proportion

  • $R_i$ = Investment level (dollars/period)

  • $w_i$ = fixed proportion or weights

$$\hat{x}_i = w_i R; \\ \sum_{t=1}^2 w_t = 1; 0 < w_t < 1$$

• Informed allocator

  • optimal allocations via marginal analysis (maximize profits)

$$max C = m \sum_{i = 1}^2 k_i (1- e^{-b_i x_i}) \\ x_1 + x_2 \le R; x_i \ge 0 \text{ for } i = 1,2 \\ x_1 = \frac{1}{(b_1 + b_2)(b_2 R + \ln(\frac{k_1b_1}{k_2b_2})} \\ x_2 = \frac{1}{(b_1 + b_2)(b_2 R + \ln(\frac{k_2b_2}{k_1b_1})}$$

21.19.2 Case study 2

S-shaped sales response function:

• Optimal vs. proportional at different investment levels
• Profit maximization perspective of aggregate function

21.19.3 Case study 3

Quadratic-form stochastic response function

• Optimal allocation only with risk averse and risk neutral investors.

References

Mantrala, Murali K., Prabhakant Sinha, and Andris A. Zoltners. 1992. “Impact of Resource Allocation Rules on Marketing Investment-Level Decisions and Profitability.” Journal of Marketing Research 29 (2): 162. https://doi.org/10.2307/3172567.