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Channel Optimization in Complex Marketing Systems

Author(s): Marcel Corstjens and Peter DoyleSource: Management Science, Vol. 25, No. 10 (Oct., 1979), pp. 1014-1025Published by: INFORMSStable URL: http://www.jstor.org/stable/2630763 .

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MANAGEMENT SCIENCEVol. 25, No. 10, October 1979

Printed in U.S.A.

CHANNEL OPTIMIZATION IN COMPLEX MARKETINGSYSTEMS*MARCEL CORSTJENSt AND PETER DOYLE$

Channel optimization in multiple-channel systems is a basic problem in marketing and onewhich has not received much attention in the literature. A model is presented whichsimultaneously solves three distribution decisions-the manufacturer's choice of channels(channel strategy), the number of outlets to operate within each channel (channel intensity),and the pricing structure between channels (channel management). The general form of thismodel is not solvable by conventional programming techniques because it is intrinsicallynonconvex. The paper shows- how signomial geometric programming can provide a theoreti-cally attractive and practical solution procedure. The model is estimated and solved on areal-life case study and the important managerial and theoretical implications are discussed.(MARKETING-DISTRIBUTION; PROGRAMMING-GEOMETRIC; CHANNELS)

1. IntroductionThis paper presents a model for optimizing the manufacturer's allocation ofresources among a set of alternative distribution channels. This is a problem which isof central importance in marketing, but it is one which has proved insoluble byconventional programming procedures. Here we show that geometric programmingcan now provide a theoretically attractive and practical method for resolving it.

Specifically, the paper presents a model which simultaneously solves three distributiondecisions-distribution strategy, distribution intensity and distribution management.Distribution strategy refers to the manufacturer's selection of channels to servedesignated end markets. Distributionintensityis the decision on the number of outletsto be operated within each of the channels selected. Distribution management is themanufacturer's use of price and other marketing mix variables to influence theperformance of the units.constituting each channel.The fact that many manufacturers today buy and sell through multiple channelstructures has not received much attention in the literature. Perhaps the mostimportant reason for this is that any practical profit maximizing model for amanufacturer employing simultaneously several channels is too complex to be opti-mized by conventional nonlinear programs. In addition, writers in the area haveassumed that multiple channel systems are either rare or ineffective (e.g. [10, p. 659]).In fact, as shown below, even the single channel optimization problem-how to selectone channel from among two or more alternatives-has not been modeled in a waysuitable for practical estimation and application. As has been noted elsewhere [19, p.225], there has been relatively little research into distribution models which seek tomaximize the profits of the firm.Multiple-distribution channels have become increasingly important, however [33].One reason is the spread of vertically integrated distribution channels as manufactur-ers have integrated into wholesaling and retailing. Three motives for such investmentshave been the desire to secure market share, to better control the operations ofintermediaries selling the manufacturers' merchandise and to use excess funds gener-

* Accepted by Donald R. Lehmann; received December 12, 1978. This paper has been with the authors 3months for 1 revision.tINSEAD, France.*Bradford University, England.1014 0025- 1909/79/25 10/ 10 14$01.25

Copyright?B1980, The Instituteof ManagementScimensc

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CHANNEL OPTIMIZATION IN COMPLEX MARKETING SYSTEMS 1015ated in the business. Such integration invariably leaves the manufacturer with multi-ple channels as the acquired outlets are rarely sufficient to employ the full manufac-turing capacity. A second group of reasons for manufacturers operating multiple-channels is the internationalization of business and the segmentation of domesticmarkets. A manufacturer designs a channel of distribution to serve a particular targetmarket segment. As the manufacturer seeks to grow or diversify his risks by operatingin more than one market, inevitably new channels of distribution have to be created.In this common type of multiple-channel system we can assume that the manufac-turer aims to allocate resources between channels in a manner which maximizes hisprofits subject to certain operational constraints. If we assume there are K channelsavailable to the manufacturer and for each channel i there are Ni possible outletsthrough which the manufacturer can sell his output Q, then the manufacturerneeds tomake three decisions. First, how many of the set of K channels to select. Second, forany channel selected how many of the Ni possible outlets to employ. Third, whatproportion of output Q should be sold through each channel.The problem is complicated because as Kotler [19, p. 68] reminds us, one mustassume that in practice the effects of marketing decision variables are both nonlinearand interactive. Here, for example, increasing the number of outlets will eventuallyproduce diminishing returns and increasing efforts in one channel will partly be at theexpense of other company channels.Optimization will take place subject to a number of operational constraints. Thelevel of sales output Q of the firm will be strongly affected by the selection andmanagement of the distribution channels. In the short-run, however, there will besome capacityconstraint (Q*) which imposes an upper bound on potential output (themodel can be operationalized without this constraint). Second, there will usually becontrol constraints which reflect the behavioral relations among members of thechannel. There is an extensive marketing literature drawing attention to the conflict-ing objectives and activities of manufacturers, wholesalers and retailers within achannel. Given a choice, channel managers will prefer channels over which they havesignificant control, which are adaptive to a changing market environment and whichare subject to limited risks. Reflecting increased concentration in retailing andconsequential retailer power, a common control constraint for a manufacturer is toavoid being dependent upon any single channel for more than a given fraction ofsales. A third type of constraint which has to be built into a realistic distributionmodel is system inflexibilities which limit the amount of adaption and discretion amanufacturer has over any channel system. Some channels will be closed to him (e.g.he may not be able to sell through Sears), others will have output restrictions. Forexample, it may not be realistic to assume that sales through existing outlets could bedoubled. Fourth, in any programming algorithm there are technical constraints suchas nonnegativity requirements to ensure practical solutions to the optimization prob-lem. Finally, there may be other ad hoc constraints in any specific company situation.

2. Review of the LiteratureThe problems addressed in this paper have not yet been solved in the literature. Animpressive amount of research has been devoted to economic analyses of verticalmarket systems and the impact of middlemen on the performance of these systems [6],[7], [8], [26], [30]. However these have been purely theoretical and given no attentionto operationalization and estimation. In addition, they have focused on the macro-level rather than on the resource decisions of the individual firm.In suggesting management tools for determining distribution strategies, researchers


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CHANNEL OPTIMIZATION IN COMPLEX MARKETING SYSTEMS 1017constraints in our model are an attempt to reflect certain of the more importantbehavioral restrictions under which managers operate.

3. A Case StudyThe approach described in this paper arose from a manufacturer's evaluation offuture distribution strategy. This actual case study will be used to illustrate thedevelopment of the model, methods of estimating the parameters and the solutionimplications. The company was a manufacturer and retailer of high quality candy. Itsold through multiple-channels. The most important channel was a group of 132wholly-owned specialist candy stores. Next in importance were approximately 50other retailers who sold the company's candy on a franchise basis. Third, were exportsales: the company sold to distributors in a number of European countries, who inturn, sold to retailers there. Finally, the company sold to a small number of high classdomestic retail chains under the retailers' own brand labels.The main dilemmas facing the company were which channels to concentrate upon,how many outlets to develop within any channel and what margins to seek in eachchannel. In general, there appeared to be an inverse relationship between unit grossmargin and channel growth. Thus while sales through company-owned outlets offeredthe highest margins, growth was relatively low; private label sales through other retailgroups offered high growth but little profit. A second general point was cannibaliza-tion between and within the channels. While the company served a broad geographicarea and sought to avoid closely proximate outlets, expansion of sales in any one

outlet will, at least partly, be at the expense of the others. Besides new stores, pricewas the main instrument affecting demand. Advertising and promotional expenditureswere low. Retail candy sales are highly fragmented across thousands of stores,consequently market shares are small. One result is that competitive reaction is notusually a factor in pricing decisions. Finally, optimization was constrained by certaincontrol motives of management. In particular, they did not want any particularchannel to be a dominant buyer.4. Model Specification

While the study had the general brief of evaluating the distribution strategy of thecompany, when the framework of the marketing environment and corporate objec-tives and constraints emerged, a nonconvex programming problem resulted. Very fewoptimization techniques exist that can handle nonconvex problems. As we showbelow, only the most general type of geometric programming (signomial program-ming) can effectively handle the structure of this broad class of problems.The problem formulation starts with the conventional normative model of themanufacturer seeking to select a distribution policy which maximizes profits, subjectto the relevant constraints on the decision variables. The objective function, i.e. themanufacturer's total profit is composed of a set of demand and cost functions. Toavoid an unnecessarily restrictive model specification and to allow for nonlinearitiesand interactions, general polynomial forms are postulated for both the demand andcost functions. Such functions are both intuitively and empirically appealing. Intu-itively managers find it easier to think in terms of elasticities than marginal effects.The assumption of constant elasticities is usually reasonable over the feasible range ofthe decision variables. Empirically, we expect diminishing returns and interactionsamong components of the marketing mix rather than linear, additive affects. For suchreasons polynomial forms have long been the most popular specification in empiricalresearch on general marketing mix models e.g. [20], [29].


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1018 MARCEL CORSTJENS AND PETER DOYLEThe total demand structure is thus specified as follows:

K KQ = . a1((p)16i (Pj)a (Ni)Ei. (1)-i=1 j=1Here /,3represents the direct elasticity with respect to price (pi) for an average outletin channel i; S. refers to the cross price elasticity between channels i andj, and Eirepresents the economies (Ei> 1) or diseconomies (Ei< 1) from increasing the numberof outlets (Ne) within channel i.From economic theory we expect that the absolute value of /8i faced by themanufacturer will increase by expanding the number of intermediary levels in achannel [22], [23]. The cross price elasticity S. formalizes the notion of multiplechannel cannibalization. Note that 6ij is not necessarily equal to Sji. The demandfunction also incorporates a nonlinear effect,cEi, or the number of outlets selected in aparticular channel on total demand. This parameter characterizes within channelcannibalization, whereas S. represents between channel cannibalization. Hartung andFisher [17] suggest Ei> 1: the promotional impact of concentrating more stores in anarea may benefit existing stores in the channel.The total cost structure is specified as follows:

KTC= oi(qi)v(NJ) * (2)i = 1Here, vi represents economies of scale in the cost function. If vi < 1, the average costcurve is decreasing. Parameter Trs the possible economy resulting from increasing thenumber of outlets in channel i, e.g. unit savings in buying, transportation andproduction costs.Finally, as noted earlier, four constraints are relevant to the maximization of theobjective function. First, the capacity constraint:

K qi Ni)< Q (3)where Q* is the corporate production capacity constraint. Second, the controlconstraint ensures that sales through any single channel are limited to some discre-tionary percent, z, of production capacity:

qiNi < ZQ* (4)Third, the system inflexibility constraint limits the optimal values for the decisionvariables, Ni, the number of stores opened in a channel, and pi, the price charged tothat channel to within feasible ranges. That is,

NiL < Ni < NiU and pL < P?; Pi 0O and NI >O for all i. (6)


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CHANNEL OPTIMIZATION IN COMPLEX MARKETING SYSTEMS 10195. Signomial Geometric Programming

The model developed in the previous section can be summarized as follows:

Maxi at(p)(fi+) Ij(pj)YJ(Ni)j= 1

K Ksubject to iaci(pi) 1iJ (pj) "(Ni)N (7)i=l j=lj#1Ktai(p)fi (pj)6u(N.)Ei ? ZQ< for all i,j=1

j=#NIL < NJ< NJU for all i,Pi < Pi < PiU for all i.

Because of the particular nonconvex structure of our model, it is not solvable bytraditional optimization techniques. The linear programming procedure obviouslycannot be employed because neither the objective functlon, nor the constraints arelinear. Conventional nonlinear programming techniques are not suitable either be-cause of the generalized polynomial functional forms in both the objective functionand the constraints. The prototypical (posynomial) geometrical programming tech-nique described by Balachandran and Gensch [3] can handle polynomial functions.However, this method imposes two restrictions on the problem formulation: the set ofpolynomials have to be posynomial, and all the constraints have to be of the "lessthan" type. This structureof the posynomial geometrical program can be transformedinto a convex program for which global optima are guaranteed [12].

The posynomial functional form requirement, however, is a rather severe limitationto the applicability of the prototypical (posynomial) geometrical programming tech-nique to our model and to marketing systems problems in general. For a maximiza-tion problem for example, the posynomial limitation implies that the signs of all or allbut one of the polynomial terms (i.e. a product of one or more variables) is negative.Especially in the context of system optimization, this condition will never be satisfied,because these systems (e.g. multiple products, multiple markets, multiple channels)can be decomposed into components (single product, single market, single channel),each of which has its own revenue and cost function. This implies a series of positive(revenue) terms and a series of negative (cost) terms in the objective function forsystem optimization, i.e. a signomial polynomial.One approach to this problem of noncompatibility of system structure and optimi-zation tools has been to simplify the structure of the model in such a way that itbecomes solvable by existing procedures. Thus, functional forms can be linearized, orat least be made convex, or even transformed into a posynomial. These forcedproblem formulations are not always very realistic and usually lack managerialrelevance. Especially for the optimization of marketing systems this is an importantproblem. Because of the cross effects between components of the system, generalizedpolynomials are central to modelling the objective functions of the system.


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1020 MARCEL CORSTJENS AND PETER DOYLEGeneral (or signomial) geometrical programming (SGP) can handle these problemssince it places no constraints on the structure of the objective function or on the typeof constraints. As described in the Appendix, the solution procedure for SGP is basedupon a transformation of the signomial program into a "reversed program." Thebranch and bound algorithm of Gochet and Smeers [16] can then be used to find aglobal optimum.

6. ParameterEstimation and Problem SolutionTo solve this type of programming problem estimates are needed of the set ofdemand and cost functions. In principle the data for these estimates can be obtainedfrom time series or cross sectional observations, experimental methods or subjectiveprocedures. While statistical estimates based upon objective data are the classicalapproach, in practice satisfactory data are rarely available for this type of problem(see [21], [27, pp. 251-277]). There are four common reasons for this. First, few`companies have seen the value of systematically recording over time information onall the relevant variables (prices, competitive activity, distribution, etc.). Second, useof conventional budgeting methods and rules of thumb mean there is commonly alack of variability across and within channels in the key marketing instruments tostatistically estimate their effects. Third, generating the data by experimental methodsis usually viewed by managements as both too costly, time consuming and problemat-ical. Finally, the marketing environment since the mid-1970s may have been subjectto such significant shifts that past observations are seen as of questionable relevance

to the future business environment.For these reasons, the estimation of the parameters here relied heavily on thejudgments of managers as well as on observed data. The three senior managersdirectly responsible for marketing and distribution planning in the company cooper-ated in the study by providing feedback on the reality of the model formulation, thechoice of variables and by giving explicit probability estimates where necessary toestimate the effects of changes in these variables.Since within channel homogeneity is important in the model, the first step in theestimation was to split the largest, most heterogeneous group of stores, the wholly-owned outlets, according to size, to form two groups. The cost functions for each ofthese five channels were then straight-forwardly estimable from cross sectional dataon channel costs. The parameter Ti representing the impact of increasing the numberof outlets had, however, to be subjectively estimated because of insufficient variability

TABLE 1Regression Coefficientsand t-valuesfor Demand Functions:

KQi= ,(P0PY'J (p1)5u(NiEii= Ii#iiChannel a,i /A ail ai2 6i3 8i4 8i5 EiLarge own 16.03 - 1.1 0.25 0.44 0 0.53 0.95

stores (1) (3.10) (-4.26) (3.9) (1.7) (0) (2.7)Small own 1613.5 - 0.95 0.04 0.22 0 0.29 0.98

stores (2) (4.42) (-11.35) (0.59) (2.87) (0) (3.53)Franchising (3) 0.43 - 1.13 0.64 0.18 0 0.79 0.93

(6.18) (-10.76) (1.6) (5.9) (0) (6.15)Export (4) 323608.6 -.1.14 0 0 0 0 0.90

(3.31) (-12.65) (0) (0) (0) (0)Private 699.42 - 1.84 0.79 0.51 0.33 0 - 0.76

label (5) (9.61) (-8.3) (1.9) (2.1) (3.2) (0)


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CHANNEL OPTIMIZATIONIN COMPLEX MARKETING SYSTEMS 1021TABLE 2

Regression Coefficientsandt-values for Cost Functions:TCi =,wi(Qi) (Ni)

Channel "i pi TiLarge own stores (1) 1881.83 0.92 0.95(157.80) (57.11)Small own stores (2) 1819.21 0.96 0.90(71.23) (34.45)Franchising (3) 1431.34 0.95 0.98(61.11) (20.23)Export (4) 1702.32 0.89 1.05(20.81) (7.241)Private label (5) 1585.04 0.90 1.01

(14.34) (8.67)

over the time period to objectively estimate this important scale parameter. Themanagers, therefore, were shown individually how to judge the impact on the currentlevel of average costs of 10 per cent changes in the number of retail outlets making upthe channel. Managers appeared to have little difficulty grasping the idea behind theprobability estimates, and the low variance of the estimated parameters (Table 2)indicates a high degree of agreement among them.Initial insight to formulate the demand equations were obtained from a broad studyof the candy market, the company and its competitors. Management agreed that priceand the intensity of distribution were the two variables which had the dominantimpact on company sales. Advertising and promotional expenditures were relativelysmall. Being sold through thousands of stores, retail candy sales were highly frag-mented so that market shares were small and competitive retaliation was not usually amajor factor in marketing mix decisions. Again, inadequate variability between andwithin channels meant that it was impossible to estimate the main and cannibalizationeffects of price movements and changes in the number of outlets in any channel viaclassical statistical procedures. To provide a basis for subjective estimates previous

price and channel-volume changes were plotted and studied with the managers. In thelight of these data, a session was held to consider the likely implications of greaterprice and channel flexibility in the future in terms of demand and cross-elasticityeffects. Following the discussion, individual judgments were elicited on the impact of10 per cent price changes on sales of the typical outlet in that channel and on sales ofother channels. Since the model assumes a constant elasticity demand function, thisprocedure enables an estimate of the average outlet demand functions. The parameterEi was estimated from judgments of the incremental effect of additional channeloutlets.

Regression analysis was used to transform the judgments of managers into parame-ter estimates (Table 1). All but one of the coefficients are statistically significant andthe signs are in the hypothesized directions i.e. negative own price elasticities andpositive cross price elasticities. All except the larger own outlets have price elasticdemand curves (6 > 1), which is again intuitively appealing. The larger price elastici-ties on channels with multiple intermediary levels (3, 4 and 5) are consistent with theMachlup and Tauber result [22], [23]. Note that for channels one and two (own-outlets) the price is identical to that paid by the final consumer; for the other channelsthe price is that charged to the intermediary and so excludes the latter's mark-up. Thecost function is shown in Table 2. The output coefficients (/3 < 1) suggest economiesof scale across all channels. On the other hand, increasing the number of outlets is


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1022 MARCEL CORSTJENSAND PETER DOYLETABLE 3

Problem Constraints1. Production Capacity: Q* = 10, 416 Tons2. Channel Control: qiNi < 0.60Q* for all i3. System Inflexibilities: 1600 < p, < 2000 and 40 < NJ 6 1001600 < P2 < 2000 40 < N2 < 1201200 < p3 < 1600 30 < N3 < 70

1400 0 for all i

judged as leading to a less than proportionate increase in costs (T < 1) for the firstthree channels.The actual constraints, imposed on the objective functions by management, arepresented in Table 3. The branch-and-bound procedure reached a solution vectorafter 720 iterations, although the convergence was almost complete after 200 itera-tions. The solution met the constraint set to within 10 per cent (for the most bindingconstraint).Existing levels

of decision Modelvariables PredictionsNI 66 61N2 66 90N3 50 31N4 9 16N5 5 7P1 1866 2000P2 1866 2000P3 1450 1592P4 1640 1900P5 1500 1700

We show above the model results compared to the existing levels of the decisionvariables. An appreciation of the significance of these differences can be noted byintroducing the model-predicted variables into the profit function and comparing theresults with those from the existing decisions. The new gross margin increases from 24to 33 per cent and absolute profit from ?4.1 million to ?6.6 million. Even allowing forpossible bias from measurement and model specification errors which are difficult totrace in the model, these results make the method of obvious interest.To persuade management to adopt decisions in the direction of those predicted bythe model it is necessary to explore more intuitively how the profit improvement isexpected to occur. Improvements came about from changes in distribution strategy,channel intensity and pricing policy. Three of the channels were oriented towardsincreased investment, two for marginal disinvestment. Larger own stores proved to bemore profitable than the smaller own stores, due in large part to their lower priceelasticity and their ability to sustain customer franchise against expansion in alterna-tive channels (see Tables 1 and 3). Franchising, on the other hand, was scaled for lessinvestment. These smaller outlets, carrying a weaker corporate identity, proved lessresilient to competition from other channels. Export and private label business were


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CHANNEL OPTIMIZATION IN COMPLEX MARKETING SYSTEMS 1023geared to expansion. Both these channels were relatively new strategies for thecompany and appeared to offer good opportunities for profitable growth.The pricing results lead to a recommendation for higher prices in each of thechannels. This was in line with earlier independent recommendations from thecompany's management consultants. The company had traditionally employed cost-plus pricing methods and did not utilize demand elasticity considerations in its pricingformulas. Overall, the logic of these findings has been accepted by management andstrategy will be adapted broadly along the lines discussed. Under these policies, moreoutlets will be employed in total but with the average outlet expected to sell lowervolumes at higher prices. Again this is intuitively reasonable in terms of retailingstrategy, because new outlets add trading areas from which growth is obtainable athigher price levels than from growth through existing outlets.

7. Managerial and Theoretical ImplicationsThe central task of management is to allocate scarce economic resources amongalternative uses. The present model provides a practical tool to assist managers inoptimizing resource use in channel planning. This is an important area becausechannel decisions are costly, complex, long term and not easily reversible commit-ments. Given a willingness to make estimates of the relevant demand and costfunctions the model provides output on the most significant channel decision areas-which channels to select, how intensively to use them and how to influence theirbehavior.The model is open to further development and evolution. Issues of channel powerand conflict can be explicitly modelled. For example, the control constraint can bereformulated as a decision variable to investigate optimal levels of dependencybetween manufacturer and channel members. In particular, over a longer time periodimproved estimation of the parameters is possible by tracking the model's predictionsand comparing the observed results (see [21]).Theoretically, the model is interesting because it does appear capable of significantgeneralization. It can be generalized to include other marketing mix variables besidesprice, provided the demand function can be estimated (for some ideas on this problemsee [3], [21]). It also offers potential for research in marketing system optimization ingeneral. This is a long existing unresolved need in the marketing literature, mainlybecause of the absence of adequate solution methods. The general geometric program-ming method suggested in this paper can be developed to handle complex systemstructures and sophisticated system interactions.

AppendixSignomial GeometricProgramming

The solution procedure for SGP is based on a transformation of the signomialprogram into a "reversed program."To simplify the notation let:

K Kf(p, N ) = (i +n H (pj)6fY(Ni)i=1 j=1j#iand

K Kg(p, N ) = w ai(pi) iI (pi) Y (Ni )i.

i= 1j,l


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1024 MARCELCORSTJENSAND PETER DOYLETransforming our model (7) into a form suitable for SGP results in the followingformulation:Define a new variable xo, such that the objective function becomes:

Max x0where xo < f(p, N) - g(p, N)orxo+g(p,N) < f(p,N).

Define another new variable xl such that:xo + g(p, N) < xl < f(p, N)orx x- I+xl -g(p,N) < 1and x 'f(p,N)> 1.The objective function can now be formulated as:

Min xosubjectto: x -lxj 'g(p,N)< 1, (1)

xV-Y(p,N)> 1.The additional constraints, except for the nonnegativity constraints, are then normal-ized in such a way that they become of the "less than" type, i.e.

(3) becomes: K K(Q*)-f I a1(p)1i 17 pj)iy(Ni)Ei< 1.i=1 j=lji#i(4) becomes:

K(ZQ*) - a1(p1),i (pj)"ij(Ni )Ei 1.

j=#i

(5) becomes: (N.L.)(Ni)-' < 1 and (Ni)(NiU) < 1,(piL)(pi)-l < 1 and (Pi)(PiU) < 1.

Based on this result a branch and bound method developed by Gochet and Smeersis used to find a global optimum of the signomial program [16]. Gochet and Smeers[16] show that by approximating the reversed constraint ("greater than") from theoutside, we can approximate the reversed program by a prototype geometricalprogram. Then, a branch and bound scheme is used to improve on this approximationwhich guarantees convergence to the global optimum. If the actual convergencetowards the global optimum is not obtained in a reasonable number of iterations, thebranch and bound procedure can be stopped. The final result of the branch andbound algorithm can then be used as a starting value for an existing convexprogramming method. This procedure will then generate the global optimum in amore economical way. Finally, to check the validity of the globality of the optimum,an ex-post analysis can be performed by using different plausible starting values andby verifying the resulting solutions.''The authors would like to express their gratitude to W. Gochet and V. Srinivasen for their invaluableadvice and comments on this paper.


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CHANNEL OPTIMIZATIONIN COMPLEX MARKETING SYSTEMS 1025References1. ALDERSON,W. AND GREEN, P. E., Planning and ProblemSolving in Marketing, Irwin, Homewood, Ill.,1964.2. ARTLE, R. AND BERGLUND, S., "A note on Manufacturers' Choice of Distribution Channels,"

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