Transcript 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)

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
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
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I. Background and Motivation
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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.
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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
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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).
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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).
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Quantitative Target Setting
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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).
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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.
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II. A Division Manager under a
Profit Target
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A Price-setting NV under a Profit Target
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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)
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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
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A Price-setting NV under a Profit Target
When bc>(b-1), higher b  lower profit prob.
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Achievable Profit Target

A target is said to be achievable if the probability
of achieving it is larger than 0!
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III. A risk-neutral upper-manager and
n division managers
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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.
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IV. A target-oriented upper-manager and n
division managers
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The Optimization Problem
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“Fair” Target Setting
 Two reasons:
It is fair; especially when all managers know the
targets.
It leads to global optimum in some situations.
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“Fair” Target Setting
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Target setting for two divisions
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Target setting for two identical divisions
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The case of b < 2
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The case of b < 2
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The case of b < 2
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VI: Conclusions and Future Research
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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.
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Future Research
 Target setting on multiple performance measures
such as profit and revenue.
 Target setting in multiple periods.
 Empirical studies on target setting practice.
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Questions?
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