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A Quantitative Model for Profit-Target Setting

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). Outline. Background and Motivation A Single Division Manager

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A Quantitative Model for Profit-Target Setting

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  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. Outline • Background and Motivation • A Single Division Manager • A Risk-neutral Upper Manager and n Division Managers • A Target-oriented Upper Manager with n Division Managers • Conclusions and Future Research

  3. I. Background and Motivation

  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. Why target-based decision making? • It is more natural. • It is practically important: Yahoo! in the 3rd 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

  6. Empirical Research on Target-based Decision Making • 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).

  7. Theoretical Research on Target-based Decision Making • 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).

  8. Quantitative Target Setting • 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).

  9. Business Scenario • 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.

  10. II. A Division Manager under a Profit Target

  11. A Price-setting NV under a Profit Target • 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)

  12. Multiplicative Demand Model • 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

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

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

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

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

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

  18. The Optimization Problem

  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. “Fair” Target Setting

  21. Target setting for two divisions

  22. Target setting for two identical divisions

  23. The case of b < 2

  24. The case of b < 2

  25. The case of b < 2

  26. VI: Conclusions and Future Research

  27. Conclusions • 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.

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

  29. Questions?

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