Optimal Advertising Strategies Research Articles

Understanding the optimal strategy of carbon labelled product advertising delivery: A dynamic differential equation analysis

In the rapidly evolving landscape of sustainable marketing, the advertising of carbon labelled products represents a critical intersection of environmental awareness and marketing strategy. Existing studies have mainly discussed optimization strategies for content and forms of advertising. Less attention has been paid to optimization strategies related to the quantity of advertising delivery. Setting an advertiser's optimal advertising intensity is a problem that has puzzled researchers for a long time. To this end, we investigate the optimal strategy for advertising delivery based on a differential equation analysis of advertising dynamics to maximize market size for advertisers with regard to carbon labelled products. We first show that the vitality index can reflect the carryover effect of advertisers, and that there exists an optimal advertising intensity to maximize market size if competition is not taken into account. We then find that current and global solutions of optimal strategies are consistent, from which we can determine the sustainability of an advertiser's carbon labelled product market by calculating the equilibrium vitality index. Moreover, we provide numerical experiments that illustrate the quantitative relationship that exists between greenness and the proportion of green consumers jointly determining the feasibility of the optimal strategy and the sustainability of advertisers in management practices. This research not only charts a course for optimal advertising strategy but also equips managers with data-driven tools to navigate the complexities of eco-conscious marketing.

Dynamic Cooperation of the O2O Supply Chain Based on Time Delays and Bidirectional Free-Riding

Advertising and service investment can enhance brand goodwill to increase the sales of branded goods. However, the impact of advertising and services on brand goodwill is not immediate but delayed. At the same time, due to the different service characteristics provided by various channels, the phenomenon of bidirectional free-riding occurs. Therefore, this paper studies the dynamic cooperation between service and advertising in the O2O (online to offline) supply chain dominated by brand owners and explores the impacts of advertising, service delay and service free-riding among channels on the dynamic cooperation decisions of the O2O supply chain. A differential game model between brands and retailers is constructed by incorporating the delay effect and the bidirectional free-riding phenomenon. The optimal advertising and service strategies and performance problems of O2O supply chain enterprises under a centralized decision, brand cost-sharing decision and bilateral cost-sharing decision are compared and analyzed. The influence of delay time, showrooming and webrooming effects on the profit of each firm is investigated by example. The results show that the service strategy, advertising strategy and brand goodwill of the O2O supply chain members are optimal under a centralized decision. Still, the supply chain profit is not necessarily optimal under the delay time, showrooming and webrooming effect coefficients. Bilateral cost-sharing contracts can achieve Pareto improvement of supply chain performance. Appropriate setting of a bilateral cost-sharing ratio can adjust the adverse effects of delay and bidirectional free-riding. The long-term strategies to deal with the delay and bidirectional free-riding phenomena are as follows: the bilateral cost-sharing contract can improve corporate profits. Setting the wholesale price, online direct-selling price and service-sharing ratio by brand owners can effectively promote retailers’ investment in service, achieving a win-win situation. Retailers maintain high pricing and service levels to enhance the brand premium ability of physical stores and achieve long-term development.

The optimal advertising strategy with differentiated targeted effect consumers

The optimal advertising strategy with differentiated targeted effect consumers

Too Popular, Too Fast: Optimal Advertising and Entry Timing in Markets with Peer Influence

We study optimal advertising and entry timing decisions for a new product being sold in two-segment markets in which followers are positively influenced by elites, whereas elites are either unaffected or repulsed by product popularity among followers. Key decisions in such markets are not only how much to advertise in each segment over time but also when to enter the follower segment. We develop a continuous-time optimal control model to examine these issues. Analysis yields two sets of two-point boundary value problems where one set has an unknown boundary value condition that satisfies an algebraic equation. A fast solution methodology is proposed. Two main insights emerge. First, the optimal advertising strategy can be U-shaped, that is, decreasing at first to free-ride peer influence but increasing later on to thwart the repulsion influence of overpopularity causing disadoption. Second, in markets where cross-segment repulsion triggers disadoption, advertising is only moderately effective, and entry costs are high, managing both advertising and entry timing can result in significantly higher profits than managing only one of these levers. In markets without disadoption, with high advertising effectiveness or with low entry costs, in contrast, delaying entry may add little value if one already manages advertising optimally. This implies that purveyors of prestige or cool products need not deny followers access to their products in order to protect their profits, and can use advertising to speed up the democratization of consumption profitably.This paper was accepted by Juanjuan Zhang, marketing.

Sales Strategy considering Advertising in Advance-Selling and Spot-Selling Integration Mode for Fresh Product

In this paper, we look into the optimal sales strategy of e-commerce platform which sells fresh-product advertising in advance-selling period and spot-selling period, respectively, when advance-selling and spot-selling integration mode is applied. The study found that, with the increase of advertising investment, the marginal benefit of e-commerce platform is declining; whether advertising during the advance-selling period or the advertising during the spot-selling period, the e-commerce platform can improve its profit, but under the same advertising effect factor, the optimal advertising investment for the sale period is smaller, and the profit when advertising in the advance-selling period is greater. When advertising in different periods, the optimal advertising and price strategy depends on the maximum valuation of consumers about the product and the advertising effect factor.

Differential game model of cooperative advertising in a supply chain with deteriorating items, competing retailers and reference price effects

ABSTRACT The phenomenon of cooperative advertising in the market has always been widespread. Considering a supply chain consisting of one manufacturer and multiple retailers with competitive relationships, we explore advertising strategies for deteriorating items when market demand is affected by reference price. By establishing a differential game model, the equilibrium advertising strategies and supply chain profits under different situations are analysed from a long-term and dynamic perspective under decentralised and centralised control, and the trajectories of goodwill and reference prices over time are presented. The conclusions derived provide implications for managers to design optimal advertising strategies.

Offensive, Defensive, and Generic Advertising Strategies in a Dynamic Oligopolistic Market

In today’s highly competitive business environment, advertisement plays an influential role in attracting customers and increasing market share. Companies adopt different advertising strategies in a competitive market, such as offensive, defensive, and generic, to keep and increase their market share. Researchers have generally modeled this problem using a dynamic differential game. All previous research studies have focused on finding these strategies in a duopoly market. Also, to simultaneously determine the optimal equilibrium strategy for these three strategies, the model is designed as a symmetric game due to the ease of solving. In contrast with the previous researches, the purpose of this paper is to present and solve an asymmetric game model to determine the optimal offensive, defensive, and generic advertising strategies in an oligopoly market. The proposed model’s objective is to obtain the maximum equilibrium profit for each company at any moment regarding the market share of each company and those of competitors. A numerical solution method based on the Pontryagin’s maximum principle is developed to solve the model. Then, the proposed model is solved for a triopoly market. Also, the sensitivity of the results to changes in model parameters has been investigated. The obtained results denote that in markets with more than two players under the asymmetric game, the proposed model can prescribe the optimal type of offensive, defensive, and generic advertising strategies.

광고 노출과 비용을 고려한 최적 광고 선택 : 이진정수계획법 모형을 중심으로

광고 노출과 비용을 고려한 최적 광고 선택 : 이진정수계획법 모형을 중심으로

Cross-brand and cross-channel advertising strategies in a dual-channel supply chain

The economic value of private brands and online marketing channel have been widely recognized in literature and practical life. Besides, studies show that advertising, as one of the major factors, can affect consumer attitudes and has significant effects on demand and profit. On the existing basis, this paper analyzes the advertising strategies under competition between a national brand manufacturer and a retailer with private brand, where the national brand can be sold both through a direct channel and a store channel but the retailer brand can be sold only through a store channel. We study the best advertising investment strategies and the balanced profits of the national brand manufacturer and retailer in the disintegrated system and the integrated system. Specially, in the disintegrated system, we discuss the best decision-making issues for national brand manufacturer and retailer in two special cases which there is only have brand competition or channel spillover effects. We discuss the impacts of the spillover effect and brand competition on the chain members and advertising strategies of different channels. In addition, we design a unilateral advertising subsidy contract to coordinate the supply chain. The results in this paper offer structural and quantitative insights into the interplay between the manufacturer and retailer in the dual channel supply chain and can be used as a reference for choosing the optimal advertising strategy.

Dynamic generic and brand advertising decisions under supply disruption

Enterprise captures market share from competitors through brand advertising and increases consumer demand for this category of products through general advertising. In this paper, considering a supply chain with a manufacturer who is responsible for generic advertising and a retailer who undertakes brand advertising, a Stackelberg differential game-theoretic model is established to examine the impact of supply disruption faced by the manufacturer on the optimal decision-making and profits of supply chain members. When the supply of raw materials is disrupted, the optimal advertising strategies and advertising subsidy scheme designed for the initially estimated product sales need to be revised. The key to solving this problem is to explicitly consider possible deviation profit margins of supply chain members and total market demand for products caused by changes in the original product supply. Considering that the deviations of the profit margins and the total market demand are arbitrary, we analytically derive several propositions and obtain the optimal advertising strategies and the advertising subsidy scheme before and after the supply disruption. Then, we explore the impact of supply disruption through numerical analysis and provide management insights that are helpful for managers to re-design the advertising strategies and advertising subsidy schemes under supply disruption.

Stochastic Optimal Control Problem in Advertising Model with Delay

This paper investigates the optimal control problem arising in advertising model with delay. The authors reformulate the problem in Hilbert space by stochastic evolution equation and consider the optimal control problem of controlled stochastic evolution system. The necessary and sufficient optimality conditions of the control are established. The proposed approach is different from most existing studies of optimal advertising policy problem with delay. These results are applied to the optimal advertising policy problem under two different structures and the optimal advertising strategies are obtained.

Application of optimal control to the dynamic advertising decisions for supply chain with multiple delays

This paper is concerned with application problem of optimal control to a class of dynamic advertising models with multiple delays. Here, a dynamic model with state and control delays is introduced to describe the impacts of advertising delayed and memory effects on the evolution of brand goodwill. In the decentralized and centralized systems, the optimal advertising strategies of supply chain members are presented by utilizing the nonzero-sum differential game governed by differential equation with multiple delays in state and control variables. Special effort is made to analyse the geometrical shapes of advertising strategy and provide the optimal decision structure of supply chain system. Furthermore, nonzero-sum stochastic differential game is applied to explore the dynamic advertising decision problems of supply chain system with the multiple delays and stochastic cases. Finally, numerical examples are exploited to illustrate the effectiveness of the proposed results.

An optimal advertising strategy in aesthetic medicine budgets with uncertain income

ABSTRACT Considering advertising efficiency capital investment and overall revenue efficiency, this study explores how to construct the most appropriate advertising distribution of medical cosmetology, which is viewed as the overall research focus. (1) This study explores how the aesthetic medicine industry determines its optimal resource allocation ratio of advertising investment that can create maximum output value under the condition that the advertising budget for subsidiaries is limited and that advertising efficiency is uncertain. (2) The model of this study is based on the concept of dynamic programming, which is used to solve problems in multistage decision-making. Under limited advertising investment by subsidiaries in new media and traditional media advertisements, we aim to increase the number of visitors and high-consumption customers. (3) The contribution of this research is to construct a practical model for the optimal allocation of advertising investment in the aesthetic medicine industry. The research results, including a mathematical model and practical application, can be used as a reference for the aesthetics medicine industry or general companies to determine the best allocation of advertisement cost inputs.

Entry Deterrence, Coordinating Advertising and Pricing in Markets with Consumption Externalities

Abstract This paper extends the entry deterrence literature by examining coordinating advertising and pricing in markets with consumption externalities using a stochastic success function. Optimal advertising and pricing strategies are analysed when an incumbent firm faces a challenger with a product of equal quality. I show that strategic entry deterrence using advertising is possible and optimal entry deterrence involves strategic pre-commitment to over-investment relative to the non-strategic simultaneous advertising benchmark. I show that when entry deterrence is not possible the incumbent does not possess a first mover advantage and optimal entry accommodation involves strategic investment in advertising with intensified price competition congruent with the non-strategic simultaneous advertising benchmark. The findings suggest that an incumbent’s ability to deter entry through coordinating advertising in a market with products of equal quality is sensitive to the size of the fixed cost of entry that the challenger must incur and the consumption externality parameter.

Optimal advertising strategies in a sports licensing contract

Optimal advertising strategies in a sports licensing contract

New Optimal-Control-Based Advertising Strategies and Coordination of a Supply Chain With Differentiated Products Under Consignment Contract

With the aid of optimal control theory, the cooperative advertising problem is discussed for a supply chain under consignment contract in a competitive environment. Consider the case that the market demand of products is affected by advertising effort and goodwill, both the optimal advertising strategies and advertising participation rate in the centralized and decentralized settings are given. The state-dependent contract with the slotting fees is introduced to coordinate the considered supply chain. Our results demonstrate that the participation rate is closely related to the marginal profits of channel members and the competition intensity between products. Besides, the state-dependent contract with the slotting fees can effectively coordinate the supply chain when the contract parameters satisfy certain conditions. Finally, the sensitivity analysis of the competition intensity between products is conducted by using some simulations.

Feedback Equilibrium for Dynamic Competitive and Cooperative Advertising

This paper not only studies the competitive advertising between the manufacturer in direct channel and the upstream retailer which is in distribution channel, but also investigates the cooperative advertising between the upstream manufacturer and the downstream retailer in distribution channel in the case that the downstream retailer faces a competition from direct channel. Through the establishment of Nash game-theoretic model between the manufacturer in direct channel and the upstream retailer which is in distribution channel, the optimal advertising decisions of distribution channel and the downstream retailer are obtained. On the other hand, in order to obtain the optimal advertising strategies of members in distribution channel, Stackelberg game-theoretic models are established in this study. In this paper, we find that when there is a manufacturer in direct channel competing with distribution channel, the advertising participation rate from the upstream manufacturer to the downstream retailer is higher than that in no competitions. Under asymmetric and symmetric competition, the profit of the upstream retailer in distribution channel is always higher than that of the manufacturer in direct channel.

A manufacturer-retailers dynamic cooperative advertising with retail competition

This work deals with the cooperative advertising in a manufacturer retailers supply chain. It considers the manufacturer as the Stackelberg leader and the retailers as the followers playing a Nash game with each other. Using differential game theory it obtains a time consistent feedback Stackelberg equilibrium for the optimal advertising strategies and payoffs for a situation where retail advertising is subsidised and where it is not subsidised. The work shows that while the manufacturer's advertising effort reduces with subsidy, the retailers' advertising efforts and product awareness increase. These consequently lead to increase in all the players' payoffs. While a fair player would increase his advertising effort with increasing payoff, the others reduce their efforts. Further a retailer's advertising effort should be subsidised only if the rate of increase of the manufacturer's payoff through that retailer's margin to the manufacturer is twice greater than the rate of increase of that retailer's payoff.

How do loyalty programs affect goodwill? An optimal control approach

This paper examines the long-term impact of loyalty programs on a company’s profit and reputation among customers, and with different durations of product use. We analyze how the launch of loyalty programs may change the profitability of optimal advertising activities. The basis of this study is a modified goodwill model where the market is segmented according to usage experience. The main novelty is the role of loyalty programs and consumer recommendations in the creation of product goodwill, and also their influence on optimal advertising. The dynamics of goodwill are described by a partial differential equation. The firm maximizes the sum of discounted profits by choosing a different advertising campaign for each market segment. For a high-quality product, we observe that there is a trade off between the loyalty program and optimal advertising strategies. For a low-quality product, the loyalty program causes more profitable companies to invest heavily in additional advertising efforts.

Optimal impulsive control for advertising strategy problems based on a gradient-based PSO algorithm

This paper considers an optimal advertising strategy problem. This is an important problem in marketing investment for new products in a free market. The main contributions of this paper are as follows. First, the problem is formulated as an optimal control problem of switched impulsive systems with the state inequality constraints, which is different from the existing nonlinear system models. As the complexity of such constraints and the switching instants are unknown, it is difficult to solve this problem by using conventional optimization techniques. To overcome this difficulty, by applying the penalty function, all the state inequality constraints are first written as non-differentiable penalty terms and imposed into the cost function. Then, the penalty terms are smoothed by using a novel smooth function, leading to a smooth optimal control problem with no state inequality constraints, and an improved gradient-based particle swarm optimization (PSO) algorithm is proposed for solving this problem. Error analysis results show that if the adjustable parameter is sufficiently small, the solution of the smooth optimal control problem is approximately equal to the original problem. Finally, a switched impulsive system for beer sales is established to illustrate the effectiveness of the developed algorithm.