Innovation diffusion uncertainty,advertising and pricing policies

We develop and analyze a normative and structurally stochastic model of innovation diffusion by depicting the market at an aggregate level. Model dynamics are defined through the flow pattern of individuals that move from the innovation unaware stage, to the innovation aware, and ultimately to the adopter stages. The stochastic evolution of this stage-wise transition unfolds according to tractable stochastic processes and is influenced by such factors as price, word of mouth, and advertisement efforts. In this environment, techniques of contingent claims analysis and stochastic control theory are employed to obtain optimal pricing or advertising policies that maximize the value of the innovation. To account for their optimal adjustment over time, these policies are modeled as positive real-valued adapted processes. Given this setting, policy adjustments over time (i.e. advertising or pricing) are viewed as a value additive sequence of nested real options. We present closed-form analytic results regarding the optimal policies. Simulations provide a numeric insight to the models' behavior.     

A joint dynamic pricing and advertising model of perishable products

Advertising and dynamic pricing play key roles in maximizing profit of a firm. In this paper a joint dynamic pricing and advertising problem for perishable products is investigated, where the time-varying demand rate is decreasing in sales price and increasing in goodwill. A dynamic optimization model is proposed to maximize total profit by setting a joint pricing and advertising policy under the constraint of a limited advertising capacity. By solving the dynamic optimization problem on the basis of Pontryagin’s maximum principle, the analytical solutions of the optimal joint dynamic pricing and advertising policy are obtained. Additionally, to highlight the advantage of the joint dynamic strategy, the case of the optimal advertising with static pricing policy is considered. Numerical examples are presented to illustrate the validness of the theoretical results, and some managerial implications for the pricing and advertising of the perishable products are provided.     

Supply chain coordination through integration of innovation effort and advertising support

This study integrates firms’ innovation and advertising decisions in a two-echelon supply chain, where a monopoly manufacturer sells products to ultimate consumers through an autonomous retailer. Considering that both innovation and advertising contribute to the product demand, we first investigate the optimal equilibriums of channel members under two different game structures: the non-cooperative and cooperative. In the non-cooperative structure, the manufacturer controls the innovation effort and wholesale price while the retailer controls the advertising rate and retail pricing. In the cooperative structure, the manufacturer agrees to share part of retailer’s advertising expenditure. We find that both the optimal operation and marketing decisions are sensitive to effects of innovation and advertising on demand as well as the manufacturer’s cost reduction coefficient due to innovation. Further, we find that the manufacturer always prefers cooperation. Meanwhile, only when the firms’ investments significantly contribute to the market mechanism, does the retailer have incentive to implement a cooperative program. In addition, we further propose a new two-way subsidy policy to coordinate channel members’ business functions.     

Channel Coordination with Cooperative Advertising Considering Effect of Advertising on Willingness to Pay

In this paper, cooperative advertising in a manufacturer–retailer supply chain is studied. Advertising can enhance willingness to pay (WTP) of customers. This trade-off between the benefits of increasing WTP of customers and the advertising expenditure is a key to understanding the retailers optimal advertising decision. On the other hand, it is interesting to understand in which condition supporting the retailer for his advertising expenditure is beneficial for the manufacturer. In this study, in order to capture pricing and advertising strategies of the channel member, three non-cooperative games including Nash, Stackelberg retailer and Stackelberg manufacturer game-theoretic models are established. In spite of the related studies which restrict price in order to prevent negative demand, the proposed model allows channel members to increase their prices by enhancing WTP of customers. In this study, contrary to similar additive form demand functions applied in the co-op ad literature which limits their studies for cases that profit function is concave with respect to variables, optimal prices and advertising strategies are obtained for all the solution space. Surprisingly for the very high values of the advertising effect coefficient, a finite optimal advertising expenditure is achieved.     

An inventory system with two suppliers and default risk

This paper considers the problem of joint replenishment and pricing for a single product with two suppliers and supply disruption. Our objective is to maximize the total profit by choosing an appropriate replenishment and pricing policy. We not only obtain that the form of the optimal policy has a (s,S,p,σ,Σ)-type, but also analyze how supply disruption affects the profit function and the optimal policy.     

Positioning of new brands in an experiment

This paper deals with an experimental investigation of positioning new brands. For this purpose, a management game was carried out with students. The brands introduced in the cause of the game were analysed in respect to their positions in a two-dimensional feature space. We try to find out which of the two strategies, niche policy and imitation, is more frequently used in complex decision situations and if there is a difference in profits. Furthermore, we want to find out, whether differences of prices and advertising exist in our experiment depending on the positioning strategy used.     

On Controlled Linear Diffusions with Delay in a Model of Optimal Advertising under Uncertainty with Memory Effects

We consider a class of dynamic advertising problems under uncertainty in the presence of carryover and distributed forgetting effects, generalizing the classical model of Nerlove and Arrow (Economica 29:129–142, 1962). In particular, we allow the dynamics of the product goodwill to depend on its past values, as well as previous advertising levels. Building on previous work (Gozzi and Marinelli in Lect. Notes Pure Appl. Math., vol. 245, pp. 133–148, 2006), the optimal advertising model is formulated as an infinite-dimensional stochastic control problem. We obtain (partial) regularity as well as approximation results for the corresponding value function. Under specific structural assumptions, we study the effects of delays on the value function and optimal strategy. In the absence of carryover effects, since the value function and the optimal advertising policy can be characterized in terms of the solution of the associated HJB equation, we obtain sharper characterizations of the optimal policy.     

Optimal geometric process replacement model

In this paper, we study the geometric process replacement model as follows: the successive survival times of the system form a nonincreasing geometric process while the consecutive repair times of the system constitute a non-decreasing geometric process, and the system is replaced at the time of theNth failure after its installation or last replacement. Based on the long-run average cost per unit time, we determine the optimal replacement policyN* show the uniquess of the policyN* and discuss its monotonicity.     

Markdown money contracts for perishable goods with clearance pricing

It is common in practice that retailers liquidate unsold perishable goods via clearance pricing. Markdown money is frequently used between manufacturers and retailers in such a supply chain setting. It is a form of rebate from a manufacturer to subsidize a retailer’s clearance pricing after the regular season. Two forms of markdown money are percent markdown money, in which the markdown money is limited to only a certain percentage of the retail price markdown, and quantity markdown money, which is essentially a buyback contract or returns policy with a rebate credit paid to the retailer for each unsold unit after the regular season. We show both forms of markdown money contracts can coordinate the supply chain and we discuss their strengths and limitations.     

Recent developments in dynamic advertising research

A variety of continuous-time differential functions have been developed to investigate dynamic advertising problems in business and economics fields. Since major dynamic models appearing before 1995 have been reviewed by a few survey papers, we provide a comprehensive review of the dynamic advertising models published after 1995, which are classified into six categories: (i) Nerlove–Arrow model and its extensions, (ii) Vidale–Wolfe model and its extensions, (iii) Lanchester model and its extensions, (iv) the diffusion models, (v) dynamic advertising-competition models with other attributes, and (vi) empirical studies for dynamic advertising problems. For each category, we first briefly summarize major relevant before-1995 models, and then discuss major after-1995 models in details. We find that the dynamic models reviewed in this paper have been extensively used to analyze various advertising problems in the monopoly, duopoly, oligopoly, and supply chain systems. Our review reveals that the diffusion models have not been used to analyze advertising problems in supply chain operations, which may be a research direction in the future. Moreover, we learn from our review that very few publications regarding dynamic advertising problems have considered the supply chain competition. We also find that very few researchers have used the diffusion model to investigate the dynamic advertising problems with product quality as a decision variable; and, the pricing decision has not been incorporated into any extant Lanchester model. The paper ends with a summary of our review and suggestions on possible research directions in the future.     

Variational Inequalities in Hilbert Spaces with Measures and Optimal Stopping Problems

We study the existence theory for parabolic variational inequalities in weighted L ² spaces with respect to excessive measures associated with a transition semigroup. We characterize the value function of optimal stopping problems for finite and infinite dimensional diffusions as a generalized solution of such a variational inequality. The weighted L ² setting allows us to cover some singular cases, such as optimal stopping for stochastic equations with degenerate diffusion coefficient. As an application of the theory, we consider the pricing of American-style contingent claims. Among others, we treat the cases of assets with stochastic volatility and with path-dependent payoffs.     

短视型创新企业最优定价研究

率先创新使企业拥有时间和产品竞争力上的优势,获得先动优势;而模仿创新减少企业的研发成本,更能满足顾客的需求,从而可以获得更高的成功率,使模仿创新企业获得后进优势.针对短视型创新企业行为,研究以原始创新产品进入市场、模仿创新产品进入市场、原始创新产品的升级换代产品进入市场为分隔点的产品生命周期不同阶段下率先创新企业对产品的最优定价,以及模仿创新企业采用不同价格策略下的产品均衡定价.结论表明:无论企业采用什么价格策略,升级换代产品进入市场的最优时间都应满足升级换代产品进入市场前创新企业的阶段末瞬时利润率与进入市场后的初始瞬时利润率相等.     

Quality and pricing decisions in production/inventory systems

In this article, we consider the impact of finite production capacity on the optimal quality and pricing decisions of a make-to-stock manufacturer. Products are differentiated along a quality index; depending on the price and quality levels of the products offered, customers decide to either buy a given product, or not to buy at all. We show that, assuming fixed exogenous lead times and normally distributed product demands, the optimal solution has a simple structure (this is referred to as the load-independent system). Using numerical experiments, we show that with limited production capacity (which implies load-dependent lead times) the manufacturer may have an incentive to limit the quality offered to customers, and to decrease market coverage, especially in settings where higher product quality leads to higher congestion in production. Our findings reveal that the simple solution assuming load-independent lead times is suboptimal, resulting in a profit loss; yet, this profit loss can be mitigated by constraining the system utilization when deciding on quality and price levels. Our results highlight the importance of the relationship between marketing decisions and load-dependent production lead times.     

Optimal pricing and advertising in a durable-good duopoly

This paper analyzes dynamic advertising and pricing policies in a durable-good duopoly. The proposed infinite-horizon model, while general enough to capture dynamic price and advertising interactions in a competitive setting, also permits closed-form solutions. We use differential game theory to analyze two different demand specifications – linear demand and isoelastic demand – for symmetric and asymmetric competitors. We find that the optimal price is constant and does not vary with cumulative sales, while the optimal advertising is decreasing with cumulative sales. Comparative statics for the results are presented.     

Existence and uniqueness of optimal dynamic pricing and advertising controls without concavity

We consider a pricing and advertising dynamic-optimization problem where the goodwill dynamics evolve à la Nerlove–Arrow. The firm maximizes its profit over a finite-planning horizon corresponding to the product’s lifespan, and it turns out that the Hamiltonian is non-concave. We show the existence and uniqueness of an optimal solution under some mild conditions.     

Periodicity of pricing and marketing efforts in a distribution channel

Most research about cooperative (coop) advertising programs in channels relies on the assumption that manufacturers and retailers decide of pricing and marketing efforts simultaneously. This paper evaluates this central assumption and investigates the optimal periodicity (sequence of move) of pricing and marketing efforts (ME) decisions for a distribution channel. We develop a game theoretic model that accounts for pricing at each level of the channel, for the manufacturer’s ME mix strategies (a direct ME to consumers and coop advertising program offered to the retailer) and the retailer’s ME as well. We obtain solutions for a bilateral channel under different vertical interaction scenarios; when the channel is led by the manufacturer, the retailer or when channel members decide simultaneously of each of their marketing mix decisions (vertical Nash). We compare the effect of pricing and ME decision periodicity on outputs for each channel member. The main findings suggest that simultaneous decision-making of pricing and ME is optimal only for high enough levels of the manufacturer’s ME effects. For very highly effective marketing efforts, sequential play of pricing and ME allows channel members to implement equilibrium strategies and achieve maximum profits that would not be achieved with simultaneous decision-making. This highlights the importance of relaxing the simultaneous play assumption of pricing and ME in a distribution channel.     

不同决策模式下的双渠道供应链合作广告博弈分析

本文研究了双渠道供应链中非合作广告模式、合作广告模式和战略联盟模式下的合作广告问题,给出了不同决策模式下的均衡解。对比分析发现:战略联盟模式中品牌广告和零售商广告投入水平最高,网络广告投入水平最低且零售渠道的产品需求最高。合作广告模式和战略联盟模式中的系统收益与广告比率负相关,与产品网络适应度正相关。     

Joint pricing and inventory control with a Markovian demand model

We consider the joint pricing and inventory control problem for a single product over a finite horizon and with periodic review. The demand distribution in each period is determined by an exogenous Markov chain. Pricing and ordering decisions are made at the beginning of each period and all shortages are backlogged. The surplus costs as well as fixed and variable costs are state dependent. We show the existence of an optimal (s, S, p)-type feedback policy for the additive demand model. We extend the model to the case of emergency orders. We compute the optimal policy for a class of Markovian demand and illustrate the benefits of dynamic pricing over fixed pricing through numerical examples. The results indicate that it is more beneficial to implement dynamic pricing in a Markovian demand environment with a high fixed ordering cost or with high demand variability.     

A dynamic model for advertising and pricing competition between national and store brands

We study the relationship between the pricing and advertising decisions in a channel where a national brand is competing with a private label. We consider a differential game that incorporates the carryover effects of brand advertising over time for both the manufacturer and the retailer and we account for the complementary and competitive roles of advertising. Analysis of the obtained equilibrium Markov strategies shows that the relationship between advertising and pricing decisions in the channel depends mainly on the nature of the advertising effects. In particular, the manufacturer reacts to higher competitive retailer’s advertising levels by offering price concessions and limiting his advertising expenditures. The retailer’s optimal reaction to competitive advertising effects in the channel depends on two factors: (1) the price competition level between the store and the national brands and (2) the strength of the competitive advertising effects. For example, in case of intense price competition between the two brands combined with a strong manufacturer’s competitive advertising effect, the retailer should lower both the store and the national brands’ prices as a reaction to higher manufacturer’s advertising levels. For the retailer, the main advantage from boosting his competitive advertising investments seems to be driven by increased revenues from the private label. The retailer should however limit his investments in advertising if the latter generates considerable competitive effects on the national brand’s sales.