On the impact of initial performance on the effectiveness of advertising pulsation policies

Using a modified version of a Vidale–Wolfe model, proposed by Little, this paper examines the impact of initial sales rate on the performance of a variety of discrete, piecewise-continuous advertising policies for a finite planning horizon. The deployment of a non-discounted measure of performance reveals, irrespective of the shape of the advertising response function, that when the initial sales rate is different from zero at the beginning of the planning period: (1) a firm would be better off concentrating its advertising effort at the end rather than at the beginning of the planning period for a Blitz Policy (BP), (2) for an Advertising Pulsing/Maintenance Policy (APMP), it is more lucrative for a firm to alternate between a lower level of advertising followed by higher level (low–high) in a cyclic manner rather than to cycle the opposite way (high–low), and (3) in the presence of an initial sales rate, the pattern of the optimal advertising policy determined by dynamic programming can be significantly different from its alternative counterpart in its absence. In addition, it has been demonstrated, among other theoretical findings, that, for any given mean rate of advertising, the mean sales is bounded from below and is a decreasing function of the length of the planning horizon. Numerical examples are introduced to illustrate and reinforce the above research findings.     

Advertising a new product in a segmented market

We bring some market segmentation concepts into the statement of the “new product introduction” problem with Nerlove-Arrow’s linear goodwill dynamics. In fact, only a few papers on dynamic quantitative advertising models deal with market segmentation, although this is a fundamental topic of marketing theory and practice. In this way we obtain some new deterministic optimal control problems solutions and show how such marketing concepts as “targeting” and “segmenting” may find a mathematical representation. We consider two kinds of situations. In the first one, we assume that the advertising process can reach selectively each target group. In the second one, we assume that one advertising channel is available and that it has an effectiveness segment-spectrum, which is distributed over a non-trivial set of segments. We obtain the explicit optimal solutions of the relevant problems.     

Using mixture‐amount modeling to optimize the advertising media mix and quantify cross‐media synergy for specific target groups

One of the critical decisions in media planning is how to allocate advertising efforts across different media. While studies indicate that marketers can create positive synergy effects by spreading their effort across several media, there is little understanding of how much should be invested in each specific medium to optimize advertising results. In this study, we apply a novel methodology, mixture‐amount modeling, which allows advertisers to determine the optimal allocation of advertising effort across media as a function of the total advertising effort. Moreover, we test how the optimal allocation and the resulting response change for consumers with distinctive media usage patterns and varying degrees of product category experience. Based on these results, we quantify the potential synergy between media and calculate the synergistic capacity for specific target groups. We apply the model to data from 52 beauty care advertising campaigns that ran on TV and in magazines in the Netherlands and Belgium. We determine the optimal allocation of advertising investments (measured through Gross Rating Points) to maximize campaign recognition. Our findings support the existence of positive synergistic effects between magazine and TV advertising and illustrate that these effects depend on consumers' media usage and product category experience.     

On the Kryanev-Lardy Method for III-Posed Problems

Starting with a list of “reasonable” properties, called axioms, we are pointing out, that the notion of differentiability is related to the one parameter subgroups of a topological group. This justifies the idea of RISS [5] and the attempts of one of the authors in an earlier paper [1]. In a second part we define differentiable vector valued functions on topological groups. The third part is devoted to a definition of differentiable mappings satisfying the axioms stated before. In this part the considerations are restricted to a rather large class of topological groups including locally compact groups, BANACH LIE groups and current groups. All topological groups and locally convex topological linear spaces occuring in this paper are assumed to be HAUSDORFF .     

Optimal advertising pulsation policies: a dynamic programming approach

This study formulates and solves an advertising pulsation problem for a monopolistic firm using dynamic programming (DP). The firm aims at maximising profit through an optimal allocation of the advertising budget in terms of rectangular pulses over a finite planning horizon. Aggregate sales response to the advertising effort is assumed to be governed by a modified version of the Vidale–Wolfe model in continuous time proposed by Little. Using a numerical example in which a planning horizon of one year is divided into one, two through ten equal time periods, computing routines are developed to solve 150 DP problems. Computational results show among other findings that the performance yielded by the DP policy dominates the uniform advertising policy (constant spending) for a concave advertising response function and the advertising pulsing policy (turning advertising on and off) for a linear or convex response function.     

Rejoinder on “Likelihood-based belief function: Justification and some extensions to low-quality data”

This note is a rejoinder to comments by Dubois and Moral about my paper “Likelihood-based belief function: justification and some extensions to low-quality data” published in this issue. The main comments concern (1) the axiomatic justification for defining a consonant belief function in the parameter space from the likelihood function and (2) the Bayesian treatment of statistical inference from uncertain observations, when uncertainty is quantified by belief functions. Both issues are discussed in this note, in response to the discussants' comments.     

An Application of Multiple Regression Analysis to the Greek Beer Market

The object of this paper is to present a quantitative analysis of the Greek beer industry, through the use of various single regressions. The first part presents the relationship between advertising and sales through disaggregating advertising outlays, media and firm advertised, while a number of indices referring to advertising effectiveness are also estimated. The second part extends the discussion by presenting an illustrative example with regard to the implied duration interval and its importance in advertising.     

On the superiority of pulsing under a concave advertising market potential function

The authors study the superiority of advertising pulsing policy (turning advertising on and off in a cyclic fashion) over its uniform (constant spending) counterpart that costs the same under the assumption that sales dynamics follow a modified Vidale–Wolfe aggregate advertising model. The authors show that pulsing can be superior if the product of the concave market potential function and the linear or concave advertising response function is convex in advertising. Similar to previous studies in the literature, the average undiscounted profit over the infinite planning horizon is considered as a performance measure according to which alternative advertising pulsation policies are compared.     

50 Years of Data Science

More than 50 years ago, John Tukey called for a reformation of academic statistics. In “The Future of Data Analysis,” he pointed to the existence of an as-yet unrecognized science, whose subject of interest was learning from data, or “data analysis.” Ten to 20 years ago, John Chambers, Jeff Wu, Bill Cleveland, and Leo Breiman independently once again urged academic statistics to expand its boundaries beyond the classical domain of theoretical statistics; Chambers called for more emphasis on data preparation and presentation rather than statistical modeling; and Breiman called for emphasis on prediction rather than inference. Cleveland and Wu even suggested the catchy name “data science” for this envisioned field. A recent and growing phenomenon has been the emergence of “data science” programs at major universities, including UC Berkeley, NYU, MIT, and most prominently, the University of Michigan, which in September 2015 announced a $100M “Data Science Initiative” that aims to hire 35 new faculty. Teaching in these new programs has significant overlap in curricular subject matter with traditional statistics courses; yet many academic statisticians perceive the new programs as “cultural appropriation.” This article reviews some ingredients of the current “data science moment,” including recent commentary about data science in the popular media, and about how/whether data science is really different from statistics. The now-contemplated field of data science amounts to a superset of the fields of statistics and machine learning, which adds some technology for “scaling up” to “big data.” This chosen superset is motivated by commercial rather than intellectual developments. Choosing in this way is likely to miss out on the really important intellectual event of the next 50 years. Because all of science itself will soon become data that can be mined, the imminent revolution in data science is not about mere “scaling up,” but instead the emergence of scientific studies of data analysis science-wide. In the future, we will be able to predict how a proposal to change data analysis workflows would impact the validity of data analysis across all of science, even predicting the impacts field-by-field. Drawing on work by Tukey, Cleveland, Chambers, and Breiman, I present a vision of data science based on the activities of people who are “learning from data,” and I describe an academic field dedicated to improving that activity in an evidence-based manner. This new field is a better academic enlargement of statistics and machine learning than today’s data science initiatives, while being able to accommodate the same short-term goals. Based on a presentation at the Tukey Centennial Workshop, Princeton, NJ, September 18, 2015.     

Dynamic Advertising Under Vertical Product Differentiation

We investigate a dynamic advertising model where product quality is endogenous. In the differential game between single-product firms, there exists a parameter range where the low-quality firm uses a more efficient advertising technology and earns higher profits than the rival. Moreover, we show that equilibrium qualities are the same under duopoly, multiproduct monopoly, and social planning, the only distortion being concerned with the output levels.     

Using several advertising media in a homogeneous market

We propose a variety of models to represent the joint effect of several advertising media on the demand for a product in a homogeneous market, and discuss the associated profit maximization problems. An advertising productivity function represents the combination of several media and, together with demand and advertising cost functions, determines the features of the associated profit problem. We distinguish between additive and nonadditive advertising productivity functions, then between smooth and nonsmooth ones. The demand function may either be linear or not. We observe how different models may exhibit either synergy or interference effects. In some cases we obtain explicit optimal solutions.     

Allocation of Marketing Effort Among <Emphasis Type="Italic">P</Emphasis> Substitutional Products in <Emphasis Type="Italic">N</Emphasis> Territories<Superscript>†</Superscript>

Frequently, companies face the problem of allocating a given marketing budget in order to maximize their total returns. In this paper we examine the problem of allocating marketing effort, such as advertising, among P substitutional products, distributed in N different sales territories. Two models are discussed. In the first model it is assumed that at most one product is promoted in each sales territory. It is shown that a simple algorithm leads to at least a local optimum in a finite number of steps. In the second model, the restriction of one product per territory is eliminated. Applying a concept of effective effort, the model is transformed to an equivalent separable programming problem, solvable by a “single-pass” algorithm for various forms of response functions. Furthermore, a concept of successive modifications of the objective function is discussed.     

Membership functions and operational law of uncertain sets

Uncertain set is a set-valued function on an uncertainty space, and attempts to model “unsharp concepts” that are essentially sets but their boundaries are not sharply described. This paper will propose a concept of membership function and define the independence of uncertain sets. This paper will also present an operational law of uncertain sets via membership functions or inverse membership functions. Finally, the linearity of expected value operator is verified.     

An Experimental Design for Measuring Advertising Payoff

A model is described to assist retail management in developing an effective advertising strategy. The difficulties of advertising decision-making are reviewed and the nature of the particular marketing problem is outlined. It is shown how market research is used to construct an effective appeal and choice of media. An experiment, using a split-plot design, is then performed to estimate the payoff of advertising. This provides a clear framework for developing advertising decisions and for their implementation and control.     

Transfer pricing in a dynamic marketing-operations interface

A transfer price mechanism is proposed to coordinate the strategies of the marketing and operations functional areas operating in a dynamic interface environment in a decentralized firm. Marketing and operations are strategic decision-makers in a differential game, in which marketing has price and advertising and operations has production as control variables, and advertising goodwill and production backlog are state variables. A constant transfer price is entered into the objective functionals for marketing and operations, and subgame perfect feedback strategies are derived for price, advertising, and production as functions of the state variables. The feedback strategies allow a solution for the dynamic system involving goodwill and backlog, and the total payoff to the firm, the sum of the payoffs to marketing and operations, is determined as a function of the transfer price. Finally, for certain parameter conditions an interior maximum of the payoff function is achieved, and the optimal transfer price is identified.     

Topological aspects of numberings

We investigate connections between the syntactic and semantic distance of programs on an abstract, recursion theoretic level. For a certain rather restrictive notion of interdependency of the two kinds of distances, there remain only few and “unnatural” numberings allowing such close relationship. Weakening the requirements leads to the discovery of universal metrics such that for an arbitrary recursively enumerable family of functions a numbering compatible with such a metric can uniformly be constructed. We conclude our considerations with some implications on learning theory.     

Fuzzy part coding for group technology

Contemporary Group Technology (GT) methods apply coding schemes as a popular method for capturing the design and manufacturing information pertinent to the parts to be grouped. Coding schemes are very popular and many different coding systems are commercially available. The main disadvantage of current coding systems, however, is their generality and lack of informative representation of the parts.This paper presents a new methodology for coding parts using fuzzy codes. The methodology is general and applies to attributes that have a crisp value (e.g., “length”, “ratio of length to diameter”), an interval value (e.g., “tolerance”, “surface roughness”) or a fuzzy value (e.g., “primary shape”). The methodology considers the range of attributes' values relevant for the grouping, and therefore, is tuned and adjusted to the specific collection of parts of interest. This method creates a more informative coding scheme which leads to improved variant process planning methods, scheduling and inventory control as well as other manufacturing functions that utilize GT.     

Note on an extension of “Davidon” methods to nondifferentiable functions

Some properties of “Davidon”, or variable metric, methods are studied from the viewpoint of convex analysis; they depend on the convexity of the function to be minimized rather than on its being approximately quadratic. An algorithm is presented which generalizes the variable metric method, and its convergence is shown for a large class of convex functions.     

Wendland functions with increasing smoothness converge to a Gaussian

The Wendland functions are a class of compactly supported radial basis functions with a user-specified smoothness parameter. We prove that with an appropriate rescaling of the variables, both the original and the “missing” Wendland functions converge uniformly to a Gaussian as the smoothness parameter approaches infinity. We also explore the convergence numerically with Wendland functions of different smoothness.