Demon: Decision Mapping Via Optimum Go-No Networks--A Model for Marketing New Products

In this paper a dynamic, adaptive model, called DEMON, 4 is interpreted in terms of a network. The latter is here employed to reduce the problem of selecting optimal decision procedures so that these can be interpreted in terms of a conditional sequential designation of links from such a network. More is involved, however, than is immediately apparent from the network possibilities only. Thus, in the DEMON applications to new product marketing--as discussed in the present paper--it is necessary to comprehend additional chance and deterministic constraints such as (1) payback, or breakeven, conditions that may be specified for fulfillment over a given time horizon, (2) minimum expected level of profits required and (3) study budget limits which should not be exceeded. By means of preemptions or over-rides, which also form a part of DEMON, however, it is possible to relate these additional constraints to the network as we also show by means of a development via ideas associated with the right inverse of an incidence matrix. It is important to note that the chance constraints in DEMON--and hence the objective also-are associated with probability distributions that are only partially determined by the selection of a sequence of link designations in the network of (statistical) study possibilities. Thus, a link selection yields only a random variable whose sample value in turn determines a conditional probability distribution in terms of which the chance constraints (and the objective) are expressed. Also involved is the further issue of optimal allocation between the elements of a marketing plan (e.g., resource allocations to advertising, promotion, etc.) which, in turn, alters the distribution through its mean demand. Thus, the task of DEMON is to choose a best distribution through two avenues: (a) a best path through the network of study possibilities and (b) a best deployment of funds in terms of a marketing plan. To conveniently summarize this double optimization we refer to the DEMON objective as MEMP (-Maximize Expected Maximum Profit). But, of course, the selection of a best distribution in accordance with MEMP is confined only to those candidates admitted by the network of study possibilities and the chance (and other) constraints. Although it is related to previous work in chance constrained programming, DEMON evidently also effects a further development and extension of these ideas by reference to the fact that here the statistical distributions are only partially known and the chance constraints are also expressed in terms of conditional distributions which in turn may be altered by the choices that are made. It is possible, at least in principle, to relate such ideas to conventional statistical decision procedures, including Bayesian or subjective probability analysis although the developments for DEMON appear to depart from preceding developments in these areas, too, in a variety of ways, including (a) the functional to be optimized, (b) the nature of the domain of optimisation and (c) the type of probabilistic constraints specified. Substantive concepts of management and economics are also altered or extended in the use that is made of them here. For instance, in contrast to customary uses, the concept of payback is here interpreted as a risk constraint. I.e., payback here serves as a filter which eliminates projects that are too risky (or otherwise unacceptable) whereas previous uses have commonly accorded it the status of an objective. Thus a supposed conflict between payback and other objectives (such as profit maximization, etc.) is thereby avoided and a way is opened for still other combinations such as maximizing the payback probabilities subject to chance or other constraints on profit, etc., as we also illustrate by reference to a constraint on minimum expected profit as a possible safeguard against suboptimizing in pursuit of maximum profit for one of a possible wider set of activities.