Optimal control of advertising and production of a seasonal product with nondifferentiable demand

We consider an application of optimal control theory to a marketing problem, in which a firm seeks the maximum profit by producing and selling a seasonal product. We assume that the firm can advertise its product in order to improve the firm goodwill and affect the product demand positively. In particular the demand is zero when the goodwill is less than a fixed threshold. The original optimal control problem is shown to be equivalent to a nonlinear programming problem, which has an optimal solution, possibly not unique. Editor: G. Leitmann     

商誉影响下的双渠道供应链竞争广告策略研究

随着网络技术的发展,电子网络销售品台走进消费者的世界,冲击着传统的零售市场,越来越多的企业开始在新的市场结构中寻找更为广阔的商机,如何在新的消费市场结构中合理的进行资源配置成为当下企业的一个难题,为研究电子直销和传统零售混合双渠道供应链中两个零售商品牌竞争的广告投入问题,构建了一个商誉影响下的双渠道供应链品牌竞争广告策略模型,运用汉密尔顿-雅克比-贝尔曼方程,分析竞争条件下的广告投入和影响因子。研究结果表明：存在竞争关系的两个零售商在混合双渠道供应链下的广告投入不仅跟当前的市场份额相关,同时还取决于商誉对市场竞争的影响力;最后利用数值算例分析论证了理论结果。     

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.     

RFID-enabled item-level product information revelation

We consider a homogeneous product market and the incentive for oligopolists to share item-level product information with their customers. Enabled by Radio Frequency Identification technology, each firm has the option to record and reveal item-level information of a proportion of its products. We consider a two-stage game where each firm first decides its production plan and then determines its level of information revelation. With a constant clearance discount rate, we derive pure strategy equilibria that are subgame perfect and demonstrate that complete information sharing is the unique Nash equilibrium for the game when the common demand is volatile and that no information revelation is the unique Nash equilibrium when demand is not volatile. Furthermore, we show that the Nash equilibrium is the same with a decreasing clearance discount rate and that neither complete information revelation nor zero information revelation is consistent with an equilibrium with an increasing discount rate. Results are similar in a duopoly non-homogeneous product market scenario.     

The Cournot game under a fuzzy decision environment

The conventional precision-based decision analysis methodology is invalid for business decision analysis when precise assessment data seldom exist. This paper considers the Cournot game with fuzzy demand and fuzzy costs that are assumed to be triangular fuzzy numbers. Our model utilizes the weighted center of gravity (WCoG) method to defuzzify the fuzzy profit function into a crisp value. We derive the equilibrium Cournot quantity of each firm by simultaneously solving the first-order condition of each firm. Our model explicitly derives the necessary condition to avoid an unreasonable outcome of negative equilibrium quantities and lack of flexibility for modification of the ranking method. In addition, we examine the standard deviation of the fuzzy profit resulting from the fuzziness of each firm’s cost and market demand functions. We conduct sensitivity analysis to investigate the effect of parameter perturbations on firms’ outcomes. The results indicate that the center of parameter plays an important role in sensitivity analysis and dominates over variations in equilibrium quantity due to a perturbation of fuzzy parameters.     

零售商竞争下考虑产品商誉的纵向联合促销微分博弈

将产品商誉作为状态变量,借助微分博弈研究由单个制造商和两个竞争性零售商组成的供应链纵向联合促销问题.在产品需求受商誉和零售商促销努力的共同影响下,分别构建集中式和分散式微分博弈模型,引入成本分担契约对供应链进行协调,并通过算例对相关参数进行灵敏度分析.研究表明:成本分担契约的引入可提高零售商促销努力水平、产品商誉以及需求量,实现供应链协调;随着零售商竞争程度以及促销努力成本系数的增加,引入契约后供应链成员的利润增加值呈下降趋势;相反,随着零售商促销努力以及产品商誉对需求影响程度的增加,供应链成员的利润增加值呈上升趋势.     

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.     

Do e-business strategies matter? The antecedents and relationship with firm performance

Previous studies in e-business strategy focus on the issues of strategic positioning and its impact on firm performance. However, these studies do not address the antecedents to business strategies formulation and their impact on business performance or the role of business models in explaining e-business firm performance. This study applies Porter’s generic strategies to the e-business context. It also identifies business models that are applied to the e-business environment and environmental factors and then examines these factors influence on firm performance with survey data. This study finds that uncertainty has a negative impact on the choice of strategic position of e-business firms, whereas market turbulence positively affects the level of adoption of all the strategies. Among the strategic positions, marketing differentiation positively influences firm performance. The research methodology, test results, and implications are further discussed.     

To innovate or not to innovate?

In this paper, we analyze the evolution of output decisions of adaptive firms in an environment of oligopolistic competition. The firm might either choose to produce one of several existing product variants or try to establish a new product variant on the market. The demand for each individual product variant is subject to a life cycle, but aggregate demand for product variants is constant over time. Every period each firm has to decide whether to produce the product again, introduce a new product variant itself (which generates an initial advantage on that market), or follow another firm and change to the production of an already established product. Different firms have heterogeneous abilities to develop products and imitate existing designs; therefore, the effects of the decision whether to imitate existing designs or to innovate differ between firms. We examine the evolution of behavior in this market using an agent-based simulation model. The firms are endowed with simple rules to estimate market potentials and market founding potentials of all firms, including themselves, and make their decisions using a stochastic learning rule. Furthermore, the characteristics of the firms change dynamically due to “learning by doing” effects. The main questions discussed are how the success and the optimal strategy of a firm depend on the interplay between characteristics of the industry and properties of the firm     

两级供应链减排与促销的合作策略研究

首先假设在由零售商主导的供应链中, 制造商的低碳声誉和零售商的促销都能增加产品的需求, 减排对制造商的低碳声誉有正面影响; 然后运用微分博弈理论, 比较了不合作、成本分担契约以及合作3 个契约对供应链成员的影响. 研究发现, 制造商和零售商的促销及减排水平在合作契约下最高, 但供应链的总价值在合作契约下最大是有条件的. 当存在合作价值时, 为了使制造商和零售商获得更多的价值设计了利润共享契约.     

Information security breaches and IT security investments: Impacts on competitors

In current business climate, a firm’s information systems security is no longer independent from the industry’s broader security environment. A question arises, then, whether stock market values reflect the interdependence of security breaches and investments. In this paper, we used the event study methodology to investigate how a firm’s security breaches and IT security investments influence its competitors. We collected and reviewed 118 information security breaches and 98 IT security investment announcements from 2010 to 2017. We found substantial evidence supporting our hypothesis that information security breaches do, indeed, have a competition effect: when one firm is breached, its competitors have opportunities to absorb market power. For the IT security investment announcements, however, we observed the positive externalities, or contagion effect, in play: market investors feel that the security investments made by one firm increase the security level of the entire network, and hence, competitors also get benefits. Additionally, we found that the competition effect was higher when the breaches occurred after the preceding security investments than when there were no preceding investments before the breaches.     

不同权力结构下供应链减排策略随机微分博弈

在由单个制造商和单个零售商构成的低碳供应链中,制造商与零售商之间不同的权力结构决定着他们的减排策略与博弈方式.同时,低碳产品商誉与需求受到制造商与零售商减排策略及随机因素的长期动态影响.在不同的权力结构下,对制造商减排努力策略与零售商宣传努力策略进行随机微分博弈分析;在集中式决策基础上,分别构建制造商主导与零售商主导的Stackelberg博弈、无主导Nash博弈模型,求解模型并对结果进行理论分析与数值实验.研究发现:相较于自己作为主导者,对方作为主导者会促使制造商或零售商做出更大的减排努力或宣传努力;与有主导者的供应链相比,无主导者的供应链可能实现更大的低碳产品商誉;制造商作为主导者能够提升低碳产品商誉与需求以及供应链总利润.随机因素促使制造商和零售商分别提高了减排努力和宣传努力以及低碳产品商誉.     

Integrated marketing communications in markets with uncertainty and competition

Firms frequently utilize multiple communications instruments as part of their marketing campaign. Interactions between these instruments suggest that firms should apply Integrated Marketing Communications (IMC) to benefit from the synergies. We review different IMC models and then present a stochastic IMC model for which explicit closed-loop solutions of the optimal advertising and market share are obtained. This enables us to understand the role of firm and market parameters such as synergy on the optimal advertising budget and allocation. For the proposed and existing IMC models, we show that the budget and allocation decisions can be made independently, greatly simplifying the implementation of IMC. We also show that there is an optimal long-run market share that the firm should try to maintain through appropriate use of IMC. Finally, the model and results are generalized to multiple (>2) instruments and multiple competitors.     

Come together? The organizational dynamics of post-merger cultural integration

Cultural integration of two organizations following an acquisition depends on the compatibility of the contents of their respective cultures as well as the demographic flows of persons into and out of the new entity. Conducting simulations using an established formal demographic model of the enculturation process, we find that negative growth promotes cultural integration while positive growth impedes it, and that cultural integration proceeds more rapidly when the acquiring firm is large relative to the acquired firm. We also find that cultural recovery for merged firms experiencing either positive or negative growth is slower than for firms with zero growth.     

On deriving and validating comparative statics of a symmetric model of advertising competition

In this article, a market share attraction model is estimated using a data set of six manufacturers related to the ready-to-eat cereal industry in the US. For each year of the studied period, the market share of each firm is less than 50%, and these market shares are further apart from one another. In the reported application it is demonstrated, for the first time in the literature, that if model parameters change, all rivals in the industry should adjust their advertising spending in a manner consistent with the symmetric competitive structure for which all market shares are equal. Implications of this important finding are discussed.Scope and purposeUsing a market share model of advertising competition and following a game theoretic approach, this study examines analytically and empirically the sensitivity of optimal advertising to changes in model parameters in a setting of symmetric competition. The results presented in the paper suggest that the proposed approach is useful for a firm to ascertain how to adapt its advertising strategy in response to changes in the market to maintain or enhance its position.     

A continuous review production–inventory system in fuzzy random environment: Minmax distribution free procedure

In many manufacturing systems, the production process may take some time to start the initial phase due to various reasons such as delay in installation of machines, short supply of raw materials, unavailability of workers, etc. Thus, the organization should plan accordingly so that the manufacturing process can start at the desired time. In an economic production quantity (EPQ) model, lead-time plays a significant role in ensuring that the manufacturing process starts on time. As we know, when both lead-time and demand rate are deterministic and constant, then demand during the lead-time is constant, and is referred to as zero lead-time. Moreover, when either or both of them are random variables, then lead-time demand (LTD) is a random variable. In such a case, a crucial question is: “when should the order be placed?” On the other hand, the distributional information on demand may not always be available or there may be many distribution functions in the practice, which have same mean and variance, but their frequencies are different. In this study, we develop an EPQ model in stochastic framework, wherein the distribution function of demand is unknown, but the mean and variance are known. The inventory level is continuously reviewed, and an order is placed when it reaches the reorder level. The real-life business situations are so sophisticated and floating in nature that the consideration of ‘impreciseness’ along with ‘statistical variability’ in demand parameter is more preferable. To be a part of this contingency, we further extend the model in the fuzzy random environment by considering demand rate as a fuzzy random variable (FRV). Furthermore, we mathematically analyze the cost function and propose a heuristic procedure to find the global optimum. Numerical examples with sensitivity analysis are also provided for illustration purpose.     

Tuning into the digital channel: evaluating business model characteristics for Internet firm survival

More than 5,000 Internet firms have failed since the beginning of 2000. One common perception is that the downturn in the economy drove many firms out of business. But then, why have some firms survived? In this research, we provide an empirical analysis by examining how the business model characteristics of an Internet firm affect its survival. We analyze a panel data set of 130 public Internet firms using two different techniques: non-parametric survival analysis, and the semiparametric Cox proportional hazards model. We characterize the survival rates throughout the lifetimes of the public Internet firms in our sample. Our results reveal that smaller firms that facilitate customer-provider interactions, are transaction brokers, and that rely on advertising as their primary source of revenue sources have had a lower likelihood of bankruptcy or failure. In addition, the detrimental effects on failing to serve as interaction platforms for individuals and businesses, and a larger firm size diminish over time as Internet firms mature, and the weaker ones are forced out of the marketplace. Our research also points out important dimensions of an Internet firm’s business model that affect its survival.     

On optimum advertising pulsing decisions in a non-stationary market

Using empirical findings available in the literature, sales behavior in response to advertising pulsing policy has been modeled mathematically in a non-stationary market. The paper discusses in detail optimum advertising pulsing policy.This policy has been compared with an alternative policy commonly used in practice. The results of the research indicate the possibility of achieving substantial savings in the advertising budget and/or increase in sales revenues of a firm when implementing advertising pulsing policy.     

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.     

Modeling the dynamic optimal advertising in stochastic condition

An effort to model the dynamic optimal advertising was made with the uncertainty of sales responses in consideration. The problem of dynamic advertising was depicted as a Markov decision process with two state variables. When a firm launches an advertising campaign, it may predict the probability that the campaign will obtain the sales reponse. This probability was chosen as one state variable. Cumulative sales volume was chosen as another state variable which varies randomly with advertising. The only decision variable was advertising expenditure. With these variables, a multi-stage Markov decision process model was formulated. On the basis of some propositions the model was analyzed. Some analytical results about the optimal strategy have been derived, and their practical implications have been explained.