1. A Quantitative Model for Profit-Target Setting Chunming (Victor) Shi (Wilfrid Laurier Univ.) Xuan Zhao (Wilfrid Laurier Univ.) Amy Xia (Middle Tennessee State Univ., USA)

2. 2 Outline I.Background and Motivation II.A Single Division Manager III.A Risk-neutral Upper Manager and n Division Managers IV.A Target-oriented Upper Manager with n Division Managers V.Conclusions and Future Research

3. 3 I. Background and Motivation

4. 4 The Gap  Most research assumes Expected utility maximization Expected profit maximization  Target-based decision making Individuals and firms are regularly assigned targets. They make decisions to maximize the probability to achieve those targets.

5. 5  It is more natural.  It is practically important: Yahoo! in the 3 rd quarter of 2005 Reported revenue $875M (a 44% gain) Target revenue $881M Stock down 10% in after-hours trading  It is risk-averse Variance Semi-variance Critical Probability Why target-based decision making?

6. 6  In 20 larger companies, manager’s most typical goal is target return on investment (Lanzillotti, 1958).  In 728 British manufacturing firms, typical goals are target profit and target return on investment (Shipley, 1981).  For 250 MBA students and 6 professional buyers making newsvendor-type decisions, important objectives include meeting targets on sales and gross margin (Brown and Tang, 2006). Empirical Research on Target-based Decision Making

7. 7  The classical newsvendor (NV) model with a profit-target (Kabak and Schiff 1978, Lau 1980).  The two-product NV model with a profit target (Lau and Lau 1988, Li et al 1990, Li et al 1991): specific distributions.  Supply chain coordination when both supplier and retailer are profit-target oriented (Shi and Chen 2007).  Contract design when both supplier and retailer are profit maximizers and profit-target oriented (Shi and Chen, 2008). Theoretical Research on Target-based Decision Making

8. 8  Most existing research assumes exogenous targets.  Targets need to be set properly to be useful  Very limited research in target setting in OM.  Three papers indirectly relate to quantitative target setting (Lau and Lau 1988, Li et al 1990, Li et al 1991). Quantitative Target Setting

9. 9  An upper manager is in control of n divisions facing uncertain demand.  Each division manager will be rewarded based on if he can achieve a profit target.  Each division manager decides on retail price and stocking level.  The upper manager assigns a profit target to each division manager. Business Scenario

10. 10 II. A Division Manager under a Profit Target

11. 11  To decide the order quantity and retail price under a demand distribution  Multiplicative Demand Model  An individual product tends to have a high price elasticity; Chevrolet automobiles b=4.0 (Gwartney 1976) A Price-setting NV under a Profit Target

12. 12  Price affects the scale only!  Most frequently used demand specification.  Four reasons for its popularity besides it analytic appeal (Monahan et al 2004): Consistent with consumer-utility-maximization theory Nice economic interpretation Amenable to empirical analysis Good statistical fit with available sales data Multiplicative Demand Model

13. 13 A Price-setting NV under a Profit Target When bc>(b-1), higher b  lower profit prob.

14. 14  A target is said to be achievable if the probability of achieving it is larger than 0! Achievable Profit Target

15. 15 III. A risk-neutral upper-manager and n division managers

16. 16  n divisions: n products or n regions.  The risk-neutral upper manager maximizes total expected profit  Maximizes the expected profit for each division. Results Higher c  lower profit target When bc>(b-1), higher b  lower profit target.

17. 17 IV. A target-oriented upper-manager and n division managers

18. 18 The Optimization Problem

19. 19 “Fair” Target Setting  Two reasons: It is fair; especially when all managers know the targets. It leads to global optimum in some situations.

20. 20 “Fair” Target Setting

21. 21

22. 22 Target setting for two divisions

23. 23 Target setting for two identical divisions

24. 24 The case of b < 2

25. 25 The case of b < 2

26. 26 The case of b < 2

27. 27 VI: Conclusions and Future Research

28. 28  We present a first study on quantitative target setting in OM.  Optimal profit target for a division decreases in c; and decreases in b in most cases. If the upper manager is risk-neutral If the upper manager is profit-target oriented and “fair” target setting is assumed.  For the case of two identical divisions, optimal target of each division is half of the upper manager’s profit when b >=2. Conclusions

29. 29  Target setting on multiple performance measures such as profit and revenue.  Target setting in multiple periods.  Empirical studies on target setting practice. Future Research

30. 30 Questions?