Advertising channel selection in a segmented market

We consider a market with a finite number of segments and assume that several advertising channels are available, with different diffusion spectra and efficiencies. The problem of the choice of an advertising channel to direct the pre-launch campaign for a new product is analyzed in two steps. First, an optimal control problem is solved explicitly in order to determine the optimal advertising policy for each channel. Then a maximum profit channel is chosen. In a simulation example we consider the choice of a newspaper among six available and analyze the relations among the firm target market and the advertising channels environment which induce the optimal decision.     

A multiobjective approach for maximizing the reach or GRP of different brands in TV advertising

This paper focuses on a multiobjective optimization problem in TV advertising from an advertising agency's perspective, which involves deciding on which commercial breaks to air the ads of various brands to jointly maximize reach or gross rating point (GRP) for the different brands subject to budget constraints, brand competition constraints, and other scheduling constraints. We present a multiobjective integer programming formulation of this problem and develop and implement algorithms for generating provably Pareto‐optimal solutions. We also develop reduction and visualization procedures to aid a decision maker in choosing suitable subsets of the Pareto‐optimal solutions obtained. Numerical experiments on five TV advertising problems involving 20–40 objective functions and thousands of decision variables and constraints demonstrate the effectiveness of the proposed formulation and solution methods in generating Pareto‐optimal objective vectors that reflect brand priorities and that are well distributed along the Pareto front.     

Optimal dynamic advertising with an adverse exogenous effect on brand goodwill

We propose the model of a firm that advertises a product in a homogeneous market, where a constant exogenous interference is present. Using the framework of Nerlove and Arrow’s advertising model, we assume that the interference acts additively on goodwill production as a negative term. Hence, we allow that the goodwill may become negative and we associate a zero demand with negative goodwill values. We consider a piecewise linear demand function and formulate a nonsmooth optimal-control problem with an infinite horizon. We obtain that an optimal advertising policy exists and takes one of two forms: either a positive and constant advertising effort, or a decreasing effort starting from a positive level and eventually reaching the zero value at a finite exit time. In the former scenario, the demand is always positive and the firm stays in the market in the long run; in the latter, the demand becomes zero in the short run, and afterward, the firm goes out of business. In both cases we have an explicit representation of the optimal control, which is obtained through the study of an auxiliary smooth optimal-control problem. It is interesting that the fundamental choice between staying in the market and going out of business at some time depends both on the interference level and on the initial goodwill level.     

Lossless convexification of a class of optimal control problems with non-convex control constraints

We consider a class of finite time horizon optimal control problems for continuous time linear systems with a convex cost, convex state constraints and non-convex control constraints. We propose a convex relaxation of the non-convex control constraints, and prove that the optimal solution of the relaxed problem is also an optimal solution for the original problem, which is referred to as the lossless convexification of the optimal control problem. The lossless convexification enables the use of interior point methods of convex optimization to obtain globally optimal solutions of the original non-convex optimal control problem. The solution approach is demonstrated on a number of planetary soft landing optimal control problems.     

供应链动态合作广告策略

研究产品信誉受广告投入水平影响的供应链合作广告问题,建立具有广告投入水平抑制作用的产品信誉动态模型.通过哈密顿-雅可比-贝尔曼方程分别得到制造商和零售商在分散决策和集中决策下的最优广告策略以及在分散决策下制造商的最优合作广告参与率,比较发现,集中决策下制造商和零售商的最优广告投入水平高于分散决策下的相应值.设计了双边补贴策略来协调供应链.数值仿真实验验证了所得结论的正确性.     

基于用户迁徙网络的广告投放策略研究

分析了目前网络广告投放领域存在的不足。使用能够体现网站间共同用户数量的用户迁徙网络作为平台,研究广告投放的网站选择策略。通过分析传统的网络广告投放问题的数学模型,发现其本质为0-1背包问题。通过实验比较,解决0-1背包问题常用的贪心算法和蚁群算法不能解决的广告受众重叠的问题;而使用用户迁徙网络的广告投放方法,在预算一定的情况下,达到广告的受众最多,广告投放的效果最优,是广告投放的最佳策略。     

Optimization of advertising activity of an insurance company and an algorithm for its solution

The problem of optimization of advertising activity of an insurance company consisting of n divisions (branches) is considered. For each branch, an optimal control is found in a closed form (an analytic solution) under constraints on advertising expenses. The quality of behavior of optimal controls and phase coordinates is illustrated by a numerical experiment. Translated from Kibernetika i Sistemnyi Analiz, No. 2, pp. 159–165, March–April 2009.     

Finding an optimal dynamic advertising policy

In this paper a solution is presented to an important marketing problem : the timing of advertising expenditure. Using a differential equation to model the relationship between the sales and advertising rates and using profit as a criterion, a synthesis of the optimal dynamic advertising policy as a function of the current sales level and length of the campaign is derived. In addition, using profit as a criterion, the profitability under an optimal dynamic advertising policy is compared with the profits obtained using an optimal static policy. It is shown that a significant increase in profits can result from employing the optimal dynamic policy.     

Analysis of optimal production and advertising policies

In this paper, the joint production and advertising control model proposed by Parlar is extended to include a time dependent depreciation rate of goodwill (sales), the salvage value of inventory unsold, and the salvage value of goodwill. For an arbitrary form for the production cost function, necessary conditions for optimal production and advertising rates are obtained using the maximum principle. For specific forms (quadratic and linear) for the production cost function, optimal production and advertising policies are investigated. In addition, the solution technique used by Parlar to deal with the pure state inequality constraint is shown to be incorrect, and thus correct analyses to the problem are presented. An algorithm is developed to solve the necessary conditions and numerical examples are presented to illustrate the solution     

Mathematical models of the battle between parties for electorate or between companies for markets

A model of optimization of strategies for any number of political parties (companies) in election (advertising) campaigns is proposed. We formulated the problem of choosing an optimal strategy for allocating scarce resources among regions (markets) in which political parties (companies) have different influences. The optimization model is analyzed and the existence of a unique solution is proved for different functions of dependencies between investments and winning. An analytical solution to the model is found for the case of two parties (companies). A direction for further development is the study of the sensitivity of an optimal solution to model parameters and formation of a stochastic model.     

A fast exact algorithm for the allocation of seats for the EU Parliament

In this paper, we analyse the problem of allocation of seats for the EU Parliament. To solve it, we propose a fast exact algorithm which overwhelms limitations of the existing methods. It allows us to examine all feasible allocations of seats within few minutes. On this basis, an in-depth analysis of the problem is provided and some of its properties are revealed (e.g., the number of feasible allocations of seats holding the Treaty of Lisbon), which have never been presented in the scientific literature. Furthermore, the proposed algorithm is not limited to dealing with the problem of allocation of seats for the EU Parliament, but it can be applied in the expert system for any other similar problem, especially under degressive proportionality constraints.     

考虑延时效应和记忆效应的供应链广告策略

研究考虑延时效应和记忆效应的供应链广告策略问题,建立泛函微分方程以刻画广告延时和记忆双重效应对产品品牌信誉变化的影响,运用微分对策理论给出制造商和零售商在分散式决策和集中式决策下的最优广告投入水平、广告排期以及相应的产品品牌信誉,并对不同决策机制下供应链成员的均衡策略进行比较分析.研究表明:集中式决策能激励制造商和零售商的广告投入; 延时效应与记忆效应分别影响供应链成员广告时序策略与广告排期策略的制定,同时,还会影响供应链决策机制的选择.     

A problem in jointly optimal production and advertising decisions

In this paper, a production control model proposed by Holt, Modigliani, Muth and Simon and a marketing model suggested by Nerlove and Arrow, are combined to produce an optimal control problem with two state variables, two control variables and inequality constraints on these variables. The optimal production rate and advertising expenditures over time are determined using the maximum principle. Due to the complex nature of the necessary conditions, the numerical technique known as the initial-value shooting method, is used to generate optimal trajectories. A numerical example is presented to illustrate the solution.     

Budget Allocation for Maximizing Viral Advertising in Social Networks

Viral advertising in social networks has arisen as one of the most promising ways to increase brand awareness and product sales. By distributing a limited budget, we can incentivize a set of users as initial adopters so that the advertising can start from the initial adopters and spread via social links to become viral. Despite extensive researches in how to target the most influential users, a key issue is often neglected: how to incentivize the initial adopters. In the problem of influence maximization, the assumption is that each user has a fixed cost for being initial adopters, while in practice, user decisions for accepting the budget to be initial adopters are often probabilistic rather than deterministic. In this paper, we study optimal budget allocation in social networks to maximize the spread of viral advertising. In particular, a concave probability model is introduced to characterize each user’s utility for being an initial adopter. Under this model, we show that it is NP-hard to find an optimal budget allocation for maximizing the spread of viral advertising. We then present a novel discrete greedy algorithm with near optimal performance, and further propose scaling-up techniques to improve the time-efficiency of our algorithm. Extensive experiments on real-world social graphs are implemented to validate the effectiveness of our algorithm in practice. The results show that our algorithm can outperform other intuitive heuristics significantly in almost all cases.     

基于图像处理的课室人员位置分布识别

对大型课室人员位置分布识别有利于课室灯光节能管理,基于面积判据的人员位置识别算法没有应用场景的约束,但容易因人体Blob图像粘连而产生误判;基于座位网格的算法只适用于直线排列的固定座位,但算法简单可靠。实验证明:两种方法均能有效地检测出人员分布情况,后者对固定座位的课室检测准确性更好,效率更高。     

故事性广告的灵活运用

在信息膨胀的今天,人们生活在众多广告所包围的环境中,如何让消费者对一则广告过目不忘?如何让消费者对其广告感兴趣并有所期待?我们试图通过遗忘与记忆的原理来分析。我们发现,往往是有故事情节的广告更能被人们所记牢。因此,为我们的广告创造一定的场景、并赋予其故事性,加大其矛盾冲突,制造抓人眼球的悬疑,使广告的受众对其产生兴趣。从而更好的吸引消费者、强化消费者对其广告的认知并记忆。     

Profit maximization through advertising: A nonzero sum differential game approach

This paper deals with the problem of the competition between two firms who sell substitutable products. Each firm wants to maximize its own profits. A firm's share of the market is influenced by its advertising and the advertising of its competitor. The problem is modeled as a nonzero sum differential game. Various solution concepts are applied and the corresponding "optimal" advertising rates obtained.     

Co-op advertising and pricing models in manufacturer–retailer supply chains

Cooperative (co-op) advertising plays a significant role in marketing programs in conventional supply chains and makes up the majority of promotional budgets in many product lines for both manufacturers and retailers. Nevertheless, most studies to date on co-op advertising have only assumed that the market demand is only influenced by the advertising level but not in any way by the retail price. That is why our work is concerned with co-op advertising and pricing strategies in distribution channels consisting of a manufacturer and a retailer. Four different models are discussed which are based on three non-cooperative games (i.e., Nash, Stackelberg retailer and Stackelberg manufacturer) and one cooperative game. We identify optimal co-op advertising and pricing strategies for both firms mostly analytically but we have to resort to numerical simulations in one case. Comparisons are then made about various outcomes, especially the profits, for all cases. This leads to consider more specifically the cooperation case in which profits are the highest for both the retailer and the manufacturer, and how they should share the extra joint profit achieved by moving to cooperation. We solve this bargain problem using the Nash bargaining model.     

基于环保的广告机概念设计

广告机这一产品通过视频、音频的形式向公众传达信息,其主要使用环境为公共场合。在广告机概念设计上。不仅注重外观的时尚和简洁,有时为了向人们传达环保的理念,特别在广告机面板下方的广告单领取口镂空丝印一个树和海洋图标。当人们领取广告单时,广告单数量减少．图标会逐渐的产生变化。通过这种图标的变化来警示人们环保的重要性。     

Can avatar and self-referencing really increase the effects of online 2-D and 3-D advertising?

Previous studies have sought insights into how websites can effectively draw sustained attention from internet users. Do different types of information presentations on webpages have different influences on users’ perceptions of the information? More precisely, can combinations of an ever greater number of advertising elements on individual websites increase consumers’ purchase intentions? The aim of this study is to explore changes in web advertising’s verbal and visual stimulation of surfers’ cognitive process, and to provide valuable information for the successful matching of advertising elements to one another. We examine optimal website design according to the personality-trait theory and resource-matching theory. Study 1 addresses the effects that combinations of various types of online advertising can have on web design factor, and to this end, we use a 2 (visual complexity: 3D advertising with an avatar, 2D advertising) × 2 (verbal complexity: with or without self-referencing that is an advertising practice to express product claims in words) factorial design. Study 2 treats personality traits (i.e., need-for-cognition and sensation seeking) as moderating variables to build the optimal portfolio regarding the “online-advertising effects” hypothesis. Our results suggest that subjects prefer medium-complex advertising comprising “3D advertising elements with an avatar” or “2D advertising elements with self-referencing”: high-sensation seekers and low-need-for-cognition viewers prefer the former, whereas low-sensation seekers and high-need-for-cognition viewers prefer the latter.