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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.

Production emissions in the industrial sector are a major source of environmental pollution. In this paper, we explore how emission considerations are integrated with production decisions. We develop a dynamic model consisting of two firms located in the same industrial park, which satisfies exogenously given demands in separate markets. The two firms can build up or rundown stocks (full backlogging), both of which are costly. The emission cost depends on the total output of the two firms. We develop Nash equilibrium feedback strategies, where each firm decides on its output based on its inventory or the inventories of both. We also develop a social planning solution where decisions are centralized. We present the analytic results for the total profits in these settings. The results show the benefits of a decentralized approach over a centralized one, provided there is a mechanism for coordination. Finally, emission costs are compared for the various solution concepts.

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.

This paper develops an analytical model to investigate the impact of governmental funding of higher education on educational outcomes including tuition, graduation rates, and enrollment. Assuming that students make an enrollment decision based on tuition, graduation rate, and labor market prospects, we show that push and pull funding strategies are equally effective in lowering net tuition and in increasing enrollment, the expected graduation rate, and social welfare without compromising the academic standards. We also show that a policy change from enrollment-based funding to performance-based funding raises graduation rates but does not necessarily improve the performance of the education system.

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.

We present a model that forecasts sales and product evolution, based on data on market and industry, which can be collected before the product is introduced. Product evolution can be incremental but can also take place by releasing new generations. In our model adoption of a new product is motivated by attribute improvements (enabled by technology evolution), and firms' attribute improvements strategies are motivated by market growth and directed by market preferences. The interdependency between attributes' improvements and cumulative adoption level makes the problem inherently dynamic. The dependency of attribute levels on adoption levels is assessed using industry and technology analysis. Market preferences and purchase intention response to attribute levels changes are assessed based on a conjoint study. The option of collecting and interpreting data about both demand and supply aspects, before the new product is introduced, enables us to estimate sales and technology progress endogenously rather than to require them as inputs. We demonstrate the method on the hybrid car market.

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.

In this marketing-oriented era where manufacturers maximize profits through customer satisfaction, there is an increasing need to design a product line rather than a single product. By offering a product line, the manufacturer can customize his or her products to the needs of a variety of segments in order to maximize profits by satisfying more customers than a single product would. When the amount of data on customer preferences or possible product configurations is large and no analytical relations can be established, the problem of an optimal product line design becomes very difficult and there are no traditional methods to solve it. In this paper, we show that the usage of genetic algorithms, a mathematical heuristics mimicking the process of biological evolution, can solve efficiently the problem. Special domain operators were developed to help the genetic algorithm mitigate cannibalization and enhance the algorithm’s local search abilities. Using manufacturer’s profits as the criteria for fitness in evaluating chromosomes, the usage of domain specific operators was found to be highly beneficial with better final results. Also, we have hybridized the genetic algorithm with a linear programming postprocessing step to fine tune the prices of products in the product line. Attacking the core difficulty of cannibalization in the algorithm, the operators introduced in this work are unique.

The relevance of transactional and relational marketing variables in relational exchanges is now well established in the marketing literature. However, the knowledge about their relative effectiveness and their optimal mix over time remains very sparse. An analytical model is proposed to help determine optimal decision rules for transactional and relational marketing efforts. Some of the main results are as follows: (a) If the seller benefits from the interaction between the transactional marketing effort and buyer’s commitment, then the seller’s optimal decision rules change over time and depend on the level of the partners’commitment. (b) Otherwise, the seller’s optimal decision rules for the two types of marketing are constant over time. (c) The seller should allocate more resources to relational marketing at the beginning of a relational exchange and, later on, should allocate more resources to transactional marketing.

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.

This study investigates how to dynamically allocate resources with a given budget for advertising through Web portals using keyword-activated banner ads on the Internet. Identifying the factors that affect the potential number of banner ad clickthroughs in each portal, we show that the process of budget allocation between the two types of portals (generic vs specialized) that leads to the largest banner clicksthrough in the long run is an optimal control problem. Using techniques of dynamic programming, we find analytical solutions for the optimal budgeting decisions. Our analysis shows that an advertiser’s optimal portal budgeting depends nonlinearly on the number of visitors who type the same trigger keyword and the average clicksthrough rates, as well as on the advertiser and ad effectiveness. Further, we find that the maximal number of banner clickthroughs from both portals, at time t, depends on the remaining budget until the end of the planning period. The analytical results have useful managerial insight. One of the interesting features of our solution shows that, while a large visitor base may favor the generic portal, other parameters may affect it unfavorably: e.g., lower clickthrough rates of keyword banners from a more heterogeneous audience. Using a specificaction that is consistent with empirical observations, we show that, in the long run, an advertiser must always spend more ad money at the specialized portal.

Defining speed of diffusion as the amount of time it takes to get from one penetration level to a higher one, we introduce a dynamic model in which we study the link between pricing policy, speed of diffusion, and number of competitors in the market. Our analysis shows that, in the case of strategic (oligopolistic) competition, the speed of diffusion has an important influence on the optimal pricing policy. In particular, we find that higher speeds of diffusion create an incentive to strategically interacting firms to lower their prices.

The authors propose an analytic model that deals with both behavioral considerations between exchange partners and the determination of relational marketing efforts over time. On the basis of the behavioral marketing literature, they consider three main factors that drive the levels of relational commitments between two exchange partners: the trust/distrust component, the opportunism component, and the relational marketing effort of the seller. Incorporating these factors in a well-known model used in appliedmathematics for “love dynamics,” the authors claim that the issue of managing relational exchanges is an optimal control problem. Their analysis shows that the seller’s optimal policy for determining relational marketing effort over time is either time-invariant or time-variant, depending on whether or not the exchange partners are conservative and the structural and contextual environment of the relationship remains unchanged over time.

This research analyzes the strategic use of targeted promotions for customer retention and acquisition in a dynamic and competitive environment. The normative analysis shows that a firm’s optimal targeting strategies, both offensive and defensive, depend on its actual market share, the relevant redemption rate of its targeted promotions, customer profitability, and the effectiveness of its targeted promotions. These strategies have the attractive feature of being an adaptive control rule. A firm can operationalize these strategies by adjusting its planned promotional incentives on the basis of the observed differences between actual and planned market shares and between actual and planned redemption rates. In the long run, a focus on customer retention is not an optimal strategy for all firms.

In many markets, competing but differentiated firms offer a product line in order to target each product to a different type of customer. Under competition, firms, while trying to target different products to different segments, are also interested in "stealing" customers from the competitors and, in particular, customers from the most profitable segments. How should a profit-maximising firm allocate the advertising budget along a competitive product line? Devel oping a closed-loop time-variant Nash equilibrium strategy for a multi-player multi-product advertising game, we find the determinants of the optimal advertising budget allocation in a product line in an oligopoly growing market. Moreover, for a symmetric competition in a fixed market, we derive an analytic feedback time-variant Nash equilibrium strategy. Marketing implications regarding the firm's strategic orientation in product preference advertising spending, as well as comparison to rivals' spending, are discussed. Finally, we show that using a single-product advertising game instead of a multi-product advertising game, leads to over-advertising.

This article examines the pricing decision of a provider of network services in the face of a growing market of customer bases that join the network and then have a demand for the service. The authors find the optimal pricing policy consisting of an ongoing membership fee and a usage price that maximizes the sum of discounted profits. Consistent with empirical observations, the authors assume that the average usage demand declines with the number of customers. The authors find that the optimal policy consists of a penetration strategy for the membership fee, low at the beginning, increasing with network size, and a skimming strategy for the usage price, starting high and declining later. The intuition behind the results is that if early adopters are heavy users, it is better to increase network size through a low membership fee and have a high usage price for the heavy users initially.

Satisfaction Guaranteed is defined as a selling policy assuring that no consumer is worse off after purchase. The authors show that for a wide spectrum of guarantee policies, the most profitable policy is a Satisfaction Guaranteed policy. Setting a price equal to the willingness to pay of satisfied customers, but generously compensating dissatisfied customers for all costs involved, this policy can be a “creative device” to capture back-added economic value created for consumers through the guarantee. Comparing this policy with a no-guarantee policy, a Satisfaction Guaranteed policy comes with a higher price in a monopoly market and in a competitive market. Conditions under which selling with a Satisfaction Guaranteed policy is more profitable than selling without it are derived. Although this policy seems to be an attractive offer to consumers, the authors show that because of its high price, it may not. Easy-to-satisfy consumers are better off without the Satisfaction Guaranteed policy.

Relationship marketing (RM) has been a topic of serious discussions among academics and marketing practitioners for the best part of 20 years. In the 1990s it became the leading topic of discussion at academic conferences in Europe, North America, Australia and elsewhere around the globe. In this chapter we show how one can treat several problems in relationship marketing by transforming them into an optimal control problem.

A two-part tariff is a non-linear pricing technique in which the price of a product or service is composed of two parts: an entrance fee and a charge per unit of consumption. Compared to linear pricing, this methodology leads to higher profits by allowing a firm more freedom in extracting the consumer surplus. It is widely used in telecommunication services.