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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.

This paper investigates contract design by a firm in a supply chain where the quality of the product delivered to consumers is co-created by the quality decisions of the contract designer (platform firm) and the agent (the service provider) whose inputs need to be coordinated. Revenue is a function of the price charged to consumers, the product quality, and a market parameter which may be private information to the service provider. We focus on a contract with payment terms commonly used by large platforms such as Amazon. The platform firm adopts a menu-of-contracts approach to get the service provider to reveal its private information, resulting in optimal quality effort and price decisions that maximize the expected profit of the platform firm. We examine cases where the platform firm should disintermediate the service provider and make and sell the product itself. To study the coordination ability of the proposed contract, we compare the results with those obtained in the case of complete information via various benchmark scenarios.

In this paper, an extension of the Bass model is suggested that accounts for the influence of conformance quality on mixed (i.e., positive and negative) word-of-mouth in the diffusion of a new product. A primary goal is to determine how an active operational policy seeking to continuously improve conformance quality affects the optimal leveraging of marketing instruments used to diffuse new products, and the resulting sales and profits. To do so, an optimal tradeoff by a monopolistic firm between advertising effort and price, on the one hand, and conformance quality, on the other hand, is analyzed, along with the implications for word of mouth effectiveness. Our results can be summarized as follows. Price and advertising levels are respectively lower and higher under an operations–marketing policy than under a marketing policy only. As a result, the market potential and the innovation effect are higher under an operations–marketing policy than under a marketing policy only, as is the imitation effect due to conformance quality improvements over time. Also, greater cumulative sales and cumulative profits are obtained. However, higher design quality results in a lower price and greater advertising effort under an operations–marketing policy than under a marketing policy only. Finally, for lower design quality, the two policies result in different patterns (non-monotonic vs. monotonic) for price and advertising yet cumulative sales and profits are of quite similar magnitude.

Seeding the market by delivering free samples is a common strategy marketers use to promote new products, shorten the introduction stage and accelerate diffusion. There are several models for assessing seeding effectiveness and determining the optimal seeding that can maximize profits, given costs, diffusion parameters’ values and interest rates. In practice, however, managers use seeding mainly as a competitive tool, as a way to improve market position rather than to promote and accelerate the diffusion of a new product category. Actual seeding is quite small in volume compared to the optimal levels recommended by existing models. Seeding is also accompanied by other steps which do not involve giving away products. It is argued here that the problem is not the fact that marketers do not implement an optimal strategy, but rather the modeling itself. We present a method for analyzing seeding effectiveness and optimization, based on a diffusion model with a multi-stage purchase process, as suggested by Kalish. We compare the diffusion acceleration and optimal seeding assessments of our model against existing seeding assessment and optimization diffusion models that are based on a two-stage purchase process as described in the Bass model. To achieve optimization our model recommends seeding, as a means to accelerate the diffusion of new product categories, only in rare cases. This coincides much better with firms’ actual implementation of seeding strategies than seeding levels recommended by models in the literature. In particular, it is aligned with managers’ intuition that diffusion models with a two-stage purchase can lead to oversampling and an overestimated sales acceleration forecast.

Recent studies have revealed that a celebrity9s endorsement of a product or service positively influenced the purchase intention of the consumer. Such findings have created a necessity to identify the specific characteristics of celebrities that most positively influence an advertiser9s target audience. This study offers an innovative model for selecting celebrities that will most effectively endorse a specific product. By implementing adaptive conjoint analysis and genetic algorithms in the advertising process, advertisers will newly approach the method of matching product and celebrity from the perspective of product design.

Decentralized decision making is a fact in the modern business world accompanied by extensive research that looks into its consequences for overall firm profits. We study the interactions of decentralized marketing and operations divisions in a corporation and explore their impact on overall firm profits in the case with and without coordination of the two decentralized units. We assume that the marketing department is responsible for the price that influences the demand (sales), and the operations department is responsible for the production rate. We allow for backlogging over time. We model the interdependence involving marketing and operations decisions as a non-cooperative differential game, with the two divisions as strategically interacting players. We find that, without coordination, strategic interactions of marketing and production result in inefficiencies that can quantitatively be substantial. Next, we introduce a dynamic transfer pricing scheme as a coordination device and evaluate if it establishes efficient (first best and fully coordinated) outcomes. We show that if production and marketing play a game with pre-commitment strategies, there exists a dynamic transfer price that efficiently (fully) coordinates decentralized decision making and hence results in Pareto-efficient company profits. If the two decentralized divisions play a game without pre-commitment, dynamic transfer prices can partially coordinate decentralized decision making but fail to fully eliminate overall inefficiencies arising from strategic interactions among decentralized divisions.

In this paper, we propose a new model of adoption and repurchase due to upgrades driven by the utility of technology products that keep improving. The model is able to predict product life cycle patterns that could not be explained previously. Such patterns were used to challenge diffusion theory validity. Mathematically, the model is described as a nonlinear discrete system that depends on a small set of parameters. We investigate the dynamic properties of the nonlinear system using numerical stability analysis. We find domains in the parameters space in which the equilibrium point and the periodical orbits are stable. The domains correspond to population heterogeneity, tendency to upgrade, and the influence of industry response on market dynamics. We also implement our model to fit actual data of two real-world product life cycles with many irregularities and benchmark the results of our model vs. well-known models.

This paper focuses on the proactive planning of a partial switch of a prescription (Rx) drug brand to over-the-counter (OTC) status within the former's patent-protected life. The planning issues are whether and when to make this switch from the “single-status” Rx drug phase to the “dual-status” Rx+OTC phase with or without the grant of a 3-year market exclusivity period for the OTC drug by the US Food and Drug Administration. We formulate an optimal control problem that leads to a two-phase optimization problem with finite-time horizon involving switching time-dependent switching cost and terminal value. Applying a variational approach, we establish the conditions under which it can be optimal to make the partial switch. Counter to conventional thinking, the grant of market exclusivity is neither necessary nor sufficient for a partial switch before the Rx drug's patent expiry. Further, we show in a functionally specified model-based illustration, involving varying combinations of plausible ratios of OTC and Rx version margins and potential market sizes, that denial of OTC market exclusivity can imply that the firm should advance rather than delay the partial switch, and yield greater savings for Rx drug consumers. Implications for pharmaceutical Rx–OTC switch planners and policymakers are discussed.

Sellers often provide complimentary “no extra charge” add-ons (e.g., free Internet connection) to consumers who buy their primary products (e.g., a hotel stay), but recently add-ons that used to be free are offered for a fee. The conventional wisdom is that unadvertised add-ons for high fees help competitors increase profits that are competed away by advertising low prices for the basic products. This theory cannot explain why complimentary add-ons are still offered by some sellers. We show that providing complimentary add-ons can be profitable for sellers with monopoly power under certain demand conditions. If these demand conditions are not met, it is optimal to charge a supplementary fee for the add-on. We also show how pricing policy can be designed to selectively target or deter different consumer segments from purchasing the add-on to boost sellers’ profits, providing a strategic role for selling add-ons at either below-cost or at exorbitantly high prices. Yet such behavior may have repercussions for economic welfare when it results in socially inefficient giveaways when consumers would be better served with a lower price on the basic product without the add-on or, with the other extreme, when it results in excessively high prices for an add-on that restricts sales and leads to its under-provision from a societal perspective. The paper also provides managerial insights on the design and use of add-ons.

We consider a manufacturer's dual distributions channels consisting on the one hand of a virtual (online) channel operated directly by a manufacturer and on the other hand of a real (offline) channel operated by an intermediate retailer. Customers are assumed heterogeneous in their virtual acceptance, deriving a surplus according to the channel they shop at. Assuming that customers' derived benefits are random with a known probability distribution, we obtain a probabilistic model, which is used to construct an inter-temporal model for shopping online. In addition, we suppose that the retailer uses a markup pricing strategy and has a strategic role. This results in a Stackleberg differential game where the manufacturer is leader and the retailer is a follower. The optimal policy shows that the manufacturer charges the same price across both channels. This finding is consistent with classical results in economics. However, our research goes beyond this observation and indicates that the online price, the retailer's markup and the probability to buy are affected by consumers' heterogeneity in a specific manner. Moreover, we show that while the retailer sets a price equal to the product value, the online price is lower and is equal to the product value less the guarantee provided by the manufacturer for the risk the customer take to buy online. This guarantee is not discriminating and is set to the risk of the customer with the lowest virtual acceptance. Finally, we show that the introduction of the online store is a win-win strategy; both the customers and the manufacturer are better off.

The general approach to adaptive and dual control is to formulate an optimal stochastic control problem. However, for such an approach only mathematical representations of the solution are available which allow little insight into the structure of the optimal controller. Here, an alternative deterministic approach is presented based upon determining a control in which a disturbance attenuation function remains bounded for all allowable ( L 2 functions) disturbances. The disturbance attenuation function is composed of the ratio of an L 2 function of the desired outputs over an L 2 function of the disturbance inputs. This disturbance attenuation problem is converted to a differential game. For this game, the optimal control law, in a closed-form, is obtained by performing a minmax operation with respect to a quadratic cost function subjected to a bilinear system. The resulting controller is time-varying and depends nonlinearly on the state and the parameter estimates vector, and on an associated Riccati-type matrix. We provide insights into the structure of the resulting dual controller and illustrate the method by two examples. One of the examples is an application to marketing, to set promotional spending of a company, considering that the effect of promotional effort on sales is unknown.

This paper considers the nonpreemptive priority queue with MAP(Markovian Arrival Process) arrivals. Since MAPis weakly dense in the class of stationary point processes, it is a fairly general arrival process. Service times of customers of each priority class are independent and identically distributed according to a general distribution function that may differ among priority classes. Using both the generating function technique and the matrix analytic method, we derive various formulas for the marginal queue length distribution of each class. Further, we provide the delay cycle analysis of the waiting time distribution of each class and characterize its Laplace-Stieltjes transform.

In many business sectors such as airlines, hotels, trucking, and media advertising, customers' arrivals and willingness to pay are uncertain. Managers must decide whether to quote a price low enough to guarantee early sales, or to quote a higher price and risk that some units remain unsold. In allocating capacity, they face a trade-off between two types of potential losses; (1) Yield loss—selling at a low price, and losing a better price later, and (2) Spoilage loss—waiting in vain to sell at a high price, and losing the opportunity of an earlier low price offer. Yield loss means that consumers who value the product most do not get to use it, and spoilage loss means that valuable products are wasted because no consumers get to use them. Sellers typically hedge against the risk of spoilage loss by selling some units early at low prices, and against the risk of yield loss by blocking some units in hope of selling them later at a high price. In this paper we show that the use of overselling with opportunistic cancellations can increase expected profits and improve allocation efficiency. Under this strategy, the seller deliberately oversells capacity if high-paying consumers show up, even when capacity is already fully booked. The seller then cancels the sale to some low-paying customers while providing them with appropriate compensation. We derive a new rule to optimally allocate capacity to consumers when overselling is used, and show that overselling helps limit the potential yield and spoilage losses. Yield loss is reduced because the seller can capture more high-paying customers by compensating low-paying customers who give up their right to the product. Spoilage loss is reduced because the compensation decreases the price spread perceived by the seller, and as a result, the seller is less anxious to speculate and “block” units. Overselling with opportunistic cancellations assures that the product will be sold to consumers who value it most. This means that “everybody wins”, and resources are allocated more efficiently than in conventional selling.

This paper address the managerial problem of promotional budgeting and media allocation in a dynamic competitive framework. We develop an extended Lanchester model that is able to analyze multi-instrument promotion in an oligopoly. The competitors, each with a different initial position as well as economic value of the market share and communication effectiveness, adopt the strategy of maximizing their net present value of discounted profits, taking the other players' actions into account. The resulting differential game is solved using a novel method, providing both the open-loop strategy and the closed-loop strategy for each firm. We prove that our solution is a global Nash equilibrium. We develop a simple formula, that, when applied to an open-loop strategy, readily generates a feedback strategy. We also show that for both open- and closed-loop strategies, the proportion of the budget allocated to each instrument is invariant with time and depends only on instrument effectiveness. We illustrate the results and provide several managerial rules and discuss their application in practice. Finally, we show that our model favorably compares with other model in the literature in explaining actual data.

Using the Lanchester model to describe the dynamics of the market where two firms compete for customers by advertising, we solve the problem of determining an optimal advertising strategy for maximum discounted profits. We develop both open- and closed-loop strategies and explain the relationship between them. Using a new mathematical approach, we prove that our closed-loop solution is a global Nash equilibrium. The closed-loop strategy is time-variant and depends linearly on the actual market share. The time-variant coefficient incorporates the discount factor, its computation requires the solution of a backward differential equation and a set of two nonlinear differential equations for an initial value problem. The closed-loop advertising expenditures are proportional to the open-loop advertising expenditures and to the square of the competitor's actual market share. This provides a very practical adaptive control rule that allows the manager to adjust the actual advertising expenditure and to deviate from budget. We illustrate the use of our control rule, using data for the period 1968–1984 of the Cola War Marketing implications of the results are provided.

In an earlier paper by the authors in this issue (J. Math. Anal. Appl. 160, 1991) various necessary conditions to determine the boundary of the zero set have been provided in a very general setting. Here, we classify and indicate which of the arsenal of conditions should be used for various classes of problems and functions for computational convenience.

We describe an analytic method for finding the location of the zero set of a vector-valued function which depends on m real variables and n complex parameters. We apply the method to robust stabilization of multivariable linear feedback systems. We find exact measures of the extent of permissible perturbations in the plant and/or the compensator that maintain feedback stability.

This study extends the time-variant closed-loop strategy of Fruchter and Kalish (1997) to the n-player advertising game. We demonstrate that solving an n-player game using 2 players results in overadvertising.