We investigate a simple dynamic model of firm behavior in which firms compete by investing in capacity that is used to provide a good or service to their customers. There is a fixed total market of customers whose demands for the good or service are random and who divide their patronage between the firms in each period. Periodically, the market shares of the two firms can change based on the realized level of customer service provided in the prior period. We assume that the expected level of customer service can be expressed as a function of the (per customer) capacity of the firms' service delivery systems, and that service declines as the capacity decreases. The firms differ in their customers' willingness to defect when confronted by service failure. The primary issue we address is the firms' capacity decisions in response to customer service concerns and competitive pressure. We provide conditions under which the firms' optimal (i.e., equilibrium) capacity levels in a period are proportional to the size of their respective customer bases in that period. Further, we develop expressions for the value of a firm's customers and the implicit cost of service failure. Results for both single-period and finite-horizon problems are investigated and applied to two examples: (1) competition between Internet service providers who operate systems that we approximate by simple loss-type queueing models, and (2) competition between make-to-stock producers who operate systems that we approximate by newsvendor inventory models. For both examples, solutions are derived and interpreted.capacity management, game theory, customer loyalty, customer service, newsvendor model

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Recent years have seen advances in research and management practice in the area of pricing, and particularly in dynamic pricing and revenue management. At the same time, researchers and managers have made dramatic improvements in production and supply chain management. The interactions between pricing and production/supply chain performance, however, are not as well understood. Can a firm benefit from knowing the status of the supply chain or production facility when making pricing decisions? How much can be gained if pricing decisions explicitly and optimally account for this status? This paper addresses these questions by examining a make-to-order manufacturer that serves two customer classes -core customers who pay a fixed negotiated price and are guaranteed job acceptance, and "fill-in" customers who make job submittal decisions based on the instantaneous price set by the firm for such orders.We examine four pricing policies that span a range of complexity and required knowledge about the status of the production system at the manufacturer, including the optimal policy of setting a different price for each possible state of the queue. We demonstrate properties of the optimal policy, and we illustrate numerically the financial gains a firm can achieve by following this policy vs. simpler pricing policies. The four policies we consider are (1) state-independent (static) pricing, (2) allowing fill-in orders only when the system is idle, (3) setting a uniform price up to a cut-off state, and (4) general state-dependent pricing. Although general statedependent pricing is optimal in this setting, we find that charging a uniform price up to a cut-off state performs quite well in many settings and presents an attractive trade-off between ease of implementation and profitability. Thus, a fairly simple heuristic policy may actually out-perform the optimal policy when costs of design and implementation are taken into account.2

Recent years have seen advances in research and management practice in the area of pricing, and particularly in dynamic pricing and revenue management. At the same time, researchers and managers have made dramatic improvements in production and supply chain management. The interactions between pricing and production/supply chain performance, however, are not as well understood. Can a firm benefit from knowing the status of the supply chain or production facility when making pricing decisions? How much can be gained if pricing decisions explicitly and optimally account for this status? This paper addresses these questions by examining a make-to-order manufacturer that serves two customer classes -core customers who pay a fixed negotiated price and are guaranteed job acceptance, and "fill-in" customers who make job submittal decisions based on the instantaneous price set by the firm for such orders.We examine four pricing policies that span a range of complexity and required knowledge about the status of the production system at the manufacturer, including the optimal policy of setting a different price for each possible state of the queue. We demonstrate properties of the optimal policy, and we illustrate numerically the financial gains a firm can achieve by following this policy vs. simpler pricing policies. The four policies we consider are (1) state-independent (static) pricing, (2) allowing fill-in orders only when the system is idle, (3) setting a uniform price up to a cut-off state, and (4) general state-dependent pricing. Although general statedependent pricing is optimal in this setting, we find that charging a uniform price up to a cut-off state performs quite well in many settings and presents an attractive trade-off between ease of implementation and profitability. Thus, a fairly simple heuristic policy may actually out-perform the optimal policy when costs of design and implementation are taken into account.2

Recent years have seen advances in research and management practice in the area of pricing, and particularly in dynamic pricing and revenue management. At the same time, researchers and managers have made dramatic improvements in operations and supply chain management. The interactions between pricing and operations/supply chain performance, however, are not as well understood. In this paper, we examine this linkage by developing a deterministic, finitehorizon dynamic programming model that captures a price/demand effect as well as a stockpiling/consumption effect-price and market stockpile influence demand, demand influences consumption, and consumption influences the market stockpile. The decision variable is the unit sales price in each period. Through the market stockpile, pricing decisions in a given period explicitly depend on decisions in prior periods. Traditional operations models typically assume exogenous demand, thereby ignoring some of the market dynamics. Herein, we model endogenous demand, and we develop analytical insights into the nature of optimal prices and promotions. We develop conditions under which the optimal prices converge to a constant. In other words, price promotion is suboptimal. We also analytically and numerically illustrate cases where the optimal prices vary over time. In particular, we show that price dynamics may be driven by both (a) revenue effects, due to nonlinear market responses to prices and/or inventory, and (b) cost effects, due to economies of scale in operations. The paper concludes with a discussion of directions for future research.