Management Science

Montgomery, David B.

doi: 10.1287/mnsc.18.4.P1pmid: N/A

The papers in this special marketing issue of Management Science relate to three areas of marketing. The first four papers: Multiple-Product Sales Force Allocation Model, CALLPLAN: An Interactive Salesman's Call Planning System, Experience with a Sales Districting Model: Criteria and Implementation, and Allocating Sales Force Effort with Commissions and Quotas address issues arising in the management of a sales force. The next three Optimal Advertising Expenditure, Behavioral Measurement for Marketing Models: Estimating the Effects of Advertising Repetition for Media Planning, and Optimizing Consumer Advertising, Intermediary Advertising and Markup in a Vertical Market Structure deal with advertising decision models. The final two papers A probabilistic Market Model of Purchase Timing and Brand Selection, A Graph Theory Approach to Comparing Consumer Information Processing Models consider models of consumer behavior.

Hess, Sidney W.; Samuels, Stuart A.

doi: 10.1287/mnsc.18.4.P41pmid: N/A

Previously reported research documented the analogue between sales districting and legislative apportionment and described the first applications of computer techniques to the redrawing of sales and service areas.This paper summarizes what we have learned from these seven applications. We emphasizemotivation for re-alignment: Better coverage, fairer work load and change in size of sales force,criteria for measuring good districting: Single, multiple and weighted measures of salesman activity; relationship to sales objectives; and correlation between activity measures,implementation: Top management involvement and presentation to the sales force,demonstrated effectiveness of the new alignments.

Bettman, James R.

doi: 10.1287/mnsc.18.4.P114pmid: N/A

This study argues the need for, and then develops, some graph theoretic approaches for comparing complex information processing models of individual decisions. Two similarity coefficients are proposed, and a coefficient based on path and reachability structure is shown to be preferable. Some properties of this coefficient are outlined, as well as a computational method. The coefficient is applied to actual information processing models of consumer choice and stock selection. The results of this application are interpreted for insights into process structure, stability of decision processes over time, and possibilities of developing process-oriented typologies. Finally, problems and prospects for this type of approach are assessed.

Herniter, Jerome

doi: 10.1287/mnsc.18.4.P102pmid: N/A

A stochastic model of consumer purchase behavior for frequently purchased, low cost products is developed. Both brand selection and purchase timing are incorporated in the model; a first-order Markov process is used to describe brand selection, and Erlang density functions are used to describe time between purchases. The market's behavior is obtained by describing the individual consumer's behavior and then aggregating over consumers. The model's predictions of various aggregate purchase timing statistics and repeat purchase sequences are empirically verified.

Davis, Otto A.; Farley, John U.

doi: 10.1287/mnsc.18.4.P55pmid: N/A

Quotas, commissions and mixtures of the two are widely used to control salesmen's activities both in terms of overall motivation and as decentralized means to direct allocation of effort over various products in the firm's line. Sales commission plans as allocation devices for a commission-maximizing sales force and a profit-maximizing central management generally turn out to be inadequate decentralized allocation devices in themselves, regardless of whether commissions are based on sales or on profit margins. A plan based on sales fails to reconcile the interests of salesmen and management, while a plan based on profit margins generally makes each salesman's income depend not only on his performance but on the performance of all other members of the sales force simultaneously. Further, information requirements about individual salesmen and markets appear so great that setting optimal quotas centrally is impossible for practical purposes. However, an interative quota generating procedure may be used to reconcile interests of salesmen and management, and yet maintain the desirable features of decentralised allocation consistent with the independent operation of the individual salesman.

Naert, Philippe A.

doi: 10.1287/mnsc.18.4.P90pmid: N/A

Given is a vertical market structure (VMS) which consists of producers, one intermediary level and consumers. In most of the literature on VMS either equilibrium behavior is studied without consideration of objectives or some objective function is being optimized without taking into account behavior of intermediaries. This paper is a modest attempt to bring the two approaches together. The decision variables are consumer advertising, intermediary advertising and markup offered by producers to intermediaries. Behavior of intermediaries is incorporated through the use of a pseudodecision variable, the equilibrium number of middlemen in the VMS.

Ray, Michael L.; Sawyer, Alan G.

doi: 10.1287/mnsc.18.4.P73pmid: N/A

As management science models are developed in marketing, they make demands for more sophisticated inputs from the behavioral sciences. This is particularly true in the area of advertising media models. A continuing behavioral research program to develop estimates of repetition response functions for media models is reviewed. The program finds functions which differ importantly in level, slope and shape depending on the measure of response, market segment, product type, brand, advertising format, advertising illustration, advertisement color, media scheduling, ad appeal, and competitive situation. It is argued that such response function variations, found in both laboratory and field research, should be represented in media models. To illustrate this point, the results of a study of repetitive effects of one-sided (supportive) and two-sided (refutational) competitive advertisements are applied to runs of the MEDIAC planning system. Inclusion of the behavioral data produces favorable changes in MEDIAC output in terms of schedules and schedule results. The potential of further interaction between behavioral data and management science models is discussed.

Montgomery, David B.; Silk, Alvin J.; Zaragoza, Carlos E.

doi: 10.1287/mnsc.18.4.P3pmid: N/A

When several products are marketed by the same sales force, it frequently becomes impossible or impractical for salesmen to promote all items in the product line extensively in each and every time period. Management's problem is to decide how the available selling effort should be allocated across products and over time. The opportunity costs associated with using limited selling resources to promote certain products but not others must be evaluated. This paper describes a decision calculus-type modeling system for dealing with this question.The problem is analyzed by a two-step procedure. First, a response function is defined which relates selling effort to sales and profit results in a manner which represents some behavioral phenomena considered to be important. An interactive conversational program elicits judgmental data from managers which are used to parameterize the response model. A separate response function is specified for each product in the firm's line by this method. The set of response functions so obtained becomes the input for the second component of the system, an allocation heuristic. An incremental search procedure is employed to find an allocation of the sales force's time to the various products and over several time periods which is best in terms of total contribution to company profits. The model is presented in the context of an ethical drug manufacturer's multiple-product sales force allocation problem. Results of an application are summarized and implementation considerations noted. A comparison of the model-based allocation with that determined previously by management indicated that the former plan would offer a substantial improvement in profits.

Lodish, Leonard M.

doi: 10.1287/mnsc.18.4.P25pmid: N/A

CALLPLAN is an interactive computer system designed to aid salesmen or sales management in allocating sales call time more efficiently. The system increases their capacity to consider the allocation in a logical and consistent manner. CALLPLAN uses as input the salesman's own best estimates of expected contribution of all possible call policies for each account and prospect. The computer can help the estimating procedure by fitting curves through estimated points on a response function or by obtaining expected values from probability estimates. The system solves a mathematical program which determines the best time allocation to maximize contribution according to these estimates. Factors considered by the system include travel time and costs to get to geographical areas within the territory, amount of time required per call on an account within an area, account profitability, and minimum and maximum account call frequency limitations. An efficient incremental analysis routine is discussed as a solution procedure for the mathematical program.CALLPLAN seems best suited to repetitive selling situations where the amount of time the salesman spends with an account is an important factor in the magnitude of sales generated. Preliminary applications have been made by fourteen salesmen in six sales situations. A transcript of a session at the computer terminal of one application is presented.Anticipated sales increases, based on the salesman's judgmental inputs, for the call policy generated by CALLPLAN were between five and twenty-five per cent in the majority of applications.

Sasieni, Maurice W.

doi: 10.1287/mnsc.18.4.P64pmid: N/A

This paper discusses the optimal rate of advertising expenditure given the relationship between the rate of change of sales and the rate of expenditure. It is shown that we may assume that the marginal return of increased expenditure is never increasing. This is because when marginal returns increase there is always a mixed pattern in which two levels of expenditure are used, each for infinitesimally short intervals, with the property that the average cost for a given sales change is lower than with a fixed policy, and marginal returns are constant.If we assume that marginal returns do not increase, then, provided it is profitable to advertise, there exists an over-all optimal sales rate and an expenditure level, just sufficient to maintain it, with the following properties with respect to long-run discounted profits:(1) If sales even reach this level it is optimal to keep them there.(2) Starting from any other level, the optimal policy is to spend in such a way as to drive sales towards this level.The only requirements for these results are that the cost of achieving a given change in the sales rate be an increasing function of the sales rate and the rate of change of sales rate. It is also shown that the optimal sales rate to be maintained in the long run is not the rate which maximises the rate of gaining profit after advertising, unless the discount rate is zero.In practice, the mixed policy cannot be followed because discreet changes in expenditure levels cannot be made too frequently. When a mixed policy is optimal the best we can achieve is to use a cyclic policy in which we advertise for short intervals at each of the appropriate levels. A simple example calling for such a policy is when we have an advertising threshold below which expenditure has no effect, together with a relatively small market with low profit margins. Whether or not advertising thresholds exist requires psychological theory or controlled experimentation beyond the scope of this paper.