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A Quantitative Model for Profit-Target Setting

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Amy Xia (Middle Tennessee State Univ., USA) 2. Outline. Background and Motivation ... include meeting targets on sales and gross margin (Brown and Tang, 2006) ... – PowerPoint PPT presentation

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Title: A Quantitative Model for Profit-Target Setting


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
  1. Background and Motivation
  2. A Single Division Manager
  3. A Risk-neutral Upper Manager and n Division
    Managers
  4. A Target-oriented Upper Manager with n Division
    Managers
  5. 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, managers 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 b4.0 (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 bcgt(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 bcgt(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
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22
Target setting for two divisions
23
Target setting for two identical divisions
24
The case of b lt 2
25
The case of b lt 2
26
The case of b lt 2
27
  • VI Conclusions and Future Research

28
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
    managers profit when bgt2.

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

30
Questions?
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