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)

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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 assumesExpected utility maximization

Expected profit maximization

Target-based decision makingIndividuals and firms are regularly assigned targets.

They make decisions to maximize the probability to achieve those targets.

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It is more natural.

It is practically important: Yahoo! in the 3rd quarter of 2005

Reported revenue $875M (a 44% gain)Target revenue $881MStock down 10% in after-hours trading

It is risk-averseVarianceSemi-varianceCritical Probability

Why target-based decision making?

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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

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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

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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).

Quantitative Target Setting

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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

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II. A Division Manager 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)

A Price-setting NV under a Profit Target

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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 theoryNice economic interpretationAmenable to empirical analysisGood statistical fit with available sales data

Multiplicative Demand Model

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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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A target is said to be achievable if the probability of achieving it is larger than 0!

Achievable Profit Target

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

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n divisions: n products or n regions. The risk-neutral upper manager maximizes total

expected profitMaximizes the expected profit for each division.

Results

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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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

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Target setting on multiple performance measures

such as profit and revenue. Target setting in multiple periods. Empirical studies on target setting practice.

Future Research

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Questions?