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Designing Contracts for Irrational but Predictable Newsvendors
Michael Becker-Peth, Ulrich W. ThonemannUniversity of Cologne
Elena KatokPenn State University
Presented at the Wilfrid Laurier University, April 15, 2011
Agenda
• Motivation
• Traditional SCM Contract Design
• Predicting Ordering Behavior
• Contract Optimization
• Discussion
The three purposes of laboratory experiments in economics
1. Test and refine existing theory
2. Characterize phenomena leading to new theory
3. Wind tunnel testing of new institutional designs
Alvin E. RothGeorge Gund Professor of Economics and Business AdministrationHarvard UniversityRoth (1995) in the Introduction to
the Handbook of Experimental Economics
Laboratory Experiments in Operations Management
• …are often used for the same kinds of purposes.
• But OM is ultimately a practical field.• Our models and insights should be
useful for business operations.• Lab experiments can contribute to
behavioral mechanism design.
This talk is about how what we learned about the Newsvendor problem can be used to design supply chain contracts that work better.
Background: the Newsvendor Problem
• A decision-maker (“retailer”) must decide on the order amount for the upcoming selling season.
• Customer demand distribution is F() but it’s realization d~F() is not known until after the order is placed.
• Application: production/distribution time is longer than the lead time.
• Motivation: the Newsvendor problem is the building block of most stochastic inventory theory.
The Newsvendor problem solution
• Assume the retailer buys S units for w per unit, sells min(d,S) units for r per unit, and unsold S-min(d,s) units are salvaged at b per unit.
• The optimal solution balances the costs of ordering too much vs. too little: Known as the
“critical ratio”, or “critical
fractal”
The Newsvendor Behavior in the Laboratory
1551 10
Order QuantityPercentage of max demand
Round
Optimal order quantity
Average demand
Robust Findings
Orders biased towards mean demand
No risk aversion
No/slow learning
Explanations- Anchoring - Ex-post order error minimization- …
8
Typical Average Order Quantities
Round
ManagersMaster StudentsUndergraduate Student
75 = Optimal Orders
50 = Mean Demand
Mean order quantities
Result Essentially, all subjects behave “irrationally”, but predictably
Source: Bolton, Ockenfels, and Thonemann (2008)
The Buyback Contract
RetailerManufact.Cost c
Reveneue r
Contract Wholesale
price w Buyback
price b
Stackelberg Game
Manufacturer designs contract
Retailer uses Newsvendor model to determine order quantity
Manufacturer knows this and designs contract to maximize his expected profit
The first-best contract
Newsvendor Orders
First-Best Order
(1)
(2)
If the Newsvendor orders according to (1), then for any c ≤ w ≤ r, the channel can be coordinated by setting the buyback at:
(3)
The Behavioral Model
• Do average orders always fall between mean demand and optimal order?
• Are average orders independent of contract parameters?
Experiment 1
• Classroom experiment (not paid)– Demand~U(0,100)– CR = 0.5; S* = 50– N = 53, within subject
• Contract 1: r=100, w = 50, b = 0, S = 41.2• Contract 2: r=100, w = 80, b = 60, S = 59.4
Orders depend on contract parameters and do not necessarily fall between mean demand and optimal order
Note: all differences are highly significant (p<0.001)
Evaluation of Elementary Outcomes
• Revenues in the buyback contract:– From sales– From returns
• Do subjects value these two sources of income the same way?
Experiment 2
• Mr. A and Mr. B buy newspapers from a supplier and sell them during the day. Unsold newspapers are returned to the supplier.
• Mr. A generates 200 Euro sales by selling newspapers to customers. He has newspapers left over at the end of the day and returns them to the supplier. He receives 0 Euro for all the newspapers he returns.
• Mr. B generates 150 Euro sales by selling newspapers to customers. He has newspapers left over at the end of the day and returns them to the supplier. He receives 50 Euro for all the newspapers he returns.
• Who is happier?
Mr. A (18), Mr. B (51), no difference (39)?
Note: all differences are highly significant (p<0.001)
Mental Accounting (Thaler 1999)
• The source of income matters– People value and use winning an office
pool differently from an income tax refund.• We model the different values
associated with income from sales and returns by multiplying the income from returns by a factor γ.
Combination of Elementary Outcomes
• Experiment 1 subjects were asked to express the rationale for their decision:– 46% based their decision on both (r-w) and (b-w).– 78% based their decision on one or the other of the
two.– Much fewer mentioned individual contract
parameters: 11% mentioned b, 7% w and 2% r
Most subjects reframe the problem and base their decision on the profit margin and the cost of unsold products—component of the newsvendor problem.
The Model
Order Quantity:
(r-w) is the revenue, the Gain from Sold units
(w-b) is the Loss associated with Un-Sold units.
Let β be the loss aversion parameter.If income from returns is valued at γ, the utility of an un-sold unit is (w-γb)
If α is the anchoring factor, the order is anchored on mean demand μ
Testing the model
• Experiment 3:– D~U(100,200), CR = 0.5, S* = 150,N = 76– Contract I: r=100, w = 50, b=0, S = 139.6– Contract II: r=100, w = 80, b = 60, S = 157.7
• Experiment 4:– D~U(0,100), CR = 0.25, S* = 25,N = 66– Contract I: r=10, w = 70, b=0, S = 44.9– Contract II: r=100, w = 90, b = 60, S = 62.1
• Experiment 5:– D~U(0,100), CR = 0.75, S* = 75,N = 56– Contract I: r=100, w = 25, b=0, S = 52.0– Contract II: r=100, w = 70, b = 60, S = 66.2
Note: all differences are highly significant (p<0.001)
These results are all consistent with the model in which 0<α<1, β>1, γ>1
A comprehensive experiment
31 subjects 28 decisions with 1
feedback r=100
Experiment Model Parameter
Population level Individual level
Out-of-sample test
Channel profit maximizing
Compare the performance of contracts using behavioral model vs. standard model. w
5 20 35 50 65 80 95
0 x x x x x x x
15 . x x x x x x
30 . . x x x x x
b45 . . . x x x x
60 . . . . x x x
75 . . . . . x x
90 . . . . . . x
w
5 20 35 50 65 80 95
0 95 80 65 50 35 20 5
15 . 94 76 59 41 24 6
30 . . 93 71 50 29 7
b 45 . . . 91 64 36 9
60 . . . . 88 50 13
75 . . . . . 80 20
90 . . . . . . 50
Acutal ordersNewsvendor-Model
Results OverviewAverage order quantities
w
520
35
50
65
80
95
084
59
45
33
23
18
10
15 .
78
60
43
28
20
14
30 . .
77
50
37
26
16
b45 . . .
72
51
29
16
60 . . . .
71
48
19
75 . . . . .
66
31
90 . . . . . .
57
Comparing Optimal and Average Orders
0
75 030
60
90 075
0
15
30
45
60
75
90
Optimal order quantity
Actual average
orderquantity
b
Aggregate Estimate
• We used the data from all 31 subjects’ 28 decisions to estimate parameters using MLE:
Note: all parameters are significantly different from 0 (p<0.001)
SSR = 238,582, which is much lower than the SSR of 369,938 for the standard model.
An Out-of-Sample Test
• Are contracts that use the behavioral model really better at inducing some specific order?
• The order we want to induce in this experiment is first-best.
• Phase 1: Participants place orders for a range of CRs and we use this data to estimate their parameters.
• Phase 2: Use these parameters to design behavioral contracts to incentivize desired order quantities.
• Compare the resulting channel profit under the newsvendor contracts and behavioral contracts.
The Contracts Used…r=100
30 new subjects exposed to 19 (out of the 28 original) CRs.
Phase 2 ResultsCR = 0.20, 0.29, 0.41, 0.50, 0.63, 0.71, 0.76 and 0.80.
Depending on individual parameters, it is not always possible to incentivize some order quantities
Behavioral contracts resulted in 19.5% higher expected channel profit than the newsvendor contracts assumingr=100, c = 100((w-b)/(100-b))
Structural Insights
• Optimal buyback price is decreasing in α for CR<0.5 and increasing in α for CR > 0.5
Structural Insights
• Optimal buyback price is always increasing in β.
Structural Insights
• Optimal buyback price is always decreasing in γ.
The practical message from this work
• Our behavioral model, based on mental accounting and loss aversion, is a more accurate prediction of human behavior than the newsvendor model.
• Contracts designed with the use of the behavior models are likely to perform better than contracts designed assuming newsvendor behavior.
What’s new in this paper
• Behavioral findings– Contract parameters themselves affect
behavior, not just the CR.– Deviation from rationality is predictable.– A model based on mental accounting and
loss aversion is accurate– There is a great deal of heterogeneity in
human behavior. • Engineering approach to contract
design
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