MILAN| 23 June 2011 Success factors of models used for supporting sales ‐ related allocation decisions - Sönke Albers Professor of Marketing and Innovation

MILAN| 23 June 2011

Success factors of models used for supporting sales‐related allocation decisions-

Sönke AlbersProfessor of Marketing and InnovationKühne Logistics University, Hamburg

Sönke Albers: Success factors of models used for supporting sales‐related allocation decisions

AGENDA

2

Success factors for empirical estimation of aggregate sales response function

Success factors for optimizing allocation of sales effort

Conclusion


Success Factors for Empirical estimation of Aggregate Sales Response Function

3

1. Functional form must be appropriate and matters!2. Functional form should exhibit decreasing elasticity3. Long-term effects should be modeled with the help of

stock models (not Koyck)4. Separation of effects of first contact and repeated

contacts5. Heterogeneity across customers should be taken

into account6. Trends and seasonality should be taken into account

I data are from a panel


Functional Form of The Aggregate Response Function

4

Observation: Marketing & sales instruments (except for price) exhibit diminishing marginal returns at some point, otherwise marketing & sales expenditures would not be optimizable!

Proposition 1: Linear relationships are therefore inappropriate for aggregate sales response models.


Functional Form of the Aggregate Response Function

5

Example for an assumed linear relationship from a top journal:

Source: Natalie Mizik and Robert Jacobson: Are Physicians "Easy Marks"? Quantifying the Effects of Detailing and Sampling on New Prescriptions Management Science Vol. 50 (2004), No. 12, 1704-1715

We employ the following dynamic fixed-effects distributed lag regression model to assess the effect of detailing and sampling on new prescriptions:



6

Proposition 2a: The functional form is very important when diminishing marginal returns exist!

Name Function Elasticity

Constant Elasticity

Semi-logarithmic

Diminishing Elasticity

Modified Exponential

Log-Reciprocal



7

0,00

1.000,00

2.000,00

3.000,00

4.000,00

5.000,00

6.000,00

7.000,00

8.000,00

9.000,00

0 5 10 15 20 25 30

Sales

Linear

Quadratic

Constant Elasticity


Modified Exponential

Log-Reciprocal



8

Proposition 2b: The functional form for a relationship with diminishing marginal returns is important because it leads to quite different optimal solutions!

Functional Form Optimal No. Calls

Quadratic 17.7

Constant Elasticity 77.8


18.6

Modified Exponential 14.1

Log-reciprocal 24.3



9

Observation: Very often, researchers prefer to work with nonlinear functions that are linearizable.

Proposition 3a: Adding quadratic terms does not help unless the interval with the maximal or minimal outcome is supported by a sufficient number of observations.

Proposition 3b: Estimation of linearized models (e.g., taking logs) comes at the cost of creating a bias in the error terms (implicitly weighting lower versus higher values).


Taking Logs in linear estimation is different from nonlinear estimation (Proposition 3b)

10

0,00

1.000,00

2.000,00

3.000,00

4.000,00

5.000,00

6.000,00

7.000,00

8.000,00

9.000,00

10.000,00

0 5 10 15 20 25 30

Sales

Constant Elasticity

Log-log



11

Proposition 3b: Estimating constant elasticity response functions with a linearized log-log function can lead to dramatically different results for the optimal call level compared to a nonlinear estimation

Functional Form Optimal No. Calls

Log-Log 265.8

Constant Elasticity 77.8


AGENDA

12



Conclusion


Success Factors for optimal allocation of sales effort

13

1. Estimation method should have maximized information value rather than goodness-of-fit

2. Results should have face validity but also some surprising aspects

3. Any model should be offered in EXCEL4. Rather than providing numerical optimization

understandable heuristics are better accepted


Informational value versus goodness-of-fit

14

Proposition 4: Response models may be good for reproducing sales utilizing the response function, but may nevertheless be problematic if they lead to optimization errors (e.g., in the paper by Proppe and Albers (2009) where one wrong estimate affects the entire allocation task, or in case of uncertainty when non-significant variables are set to be zero)


15

Research questions

RESEARCH QUESTION CAN BEST BE SOLVED BY SIMULATION STUDY

Simulation

Dennis Proppe and Sönke Albers: Choosing Response Models for Budget Allocation in Heterogeneous and Dynamic Markets: Why Simple Sometimes Does Better, Marketing Science Institute Special Report 09-202, April 2009

Key question: Which econometric methods deliver the most reliable estimation results that can be used for a successful budget allocation task?

Which data properties are especially influential for good estimation when it comes to optimal budget allocation?

Under what circumstances may simple allocation heuristics perform better than the allocation based on econometric estimation?

When analyzing real data, the true model remains unknown.

Results of econometric estimation procedures can only be evaluated by goodness-of-fit-statistics and not by their closeness to the true relationship.

In a simulation study the data is generated by a true model which is specified by the researcher.

Thus, the real model parameters are known and the estimation result can be compared to the true relationship.


16

DATA QUALITY HAS A SUBSTANTIAL INFLUENCE ON THE OPTIMALITY OF THE BUDGET ALLOCATION


Best case: Small error, many observations, many response units

Worst case: Large error, few observations, few response units

Scenario Measure Simple least squares

regression

Fixed effects Hierarchical Bayes

Maximum simulated likelihood

Empirical Bayes

Equal allocation

Proportion-al-to-sales

Mean 91.98% 94.21% 94.92% 96.24% 95.85% 80.86% 87.90%

Standard deviation

(7.22%) (2.55%) (4.81%) (3.39%) (3.92%) (5.83%) (3.10%)

5* 4* 3 1 2* 7 6*

Best Case, N=30

Rank (*=significant difference to next lower

rank)

Scenario Measure Simple least squares

regression



Empirical Bayes

Equal allocation


Mean 6.03% 71.61% 55.37% 68.27% 26.78% 80.86% 87.28%

Standard deviation

(22.92%) (29.33%) (38.16%) (30.03%) (34.95%) (5.83%) (3.22%)

7 3* 5* 4* 6* 2 1*

Worst Case, N=30


rank)


17

GOOD ECONOMETRIC TECHNIQUES BENEFIT FROM HETEROGENEITY AND a LARGE No. of OBSERVATIONS


Heterogeneous parameters, large number of observationsScenario Measure Simple least

squares regression



Empirical Bayes

Equal allocation


Mean 76.40% 93.33% 88.56% 95.35% 90.97% 75.18% 84.86%

Standard deviation

(28.00%) (3.10%) (14.73%) (3.79%) (10.48%) (1.00%) (0.41%)

6 2 4 1* 3* 7 5Rank (*=significant

difference to next lower rank)

Hetero-geneous,

many obser-vations

Homogeneous parameters, small number of observationsScenario Measure Simple least

squares regression



Empirical Bayes

Equal allocation


Mean 30.69% 76.28% 62.52% 86.16% 45.07% 95.28% 95.52%

Standard deviation

(35.94%) (31.93%) (39.87%) (21.30%) (40.27%) (0.33%) (0.37%)

7 4* 5* 3* 6* 2* 1*

Homo-geneous,

few observ-ations


rank)


Implementation success depends on ease-of-use

18

Proposition 5: Managers like to make use of instruments that they can master. EXCEL is such an instrument, and thus decision support should be made available in EXCEL tools.



19

“As Albers (IJRM 2000) notes, the use of marketing models in actual practice is becoming less of an exception and more of a rule because of spreadsheet software. It is our hope that the ease with which the BG/NBD model can be implemented in a familiar modeling environment will encourage more firms to take better advantage of the information already contained in their customer transaction databases. Furthermore, as key personnel become comfortable with this type of model, we can expect to see growing demand for more complete (and complex) models—and more willingness to commit resources to them.”

Peter S. Fader, Bruce G. S. Hardie, and Ka Lok Lee: “Counting Your Customers” the Easy Way: An Alternative to the Pareto/NBD Model, Marketing Science, Vol. 24, No. 2, Spring 2005, pp. 275–284



20

Proposition 6: Managers want to understand why certain decisions are recommended. Optimization models for determining key marketing budgets will only be applied if the solution is provided in terms of understandable heuristics.


Example for easy-to-understand Heuristic

21

Sales effort should allocated proportionally to

• Past sales• Contribution margin• Elasticity of Sales with respect to changes of sales

effort


AGENDA

22



Conclusion


Conclusion

23

1. The functional form matters: Aggregate response functions should exhibit diminishing marginal returns and decreasing elasticities

2. Goodness-of-fit is not everything. Sometimes it is better to know whether an estimation provides values that lead to correct optimization, as is the case with allocation.

3. Instead of very complicated optimization approaches, we need heuristics that are understandable and easy to implement in Excel for managers.


24

Thank you very much for your attention!

Documents

MILAN| 23 June 2011 Success factors of models used for supporting sales ‐ related allocation decisions - Sönke Albers Professor of Marketing and Innovation