1. Designing Contracts for Irrational but Predictable Newsvendors Michael Becker-Peth, Ulrich W. Thonemann University of Cologne Elena Katok Penn State University Presented at the Wilfrid Laurier University, April 15, 2011

2. Agenda Motivation Traditional SCM Contract Design Predicting Ordering Behavior Contract Optimization Discussion

3. 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. Roth George Gund Professor of Economics and Business Administration Harvard University Roth (1995) in the Introduction to the Handbook of Experimental Economics

4. 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.

5. 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.

6. 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”

7. The Newsvendor Behavior in the Laboratory 155110 Order Quantity Percentage 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. 8 Typical Average Order Quantities Round Managers Master Students Undergraduate Student 75 = Optimal Orders 50 = Mean Demand Mean order quantities Result Essentially, all subjects behave “irrationally”, but predictably Source: Bolton, Ockenfels, and Thonemann (2008)

9.  The Buyback Contract Retailer Manufact. 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

10. 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)

11. The Behavioral Model Do average orders always fall between mean demand and optimal order? Are average orders independent of contract parameters?

12. 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)

13. Evaluation of Elementary Outcomes Revenues in the buyback contract: –From sales –From returns Do subjects value these two sources of income the same way?

14. 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)

15. 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 .

16. 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.

17. 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 , the utility of an un-sold unit is (w-b) If  is the anchoring factor, the order is anchored on mean demand 

18. 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 1, >1

19. 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 5203550658095 0xxxxxxx 1515.xxxxxx 3030..xxxxx b 4545...xxxx 6060....xxx 7575.....xx 9090......x

20. w 5203550658095 0 80655035205 15.94765941246 30..937150297 b45...9164369 60....885013 75.....8020 90......50 Acutal ordersNewsvendor-Model Results Overview Average order quantities w 5 2020 3535 5050 6565 8080 9595 0 8484 5959 45453 2323 1818 1010 1515. 7878 6060 4343 2828 2020 1414 3030..7 5050 3737 2626 1616 b 4545... 7272 5151 2929 1616 6060.... 7171 4848 1919 7575.....6 3131 9090...... 5757

21. Comparing Optimal and Average Orders 0 75 0 30 60 90 0 75 0 15 30 45 60 75 90 Optimal order quantity Actual average order quantity b

22. 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.

23. Predicted and Actual Mean Orders

24. 24 Order Variability

25. Individual Estimates

26. Example: Predictions for Subject 26

27. 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.

28. The Contracts Used… r=100 30 new subjects exposed to 19 (out of the 28 original) CRs.

29. Individual parameters from the confirmation experiment

30. Phase 2 Results CR = 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 assuming r=100, c = 100((w-b)/(100-b))

31. Structural Insights Optimal buyback price is decreasing in  for CR 0.5

32. Structural Insights Optimal buyback price is always increasing in .

33. Structural Insights Optimal buyback price is always decreasing in .

34. 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.

35. 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