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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.

The evolution of quality expectations over time is an important driver of customer satisfaction and retention. This study investigated the dynamic properties of customers’ quality expectation updating from an analytical perspective and provides new evidence on the psychological correlates of the discrepancies between expectations and experiences in the realm of consumer decision making. In doing so, we focus on the dynamics of expectation formation by adopting a nonlinear complex systems approach based on well-established behavioral theories. Using stability analysis, we find analytical results which are supported empirically by an experiment that there is considerable heterogeneity in how consumers calibrate their quality expectations. Specifically, we demonstrate analytically that in some cases individuals will converge to a specific quality expectation (reach a stable fixed point), while in other cases their expectations will oscillate between a small number of points periodically. This is remarkable because the existence of the latter is not due to changes in quality performance but merely accrue endogenously and depend on individuals’ disconfirmation functions. To our knowledge, this is the first time in the marketing literature that the corresponding gaps between quality expectations and quality provided are analyzed in the long run. Our analytical and empirical findings also suggest that being more responsive to a person’s expectations can increase the portion of those individuals that are able to better calibrate. Finally, we also demonstrate that calibration ability is associated with how thoughtful or impulsive information is used to update one’s expectation. A more deliberative processing style, which includes using a wider range of information, seems to be related to fewer unrealistic expectations and better calibrations, while a more impulsive processing style is related to more unrealistic expectations. In addition to providing a better understanding of dynamic expectation formation, these results can pave the way for interventions that foster more accurate quality expectations. From a managerial perspective, our findings imply that communicating quality perceptions are only to a certain extent under managerial control. To recognize this, firms are advised to segment customers based on their information processing style and to customize their marketing actions accordingly.

This paper introduces a model for the diffusion of add-ons that consist of new industrial technologies embedded in mature products. These new technologies are targeted to improve attributes such as the performance, convenience, safety, etc., of the carrier product that incorporates them. Although the rationale for the purchase of the carrier product is driven primarily by mature market factors such as physical wear-out or changing personal needs, the innovative technologies embedded in the design of these products and the advantages they offer provide a competitive edge to the brands that incorporate them. We examine the potential growth of the market share of products that incorporate new technologies within this overall carrier market. We apply our model to the diffusion of green buildings that incorporate better thermal insulation through the use of new materials. For this purpose, we draw on surveys and industry data to estimate the parameters of the model.

In this paper, based on well-established behavioral theories, we propose a new model for dynamic formation of customer’ quality expectations. The model is described by a one-dimensional non-linear discrete dynamical system which depends on several parameters with links to behavioral theories. Applying stability analysis, we investigate the dynamic properties of the non-linear system. We find those domains in the parameter space in which the equilibrium point of the system (the fixed point) and the periodic orbits are stable and in which they are unstable. These domains correspond to the cases customers will converge to a specific expectation of the offering, while in other cases their expectations will oscillate between a small number of points periodically. These results can help identify target segments for companies and pave the way for interventions that foster more accurate customer expectations.

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.

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.

This paper investigates the use of pricing schemes in subscription services that consist of various combinations of activation, subscription, and cancellation fees. When customers exclusively consider what is directly perceivable, the activation fee starts low and increases as the network grows (penetration strategy), whereas the cancellation fee starts high and decreases as the network grows (skimming strategy). The activation and cancellation fees take various other forms otherwise. The subscription fee remains low at the early stages and increases only when a reasonable number of subscribers is secured. Finally, the authors discuss the theoretical and managerial implications of their findings.

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.

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.

This paper extends the existing quality-signaling literature by investigating the roles of price and advertising levels as quality indicators in a dynamic framework. Considering perceived quality as a form of goodwill, we modify the well-known Nerlove-Arrow dynamic model to include price effects. In our model, price is used both as a monetary constraint and as a signal of quality, while advertising spending is used only as a signaling device, and thus purely as a dissipative expense. Utilizing optimal control, we determine optimal decision rules for a firm regarding both price and advertising over time as functions of perceived quality. The results indicate that, when prices act as monetary constraints and are reduced to increase demand, the firm should use the signaling role of advertising by increasing spending to accelerate perceived quality increases. In cases when the value of the perceived quality goes up together with the increase in the perceived quality by more than the demand, in percentage terms, the firm should increase the price (use its signaling role). At steady-state, we find that the level of optimal profit margin relative to price decreases with the elasticity of demand with respect to the brand price. However, higher elasticity of demand with respect to the firm’s perceived quality and/or a higher impact of price (advertising) lead/leads to a higher optimal profit margin (advertising spending) relative to price (revenue).

The dual role of price, as a product attribute signaling quality and as a measure of sacrifice, serving as a benchmark for comparing the utility gains from superior product quality, is now well established in the marketing and economic literature. However, knowledge about their long-run impact and the influence of competition on these effects still remains very sparse. In the current paper, with reference to a dynamic and competitive framework, an analytical model is proposed to help determining optimal decision rules for price incorporating both roles. The main results are as follows: (i) The optimal pricing policy is determined as a Nash equilibrium strategy. (ii) The resulting equilibrium price is higher than an equilibrium that disregards the carryover price effects. (iii) For a symmetric competition, we provide normative rules on how firms should set prices as a function of the perceived quality; particularly, how the price should be set initially, when there is little product familiarity and the perceived quality is low, and how this price should vary as the perceived quality increases. (iv) At steady state, we find that the level of equilibrium margin, in percentage terms, decreases with the elasticity of demand with respect to the brand price, but this decrease is moderated by the elasticity of demand with respect to the brand perceived quality, the cross elasticity of demand with respect to the competitor’s perceived quality and the effect of the competitor’s current price on the firm’s perceived quality deterioration.

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.

In this paper, we study the dynamic production location decisions of a manufacturer of a certain branded product. Considering brand-image as a form of goodwill, we extend the well-known Nerlove–Arrow dynamic model by adding both country-image and price. Formulating an optimal control problem for a group of countries in which the cost of production is convexly increasing with country-image, we are able to develop optimal decision rules for a manufacturer regarding the location of production and pricing over time. The resulted optimal policy has a very interesting pattern. Assuming that the demand rises by more than the value of the new brand-image in percentage terms, then, if brand-image is increasing toward a stationary value level, the optimal policy should be to initially locate production in countries with high image and set a high price that signals high quality. Later, the production should gradually shift to countries with lower production costs and lower image and the price lowered until the stationary value level is reached. For brand-images beyond the stationary value level, the location of production should start in a country with low costs and country-image while setting prices that signal relatively low quality. Over time, production should be shifted to countries with gradually higher costs and images while setting higher prices until the brand-image approaches the level of stationary value.

We study the dynamic pricing decisions for competitive network service providers. We assume that each competing firm follows a three-part pricing scheme, which consists of an ongoing membership fee, a usage fee for communications within the networks, and another usage fee for communications across the networks. The difference between the two usage fees is the network-based price discount that allows price discrimination. We study the firms problems as a differential game and establish the optimal pricing policy as a Nash equilibrium feedback strategy depending on only the network sizes (i.e., the number of subscribers). We compare the dynamic network-based discount with the static discount. In the special case of a uniform calling pattern, we find that the firm network-based dynamic discount is always lower than the static discount; we find also that the firm that has a larger network can offer a bigger discount. These results are useful particularly for managers. To get further insights into the dynamic pricing policies, we explore the case of symmetric competition using numerical simulation.

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 this paper, we investigate the problem of a dominant company facing entry of a “competitive fringe” (smaller competitor or fringe of smaller competitors). We seek to identify pricing and advertising (or other promotional strategies) that maximize long-term profits for the dominant firm, under possible reactions of the competitive fringe. Two main situations are considered: • The firms in the fringe are price-takers, but they advertise. • The firms in the fringe are not price-takers and advertise. The possibility of a passive reaction, in the case of a very small fringe, is considered as a particular case. We assume that the rate of change of fringe sales is dynamically related to the current sales, price and advertising efforts of both the dominant firm and the fringe. The higher the dominant firm price, the faster fringe entry. The higher dominant firm advertising effort, the slower fringe entry. Fringe advertising and pricing may counterbalance these effects. Formulating a dynamic game, with the dominant firm as a leader and the fringe as a follower, we present a new methodology for providing time-invariant feedback Stackelberg equilibrium. The methodology relies on finding the relationship between the co-state variables and the state variable. The equilibrium solution is obtained in an implicit form by solving a set of two backward differential equations. To show the applicability of our solution to real situations, we use data from the U.S. long-distance market and find optimal decision rules for AT&T facing the entry of MCI and Sprint during the 1980–1990 period. The feedback equilibrium indicates that while AT&T's price is decreasing when fringe (MCI and Sprint) sales increase, the fringe price is increasing. AT&T's advertising is increasing with fringe sales while the fringe's advertising increases and then decreases. The comparison with actual behavior indicates that AT&T has adhered closer to the optimal solution in both price and advertising than the fringe.

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.

We introduce a general objective function, which incorporates competitive situations, such as conservative, punitive, and predatory advertising. Linking together the particular situations into a two-parameter family of max–min problems, and using the Lanchester model to describe the dynamics of the market, a bilinear-quadratic differential game is obtained. For this game, we find saddle-point feedback time-invariant advertising strategies and show when these strategies are Nash equilibrium strategies. In an empirical application involving duopolistic competition in the cola market, we find evidence of a punitive motivation for the advertising strategies.

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.

This study extends the literature of dynamic advertising competition by allowing oligopoly competition and market expansion that results from advertising. We find how advertising actions affect market development and how, conversely, market development influences advertising policies over time. Modelling the competition by a differential game, we solve for both time-variant closed-loop and time-invariant feedback Nash equilibrium strategies. The time-variant closed-loop strategy depends on a firm's own sales rates and the time-invariant feedback strategy depends on the growth of the market. We discuss the marketing implications of the results. Copyright © 1999 John Wiley & Sons, Ltd.

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.

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.

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.