Marketing Leners 3:4, (1992): 393-393 © 1992 Kluwer Academic Publishers, Manufactured in the Netherlands.

Optimal Multiple-Objective Marketing Strategies STEPHEN S. BELL Stern School o f Business, Neu, York University, New York, New York 10003

GREGORY S. CARPENTER* J. L. Kellogg Graduate School o f Management, Northwestern University, Evanston, IL 60208

Key words: Marketing Strategy, Multiple-Objective Decision Making

[June 1992]

A b s t r a c t

Brand managers often design strategies to achieve multiple objectives, but how managers choose among alternatives and consequently how multiple objectives should be incorporated into models of marketing strategy have received little attention. This paper explores the incorporation of mul- tiple objectives into models of optimal marketing strategies. We focus on one marketing strategy issue, defensive marketing strategy, and develop a multi-objective marketing strategy model. We derive optimal changes in price and advertising spending given the defending brand's multipie objectives. Our analysis produces new descriptive insights about the links between decision mak- ing and competition, as well as new insights into defensive marketing strategy. We also discuss the potential for fl~ture work along these lines and extensions in other areas of marketing strategy.

Brand managers often design marketing strategies to achieve multiple objectives. For example, Kotler (1991) identifies a number of different objectives for market- ing strategies at different stages of the product life cycle. When launching a new product, generating consumer trial, awareness, and repeat purchase are critical to generating growth and, to a lesser degree, profits. In mature or declining markets, brands offen seek greater profits rather than high growth, although they may gen- erate higher profits through increasing usage among existing customers or by ex- tending the product line to generate greater volume, in designing defensive mar- keting strategies, brand managers often seek high profits, but often seek to preserve sales or market share. For instance, facing intense new competition in the U.S, luxury car market, BMW has explicitly stated its desire to maintain mar- ket share (Ross 1989).

Analyses of marketing strategy have for the most part assumed a single objec- tive. In the case of new product strategy, theoretical modets analyze the optimal positioning of a brand to maximize profits (e.g. Carpenter and Nakamoto 1990, Choi, DeSarbo and Harker 1990, Lane 1980; one exception is Carpenter and Nak-

*Our thanks to John Hauser, Don Lehmann, and D. Sudharshan for comments. Financial support provided to the second author by the Richard M. Clewett Research Professorship is gratefully acknowled~ed.

384 S T E P H E N S. B E L L A N D G R E G O R Y S. C A R P E N T E R

amoto 1992). On the other hand, empirical analyses of new products model con- sumer reaction using conjoint analysis, multidimensional scaling and other tech- niques to evaluate sales rather than profit potential (e.g. Urban and Hauser 1980, Wind 1982). In the case of defensive marketing strategy, Hauser and Shugan (1983), subsequently dubbed "Defender," identify profit-maximizing adjustments to the defending brand's marketing mix using an empirically-grounded consumer model of perceptually differentiated brands.

Expanding conventional models to include multiple objectives raises challeng- ing issues about decision making. A growing number of empirical studies on de- cision making show that choosing among multidimensional alternatives often in- volves heuristics and biases such as anchoring and adjustment or elimination by aspect (e.g. Tversky and Kahnemann 1974). When managers choose among var- ious strategic alternatives based on multiple objectives, similar biases and heuris- tics may be operating. For example, previous market share or profit levels may become anchors or reference points in evaluating alternatives, as BMW's desire to maintain market share suggests. Multi-objective marketing strategy models re- flecting these aspects of decision making should have both high descriptive and normative value.

This paper explores the impact multiple objectives have on marketing strategy. We focus on one strategic marketing problem, defensive marketing strategy, and consider the impact on pricing and advertising decisions if the defending brand seeks to maximize profit and to maintain its market share (or some significant portion of it). To explore the impact of these objectives on defensive strategies, we employ the Defender consumer model (Hauser and Shugan 1983). This model is particularly appropriate because it performs weil in empirical tests (Hauser and Gaskin 1984) and the insights it generates are robust across a variety of assump- tions about competition (Kumar and Sudharshan 1988, Hauser 1988, Hauser and Wernerfelt 1988). Using the Defender consumer model, we construct a multi-ob- jective defensive strategy model that reflects the nature of defending manager's decision making. We solve it to derive optimal multi-objective pricing and adver- tising strategies and we compare those with the profit-maximizing strategies.

Our analysis and results have significant descriptive value. The insights for competition are especially important. Under traditional assumptions about man- agerial decision making, competition is the interplay of decisions made by fully informed, perfectly rational managers seeking maximum profit and consumers seeking maximum utility. Mounting evidence suggests real consumers behave dif- ferently. Presumably, so do real managers. Departures from the traditional as- sumptions by managers affect the strategies they choose and ultimately the pro- cess of competition. By relaxing traditional assumptions about managers, we draw a closer tink between decision making and marketing strategies, which pro- vides a richer description of competition.

Our analysis also provides new normative insights in the area of defensive mar- keting strategy, extending Hauser and Shugan (1983). Our analysis shows that under identical market conditions multi-objective defensive strategies will differ considerably from profit-maximizing defensive strategies. Some differences such

M U L T I P L E - O B J E C T I V E M A R K E T I N G S T R A T E G I E S 385

as simple qualitative differences are of course to be expected. However , we show that considering multiple objectives produces insights that are qualitatively and quantitatively different. We also show that the process of creating defensive mar- keting strategy differs.

We begin with a review of the Defender consumer model. We extend it by in- corporating multiple objectives and we derive the pricing and advertising reac- tions to new entry. We conclude with a discussion of potential directions for future work in the area of multi-objective marketing strategy.

1. Defending Market Share and Profit

1.1. Defender consumer model

The Defender consumer model, summarized in the figure (a), shows the position- ing of three detergent brands (Ivory, Joy, Ajax) in a two dimensional space and the fraction of buyers who prefer each. The market share for each brand is

where %_ and % + are the angles shown, and f(cO is the distribution of consumer tastes. For example, numbering brands counterclockwise, the market share of

I cxl2 fc~ ~23 Ajax is m~ = fled da, of Joy is m2 = f(o0 &x, and so on. J0 12

Figure 1. Defender c o n s u m e r model for a th ree-brand marke t (a) before and (b) af ter en t ry of At tack.

386 STEPHEN S. BELL AND GREGORY S. CARPENTER

The entry of a new brand, represented in the figure (b), shows Attack has en- tered competi t ively and lower adjacent to Ajax. At tack ' s entry reduces the marke t share of the adjacent brand because now the lower bound on its share, denoted by %n, is greater than its pre-entry lower bound, %i (i.e., c9~ > %»). For example , the share of Ajax in figure (b) falls from [%2 - 0]/90° to [%2 - O t n I ] / 9 0 ° if the distribution of consumer tastes is uniform. Fur thermore , if spending on awareness advertising is reduced, then market shares adjusted for awareness will fall further.

Like most other previous analyses, we consider " rec tangular" markets in which tastes are uniformly distributed. This enables us to focus more clearly on the competi t ion between the defender and the entrant, and regularity can be relaxed for empirical application (e.g., Hause r and Gaskin 1984). We also limit our atten- tion to one non-price market ing mix variable, advertising. Generalizations to dis- tribution and other promotional expenditures is straightforward.

1.2. Brand decision model

If the defending brand seeks profit alone, its objective function can be simply stated as

Max II(p,k) = N(p - c)m(p)A(k) - k. (1)

where II(p,k) is the profit of the defending brand, N is the number of buyers; p the defending brand 's price; c is its cost; ra(p) = [%j+ - &]/90 ° is its market share; and cC is a paramete r that denotes the defending brand 's lower market boundary, such as c% = ot ° after entry and a ° = %j_ before entry; A(k) is its awareness level, and k is its awareness-advert is ing expenditure.

If both profits and market share are sought, a number of objective functions are reasonable. One possibility is a compensa to ry model in which managers seek to maximize

v = y II(p,k) + ( 1 - y ) s(p,k) (2)

where s(p,k) = A(k)m(p) is the defending brand 's market share adjusted for awareness and y is a constant such that 0 -< y -< 1. Equation (2) implies that profit and marke t share are traded oft in a constant manner. This may be suitable in some situations, but in the case of defensive marketing strategy, our discussions with managers suggest that the pre-at tack market share takes on a special signif- icance - it becomes a reference point or anchor (Tversky and Kahnemann 1974). As such, a suitable objective function should reflect manager ' s desire to achieve high profits and to preserve the pre-at tack market share or some significant por- tion of it. This suggests that managers will choose the highest profit s trategy among all strategies that satisfy their marke t share objective. More formally, this is simply

MULTIPLE-OßJECTIVE MARKETING STRATEGIES 387

Max H(p,k) subject to s(p, k) >- s ° (3)

where s ° is the defending brand's target share. In equation (3), s ° is a parameter that can vary from zero to one. Its value

reflects the target share set by the defending brand's managers. This target can be set above or below the sales level associated with the profit-maximizing defen- sive marketing strategy, s*. We focus on the case in which s ° > s*, because man- agers exhibit a preference for holding larger not smaller market shares. Further- more, for s ° > s*, there are two possible sub-cases; we focus on the case where actual sales equal the target value (that is, s = s °) because out interest is in ex- amining how a binding market share objective influences the defending brand's strategy. We also examine defense against lower adjacent, competit ive new brands; generalization to defending against upper-adjacent entrants is immediate.

2. Optimal marketing mix reaetions

2.1. Pricing strategy

One property of the solution to equation (3) illustrates the first important differ- ence between profit-maximizing defensive strategies and those designed to achieve multiple objectives. Rather than suggesting qualitative or quantitative dif- ferences in actual defensive strategies, our first result indicates an important dif- ference in the process by which defensive strategy is formulated:

PROPOSlTION I: PRICE-ADvERTIS1NG COUPLING. Thê optimal multi-objective de- fensive price and advertising level depend on each other, j

Proposition 1 has managerial implications for the process by which defensive strategy is formulated. If the sole objective of the defending brand is to max[mize profit, then its pricing and advertising decisions are decoupled, given the nature of the response model used here (Hauser and Shugan 1983). The immediate prac- tical consequence of decoupling is that pricing and advertising decisions can be made independently. This suggests a sequential decision process with price set first, followed by the advertising budget. If so, it may be useful to make the price decision at a higher organizational level because it precedes the advertising bud- geting decision and thus is, in one sense, more important. In contrast, Proposition 1 shows that pricing and advertising decision must be made simultaneously if market share and profit are objectives. Thus, the selection of brand objectives will have implications for the optimal process of strategy formulation.

Multiple objectives will also lead to important quantitative differences in defen- sive strategy. The impact of entry on optimal pricing in regular, 2 rectangular mar- kets is unambiguous if the defending brand seeks both market share and profit.

388 STEPHEN S. BELL AND GREGORY S. CARPENTER

PROPOSITION 2" DEFENSIVE PRICING. I f c o n s u m e r t a s t e s are uniform@ distrib- uted and the market is regular, then the optimal multi-objec- tive defensive pricing strategy includes reducing price. How- erer, the optimal multi-objective defensive price never exceeds the proß't-maximizing defensive price.

Proposition 2 provides useful insights into defensive pricing and draws an in- teresting comparison with the profit maximizing case. Reducing price is a useful rule of thumb for brands pursuing either profits alone or profits and market share in an unsegmented market. Thus, lowering price in response to new entry is an optimal rule of thumb regardless of whether the objective is profit alone or market share and profit. However, the extent of price decrease depends on one's objec- tive. Maintaining market share requires greater price reductions than those re- quired for maximizing profit.

The logic of this result is straightforward. The entry of Attack leads to lower sales for the defending brand; lower sales reduce optimal prices if the defending brand is maximizing profit (Hauser and Shugan 1983). Similar results are obtained in models of spatial competition between established competitors and between early and late entrants (e.g. Carpenter 1989, Carpenter and Nakamoto 1990, Hau- ser 1988). If the defending brand seeks to maintain some or all of the share threat- ened by Attack, it can cut price further to attract new buyers from other compet- itors or retain old buyers who otherwise would be lost to Attack.

2.2. Advertising strategy

For advertising strategy, however, the rules of thumb change with the defending brand's objective:

PROPOSITION 3: DEFENSIVE ADVERTISING. I f consumer tastes are uniformly dis- tributed and the market is regular, the optimal multi-objective defense advertising strategy includes increasing spending on awareness advertising if the market size does not decrease.

Proposition 3 shows that different objectives lead to fundamentally different recommendations for advertising spending. The profit-maximizing defender opti- mally reduces spending on awareness advertising. The intuition behind such a result is that the new competitor has stolen some market share, leaving fewer buyers for the defending brand. Fewer buyers require fewer advertising dollars; moreover, smaller margins reduce the incentive to advertise by reducing the ben- efit of each sale. However, if one seeks to maintain market share, higher adver- tising spending is required. Awareness tevels among potential Attack buyers as well as arnong buyers of other brands must be increased to maintain the defending

MULTIPLE-OBJECTIVE MARKETING STRATEGIES 389

brand's market share. These differences in optimal advertising spending levels are due entirely to differences in the defending brand's objectives.

Propositions 2 and 3 are consistent with observation. Consider the early 1987 introduction of Kellogg's Nutrigrain Nuggets into a market dominated by Post Grape Nuts. Faced with the loss oflucrative market share it had held for 90 years, Post reacted aggressively, temporarily cutting price by 50% (through a buy-one- get-one-free offer) and boosting its promotional budget nearly 50% from $29 mil- lion the previous year to over $43 million in 1987 (Woodland i988). Tytenol's and Excedrin's management reacted in a similar way to Bristol Myers' introduction of Nuprin (Hamilton 1988). Defensive strategies in these cases are consistent with the results derived in the case in which the defending brand seeks both high profit and the retention of its pre-attack market share.

Summary

If maintaining market share is important to the defending brand, the direction of price change remains the same for either profit-maximizing or share-maintaining defensive strategies, but the magnitude of the price change differs. In contrast, optimal multiple-objective defensive advertising differs qualitatively. Further- more, out analysis shows that the process of formulating defensive strategy differs depending on the objectives sought.

3. Future work and conclusion

3.1. Future work

These findings suggest a number of research topics about how managers make decisions if they have multiple objectives. Previous studies show that consumer decision making is highly context dependent. Orte might suspect the same will be true of managerial decision making. Among brand managers, in the case of new product introduction, greater awareness might compensate for giving up some consumer trial, but in the case of setting market share and profit targets, conjunc- tive choice may prevail. These objectives may be strongly influenced by recent experience. Eli Lily, the pharmeceutical giant, has enjoyed over 100 quarters of consistent growth in profits. It seems plausible to suspect that the previous quar- ters' profits will play a large role in Eli Lily's strategy formulation. Next Com- puter, lacking that same history, may make decisions with complete disregard for similar numbers and thus use entirely different decision rules. Exploring how the context - competitive position and culture - affect decision making would appear to be a potentially rich research direction.

390 STEPHEN S. BELL AND GREGORY S. CARPENTER

Incorporating these different decision rules into models of competitive strategy suggests other possibilities. Two brands in the same market may use different decision rules for selecting their objectives, have different objectives as a result, and thus compete in a fundamentally different way. The automobile and consumer electronics industries would appear to be examples of competition with different objectives. Extending models of brand strategy to cases in which decision rules or objectives differ across competitors would therefore appear to be an important and potentially fruitful direction for future work.

Another interesting area may be to examine objectives and the decision making process. An implicit assumption in many dynamic models of marketing strategy is that buyers and managers have fixed, unchanging objectives and preferences. Recent studies suggest that preferences may evolve with the market (e.g. Carpen- ter and Nakamoto 1989) or more generally that preferences may be constructed to respond to a particular situation as opposed to being revealed by the situation (e.g. Tversky, Sattath, and Slovic 1988). Managers' preferences and objectives may change given the context of competition, evolve over time, and thus be con- structed as opposed to fixed. Examining and incorporating these dynamic ele- ments of preferences and objectives would likewise be a future direction for mar- keting strategy models.

3.2. Conclusion

Achieving multiple objectives is often an important goal for marketing strategies. Extending models to reflect this can have significant implications for the insights generated by the analysis. These objectives, the foundation of models of market- ing strategy, have received surprisingly little attention. Recent research on tradi- tional assumptions about consumer decision making suggests that managerial de- cision making may be a fruitful area for research. Our results suggest that the impact on optimal marketing strategy could be significant.

Notes

1. All proofs appear in the Appendix. 2. See Hauser and Shugan (1983).

Appendix

Proof of proposition 1

Let Z = (p - c)Nm(p)A(k) - k + X[s ° - mA] be the Lagrangian implied by equation (3) for the case in which s = s °. Then 0Z/0p = 0Z/0k = 0Z/0X = 0 implies that

MULTIPLE-OBJECTIVE M A R K E T I N G STRATEGIES 391

OZ/Op = N m + [(p - c ) N - X](Om/Op) = 0 ( A . I )

OZ/O/k = [(p - c ) N - X ] m A ' - 1 = 0 (A.2)

0Z/0X = s ° - m A = 0. (A.3)

N o t i n g tha t 0m/0p = - N m 2 A ' a n d tha t [(p - c ) N - X] = 1 / m A ' , we c a n s o l v e

fo r t he o p t i m a l p r i c e a n d a d v e r t i s i n g o u t l a y as

pO = c + (X/N) + ( I / N m A ' ) k o = [(pO _ c ) N - X ] m G A

w h e r e G = A ' ( A / k ) . C l e a r l y pO d e p e n d s on k ° t h r o u g h A ' ( k °) and k ° is a f u n c t i o n

o f p°. Q. E. D.

Lemma

G i v e n a unique pO a n d k °, g(p°, k°; «° , s °) d e f i n e s pO a n d k ° as an i m p l i c i t f u n c t i o n

o f o~ ° a n d s ° w h e r e

g ( p ° , k ° ; o ¢ ° , s ° ) = H d w ° + h ~ d « ° + h_,ds ° = 0

w h e r e H is t he b o r d e r e d H e s s i a n m a t r i x o f Z (p , k, X), w ° = (k °, pO), a n d h, a n d

h 2 a r e v e c t o r s o f d e r i v a t i v e s o f ( A . I ) t h r o u g h (A.3) w i t h r e s p e c t to OL ° a n d s ° re- s p e c t i v e l y .

Proof. T o t a l l y d i f f e r e n t i a t i n g (A. 1) through (A.3) produces g(p°, k°; o~ °, s °) = 0 as d e f i n e d a b o v e . Q. E . D.

Proof of proposition 2

L e t ds ° = 0 so tha t H d w ° = - h a de, °, w h i c h c a n be s o l v e d fo r dp°/do~ °

as

dp° /d~~, = A - I -Zo«o 0 Zpxl - Zko Zkk z - Z x o Zxk O kx

392 S T E P H E N S. BELL AND GREGORY S. C A R P E N T E R

where A = det(H) > 0. Expand ing this de te rminant p roduces

dp°/dot = A-I(Om/Oot°)Nm2[(A')2(I + A) - A"]

where 2x-~ > 0, óm/O~ ° <- 0; N, m 2 -> 0, and (A')2(1 + A) - A"-> 0. Therefore dp°/d~ ° -< 0. Le t p°(«jn) and p°(c%) denote the opt imal price given %o and ~»_ re- spectively. Brand n is compet i t ive and lower adjacent so e% > %j_. But dp°/doÜ -< 0 so that pO (%n) -< pO (C~~j.).

Next , cons ider the relat ionship be tween p* and p°, where p* is the prof i t -max- imizing defens ive price. To do so we der ive dp°/ds ° by letting d & = 0, and solving H dw ° = - h 2 ds ° for

dp°/ds ° = A 1 0 0 Zvx

0 Zkk Zkh " -- 1 ZXk

which can be simplified to dp°/ds ° = A - ~ N m 2 A A '' _< 0. Le t p°(s°) denote the op- timal mult i -object ive price given s °. I f s ° = s*, equa t ion (1) reduces to an uncon- s trained model so pO = p , . I f s ° -> s*, then pO < p , because dp°/ds ° -< 0. Therefore , pO < p , for all s ° -> s*. Q. E. D.

PIvo f o f proposition 3

Let t ing ds ° = 0, H dw ° =

zpp dkO/daO = Æ I Zxp

-- h I da°; solving for dk°/da ° yields

- Zp«o Zpa -- Zkeo _ Zx~° Ôkx

which can be expanded and simplified to p roduce

dk°/dc~ = A-~(0m/aed)[m" + (A - I)(A')2N2m 3]

Hefe A > 0, 0m/0c~ ° --< 0; m" = 0m2/Op 2 --< 0 for regular, rec tangular marke ts , and (A - 1)(A')2N2m 3 <- 0 so that dk°/dc~ ° -> 0. Le t k°(otjn) deno te the opt imal adver- tising expendi ture given 0% and k°(cq>) given «jj_. Brand n is compet i t ive and lower adjacent so e% > «jj_ and, by our analysis , dk°/d« ° >- 0 so that k°(%1) -> k °

(Otii_). O . E . D .

MULTIPLE-OBJECTIVE MARKETING STRATEGIES 393

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