designing incentive systems for truthful information sharing · 2 45 0 0 45 product 1 actual demand...

Designing incentive systems for truthful information

sharing

Ulrich W. Thonemann

New Directions Seminar

Stanford University

April 25, 2013

Based on joint work with Lisa Scheele (University of Cologne) and Marco Slikker (Eindhoven

University of Technology). The authors gratefully acknowledge the support of the Deutsche

Forschungsgemeinschaft through the research group “Design and Behavior.”

Ulrich W. Thonemann (University of Cologne)

AGENDA

1

Motivation

Model

Laboratory Experiment

Validation

Discussion


FORECAST INFLATION AT PHARMACEUTICAL COMPANY Forecast vs. demand in thousand units

2

45

0

45 0

Product 1

Actual demand

Dem

and fore

cast

70

0

70 0

Product 2

120

0

120 0

Product 3 Product 4 75

0

75 0 Actual demand Actual demand

Actual demand D

em

and

fore

cast

Dem

and

fore

cast

Dem

and

fore

cast

Average demand

forecast inflation:

16 %

Over-forecasting

Under-forecasting

Forecast = 20

Demand = 10


SECOND EXAMPLE SUPPORTS DATA OF FIRST EXAMPLE

3

Forecast bias High Low

Forecast error Low High

Demand ≈ 200

Forecast ≈ 900

System forecast

Log-scale

Sales force forecast


TYPICAL INCENTIVE SYSTEM STRUCTURE

Sales 8%

Profit

30%

Qualitative

objectives

Revenues 30%

32%

Market share

Operations

7%

Stock levels

30% Profit

53% Qualitative

Objectives

Service level

3%

Others

7%

Department

CASE EXAMPLE


INCENTIVE SYSTEMS OF SALES

5

Sales-bonus-only

Absolute forecast error

Differentiated forecast error

Forecast error not penalized

Incentive system often used in practice

Absolute deviation of forecast from demand penalized

Incentive system is based on MAD and used in practice

Over-forecasting harder penalized then under-forecasting

Incentive system not/hardly used in practice


AGENDA

6

Motivation

Model


Validation

Discussion


Sales Operations

GENERAL SETTING

7

Market demand d

= Market condition f

+ Market uncertainty e

Sales observes

market

condition f

(e.g., 100)

Sales sends

forecast of market

condition f

(e.g., 120)

^

Operations

estimates

market

condition

based on f,

m(f| f)

^

^

Operations

determines

order

quantity q

Demand d = f + e

is realized and

min(q, d) is sold

Sales and operations

receive their

compensations

Sales Operations


E[sales bonus]

Order q

Sales bonus

E[forecast penalty]

f ^ Forecast f

Over-forecasting

penalty Under-forecasting

penalty

𝜋𝑆 𝑞,𝜙 𝜙 = 𝐶𝑆 + 𝑏𝐸 min(𝐷, 𝑞) − 𝑝𝑜𝐸 𝜙 − 𝐷+

− 𝑝𝑢𝐸 𝐷 − 𝜙 +

PAYOFF FUNCTION OF SALES

8

Fixed

Incentive systems

Sales-bonus-only (common practice): po = pu = 0

Absolute forecast error (recommended by practitioners): po = pu > 0

Differentiated forecast error (new): po > pu ≥ 0

Total


HOW ARE THE ELEMENTARY OUTCOMES EVALUATED?

9

Mr. A and Mr. B work for the sales division of a company. At the beginning of each month,

Mr. A and Mr. B must provide a demand forecast for the following month. At the end of the

month, they both receive a fixed compensation and a performance-based compensation.

Last month, Mr. A provided a demand forecast of 1,500 units, demand was 1,000 units,

and 1,000 units were sold. He receives a 100 euro sales bonus for the sold quantity in

addition to his regular salary.

Mr. B also provided a demand forecast of 1,500 units, demand was 1,000 units, and

1,000 units were sold. He receives a 150 euro sales bonus for the sold quantity, minus a

50 euro penalty for the deviation of the demand forecast from the actual demand, that is,

Mr. B also receives 100 euro in addition to his regular salary.

Who is happier? Mr. A (40), Mr. B (1), no difference (7).

Sales bonus Fixed Forecasting penalty

𝜋𝑆 𝑞,𝜙 𝜙 = 𝐶𝑆 + 𝑏𝐸 min(𝐷, 𝑞) − 𝑝𝑜𝐸 𝜙 − 𝐷+

− 𝑝𝑢𝐸 𝐷 − 𝜙 +

A: CS + 100 = CS + 100 – 0

B: CS + 100 = CS + 150 – 50

Total


Fixed

Fixed

Underage

cost

Overage

cost

„Lying“ Forecast error penalty Sales bonus

Loss aversion

EXPECTED UTILITY FUNCTIONS

10

𝑢𝑆 𝑞, 𝜙 𝜙 = 𝐶𝑆 + 𝑏𝐸 min(𝐷, 𝑞) − 𝛾𝐸 𝑝𝑜 𝜙 − 𝐷+

− 𝑝𝑢 𝐷 − 𝜙 +

− 𝛽 𝜙 − 𝜙 Sales

Loss aversion Lying aversion

Operations 𝑢𝑂 𝑞 = 𝐶𝑂 − 𝛾𝐸 𝑐𝑜 𝑞 − 𝐷 + + 𝑐𝑢 𝐷 − 𝑞 +


PERFECT BAYESIAN EQUILIBRIUM

11

Theorem 1 For sufficiently large 𝑝𝑜, there exists a separating equilibrium with

𝜙 = 𝜙 + 𝛿 (i) signaling strategy of sales

𝑞 = 𝜙 − 𝛿 + 𝐺−1 ∝ (iii) ordering policy of operations

𝜙 = 𝜙 − 𝛿 (ii) believe update of operations

and distortion factor

𝛿 =

> 0 for 𝑝𝑜 < 2𝑏 1 − 𝛼 − 𝛽

𝛾+ 𝑝𝑢

0 for 2𝑏 1 − 𝛼 − 𝛽

𝛾+ 𝑝𝑢 ≤ 𝑝𝑜 ≤ 2

𝑏 1 − 𝛼 + 𝛽

𝛾+ 𝑝𝑢

< 0 for 2𝑏 1 − 𝛼 + 𝛽

𝛾+ 𝑝𝑢 < 𝑝𝑜.

Corollary 1 For (reasonable values of) 𝛽 < 𝑏 1 − 𝛼 the absolute forecast error

incentive systems incentivizes demand forecast inflation

Note: γ = loss aversion factor, β = lying aversion


AGENDA

12

Motivation

Model


Validation

Discussion


TREATMENTS

Production incentives at 𝑐𝑢 = 10 and 𝑐𝑜 = 10 (implies critical ratio α = 0.5)

Market condition normally distributed with Φ ∼ 𝒩 100,30

Market uncertainty normally distributed with Ε ∼ 𝒩 0,30

13

16/0/0

14/3/3

12/7/7

10/10/10

Treatment

b/po/pu

10/6/4

10/8/2

10/10/0

10/12/2

8

8

8

8

Periods

8

8

8

8

Experiment Incentive system

Experiment 1 Sales-bonus-only




Experiment 2 Differentiated forecast error




Subjects

32

32


MODEL FIT

Model 1

Loglike

BIC

-3,533

7,107

μ𝛾

μ𝛽

3.174 (0.372)

2.199 (0.504)

Model 2 Model 3

-3,595

7,210

-3,797

7,615

4.380 (0.479)

5.870 (0.223)

Note: Standard errors reported in parentheses

14 Note: γ = loss aversion factor, β = lying aversion


AGGREGATE RESULTS

15

∝=𝑐𝑢

𝑐𝑜 + 𝑐𝑢= 0.5 Note: Critical ratio in our experiments

16/0/0

14/3/3

12/7/7

10/10/10

Treatment

b/po/pu

10/6/4

10/8/2

10/10/0

10/12/2

n/a

n/a

44.0

20.2

Standard

model

38.4

15.7

0.0

0.0










n/a

20.4

6.5

3.3

0.0

-5.5

-22.5

-15.3

Behavioral

model

Average forecast inflation

13.3

6.9

3.9

1.2

-8.4

-16.7

-14.8

Actual

40.7


TREATMENT 12/7/7

16

Market condition

Average

inflation: 6.9

0

50

100

150

200

0 50 100 150 200

Demand forecast

Behavioral model

Standard model

Demand forecast

Average

correction: 3.9 0

50

100

150

200

0 50 100 150 200

Order quantity


Demand forecast

Average

correction: -12.3 0

50

100

150

200

0 50 100 150 200

Order quantity

TREATMENT 10/10/0

17

Market condition

Average

inflation: -17.7

0

50

100

150

200

0 50 100 150 200

Demand forecast

Behavioral model

Standard model


OVERVIEW OF RESULTS OF MAIN EXPERIMENT

18

Significances of differences between model predictions and actual averages (Wilcoxon signed-rank test): *** p < 0.01, ** p < 0.05, * p < 0.1

16/0/0

14/3/3

12/7/7

10/10/10

Treatment

b/po/pu

10/6/4

10/8/2

10/10/0

10/12/2

n/a

n/a

44.0

20.2

Standard

model

38.4

15.7

0.0

0.0

40.7

13.3

6.9

3.9

Actual average

1.2

-8.4

-16.7

-14.8

Forecast distortion ϕ − ϕ

n/a

n/a

-44.0

-20.2

Standard

model

-38.4

-15.7

0.0

0.0

-38.9

-15.4

-3.9

1.0

Actual

average

3.2

7.1

12.3

11.6

Forecast correction q − ϕ

n/a

20.4

6.5

3.3

Behavioral

model

0.0

-5.5

-22.5

-15.3

n/a

-20.4

-6.5

-3.3

Behavioral

model

0.0

5.5

22.5

15.3

***

***

**

***

***

***

***

***

***

***

***

***

***

***

***


AGENDA

19

Motivation

Model


Validation

Discussion


INCENTIVE SYSTEM DESIGN FOR TRUTHTELLING FORECASTING

Model 1

3.174 (0.372)

2.199 (0.504)

2𝑏 1−𝛼 −𝛽

𝛾+ 𝑝𝑢 ≤ 𝑝𝑜 ≤ 2

𝑏 1−𝛼 +𝛽

𝛾+ 𝑝𝑢 Theorem 1 Truthtelling solution (δ = 0):

Examples b = 10 / po = 12 / pu = 10 and 10/7/5

μ𝛾

μ𝛽

2𝑏/2−2.199

3.174+ 𝑝𝑢 ≤ 𝑝𝑜 ≤ 2

𝑏/2+2.199

3.174+ 𝑝𝑢

Note: γ = loss aversion factor, β = lying aversion


RESULTS OF VALIDATION EXPERIMENT

21

0

50

100

150

200

0 50 100 150 200

Demand forecast

Market condition

Treatment 10/12/10

Average

inflation -0.2

0

50

100

150

200

0 50 100 150 200

Order quantity

Demand forecast

Average

correction -1.6

0

50

100

150

200

0 50 100 150 200

Demand forecast

Market condition

Treatment 10/7/5

Average

inflation +3.6

Order quantity

200

150

100

50

0

200 150 100 50 0

Demand forecast

Average

correction -2.9


AGENDA

22

Motivation

Model


Validation

Discussion


SUMMARY

23

Proposed including forecast error penalties in incentive system of sales

Developed and tested behavioral model for forecasting and ordering behavior

Showed that forecasts are always inflated under absolute forecast error incentive system

Showed that truthful information sharing can be achieved by differentiated forecast error

incentive system

Next: Validation at pharmaceutical company

15

20

25

30

35

40

45

50

55

60

65

70

75

80

85

11 10 09 08 06 05 04 03 02 01 12 11 10 09 08 07 06 05 04 03 02 01 12 07 12 11 10 09 08 07 06 05 04 03 02 01

-5.9

Forecast accuracy included

in sales managers

performance review at 5 %

weight since January 2010

Inflated demands

Percentage of SKUs

2008 2009 2010


OUTLOOK

24

Designing incentive systems for truthful information

sharing

Ulrich W. Thonemann

New Directions Seminar

Stanford University

April 25, 2013

Based on joint work with Lisa Scheele (University of Cologne) and Marco Slikker (Eindhoven

University of Technology). The authors gratefully acknowledge the support of the Deutsche

Forschungsgemeinschaft through the research group “Design and Behavior.”


MODEL FIT

26 Note: γ = loss aversion factor, β = lying aversion

Ulrich W. Thonemann (University of Cologne) 27

HUMAN VS. SYSTEM-GENERATED FORECASTS Share of SKUs per year with forecast > sales, in percent

SOURCE: Data of anonymous pharmaceutical company

CASE EXAMPLE

+3.6 pp +3.9 pp

2010

53,6 49,9

2009

55,4 51,5

Business unit 1 Business unit 2

+6.7 pp +5.6 pp

2010

58,2

51,5

2009

57,3 51,7

Human

System


DESIGN OF EXPERIMENT AND AGGREGATE RESULTS

28

∝=𝑐𝑢

𝑐𝑜 + 𝑐𝑢= 0.5 Note: Critical ratio in our experiments

16/0/0

14/3/3

12/7/7

10/10/10

Treatment

b/po/pu

10/6/4

10/8/2

10/10/0

10/12/2

n/a

n/a

44.0

20.2

Standard

model

38.4

15.7

0.0

0.0










n/a

20.4

6.5

3.3

0.0

-5.5

-22.5

-15.3

40.7

13.3

6.9

3.9

1.2

-8.4

-16.7

-14.8

Behavioral

model Actual

Forecast inflation


SALES BONUS ONLY INCENTIVE SYSTEM: TREATMENT 16/0/0

30

0

50

100

150

200

0 50 100 150 200

Demand forecast

0

50

100

150

200

0 50 100 150 200

Order quantity

Market condition Demand forecast

Average

inflation: 40.7

Average

correction: 38.9

Behavioral model

Standard model (n.a.)

designing incentive systems for truthful information sharing · 2 45 0 0 45 product 1 actual demand...

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