Distributions with an increasing generalized failure rate (IGFR) have useful applications in pricing and supply chain contracting problems. We provide alternative characterizations of the IGFR property that lead to simplify verifying whether the IGFR condition holds. We also relate the limit of the generalized failure rate and the moments of a distribution.

Traditional analysis of managing services has emphasized that services cannot be held in inventory. Consequently, the focus has been operating services in a make-to-order fashion ignoring lessons learned from operating make-to-stock supply chains. We argue that this conventional view is built on a very limited notion of inventory as finished goods. In reality, inventory can be held in partially completed forms that serve to store work. This notion of inventory as a way to store work is valid for both goods and services and provides a novel way to think of designing service processes. In this article, we define service inventory as all process steps that are completed prior to the customer’s arrival. Much like inventories of physical products, service inventories affect how quickly – and at what cost – a firm can fill demand. By leveraging service inventories, companies have the potential to offer greater quality, speed, and variety to its customers at reasonable prices. We discuss how service inventories allow firms to improve service operations, how service inventories interact with other drivers of process performance, and how lessons from conventional supply chain management apply to the management of service inventory.

With a revenue-sharing contract a retailer pays a supplier a wholesale price for each unit purchased plus a percentage of the revenue the retailer generates. This contract form has become more prevelant in the video cassette rental industry relative to the more conventional wholesale price contract. This paper studies the application of revenue-sharing contracts to a general supply chain model. We demonstrate that revenue-sharing contracts maximize the supply chain's profit (i.e., coordinate the supply chain) in a number of settings, including a supply chain with a single retailer and price-dependent revenue as well as a supply chain with multiple, competing retailers. In addition, we show that a variation on the revenue-sharing contract coordinates a single retailer supply chain with effort-dependent revenue. We compare the revenue-sharing contract to several other contracts that enhance channel coordination, e.g., buy-back contracts, quantity-flexibility contracts and sales-rebate contracts. None of these contracts matches revenue sharing's ability to coordinate a wide range of supply chains. We quantify when a revenue-sharing contract provides significant incremental improvement over the simpler wholesale price contract. Finally, we identify several limitations of revenue-sharing contracts to (at least partially) explain why they are not prevalent in all industries.

A delay-sensitive customer prefers arriving for service when few or no other customers are in the system. We consider how such a customer should strategically arrive to a service system. We present a model in which strategic customers acting in a self-interested fashion give rise to Poisson arrivals.

Forecast sharing is studied in a supply chain with a manufacturer that faces stochastic demand for a single product and a supplier that is the sole source for a critical component. Optimal supply chain performance requires the manufacturer to share her initial forecast truthfully, but she has an incentive to inflate her forecast to induce the supplier to build more capacity. The supplier is aware of this bias, and so may not trust the manufacturer's forecast, harming supply chain performance. The contracts that allow the supply chain to share demand forecasts credibly under either compliance regime are studied.

We consider a simple supply-chain contract in which a manufacturer sells to a retailer facing a newsvendor problem and the lone contract parameter is a wholesale price. We develop a mild restriction satisfied by many common distributions that assures that the manufacturer's problem is readily amenable to analysis. The manufacturer's profit and sales quantity increase with market size, but the resulting wholesale price depends on how the market grows. For the cases we consider, we identify relative variability (i.e., the coefficient of variation) as key: As relative variability decreases, the retailer's price sensitivity decreases, the wholesale price increases, the decentralized system becomes more efficient (i.e., captures a greater share of potential profit), and the manufacturer's share of realized profit increases. Decreasing relative variability, however, may leave the retailer severely disadvantaged as the higher wholesale price reduces his profitability. We explore factors that may lead the manufacturer to set a wholesale price below that which would maximize her profit, concentrating on retailer participation in forecasting and retailer power. As these and other considerations can result in a wholesale price below what we initially suggest, our base model represents a worst-case analysis of supply-chain performance.

Since Blockbuster video stores began sharing rental revenues with its suppliers, both parties have seen increased profits. Even though Blockbuster keeps only half of the rental revenue, it breaks even after each tape has been rented a mere 6 times. It can now justify purchasing many more tapes. Research indicates that revenue sharing will work for many products but only when 2 conditions are met. First, the cost to produce the additional units must be less than the incremental revenue they generate. The 2nd criterion is that the administrative burden associated with revenue sharing must be small enough that the cost of running the program does not eat up all the gains.

A firm faces many problems that are inherently cross-functional. To solve them successfully requires the coordinated actions of many functional representatives acting in a decentralized setting. Functional managers, however, respond to their own individual incentives and may consequently fail to maximize the overall profits of the firm. This issue is examined in a setting in which the output of early actions limits the range of later actions, and an incentive scheme is proposed that allows the system to be successfully decentralized. The mechanism is based on linear transfer prices for the intermediate output that are implemented through an internal market; a market maker buys the output from one function and sells it to another. She is not obliged to sell at the same price at which she bought and may set prices solely to provide incentives. The flexibility of the scheme is illustrated by applying it to several models in the operations management literature.

In many industries, a supplier's total demand from the retailers supplied frequently exceeds the supplier's capacity. In these situations, the supplier must allocate capacity in some manner. Three allocation schemes are considered: proportional, linear and uniform. With either proportional or linear allocation a retailer receives less than his order whenever capacity binds. Retailers then order more than they desire in an attempt to ensure that their ultimate allocation is close to what they truly want. If capacity does not bind, they will receive too much. In the capacity allocation game, each retailer must form expectations on how much other retailers actually desire and how much each will actually order, knowing that all retailers face the same problem. Methods to find Nash equilibria in the capacity allocation game with either proportional or linear allocation are presented. It is found that behavior in this game with either of those allocation rules can be quite unpredictable, primarily because there may not exist a Nash equilibrium. In those situations any order above one's desired quantity can be justified, no matter how large. It is demonstrated that with uniform allocation there always exists a unique Nash equilibrium. In that equilibrium the retailers order their desired amounts. Supply chain profits across the 3 allocation schemes are compared.

Consider a supplier selling to multiple retailers. Demand varies across periods, but the supplier's capacity and wholesale price are fixed. If demand is high, the retailers' needs exceed capacity, and the supplier must implement an allocation mechanism to dole out production. How the choice of mechanism impacts retailer actions and supply chain performance is examined. In particular, turn-and-earn allocation, a method commonly used in the automobile industry, is examined. This scheme bases current allocations on past sales and thus enables retailers to influence their future allocations; they compete for scarce capacity even if they do not compete for customers. It is shown that turn-and-earn induces the retailers to increase their sales when demand is low and the supplier's capacity is otherwise underutilized. Supplier profits thus increase. The impact on the supply chain depends on how restrictive capacity is.

A simple supply chain in which a single supplier sells to several downstream retailers is considered. The supplier has limited capacity, and retailers are privately informed of their optimal stocking levels. If retailer orders exceed available capacity, the supplier allocates capacity using a publicly known allocation mechanism, a mapping from retailer orders to capacity assignments. It is shown that a broad class of mechanisms are prone to manipulation; retailers will order more than they need to gain a more favorable allocation. Another class of mechanisms induces the retailers to order exactly their needs, thereby revealing their private information. However, there does not exist a truth-inducing mechanism that maximizes total retailer profits. The supplier's capacity choice is also considered. It is shown that a manipulable mechanism may lead the supplier to choose a higher level of capacity than one would under a truth-inducing mechanism. Nevertheless, one's choice will appear excessively restrictive relative to the prevailing distribution of orders.

Retailers are frequently uncertain about the underlying demand distribution of a new product. When taking the empirical Bayesian approach of Scarf (1959), they simultaneously stock the product over time and learn about the distribution. Assuming that unmet demand is lost and unobserved, this learning must be based on observing sales rather than demand, which differs from sales in the event of a stockout. Using the framework and results of Braden and Freimer (1991), the cumulative learning about the underlying demand distribution is captured by two parameters: a scale parameter and a shape parameter. An important simplification which allows the scale parameter to be removed form the optimization is shown to extend to this setting. Examples are presented that reveal: 1. A retailer may hope that, compared to stocking out, realized demand will be strictly less than the stock level, even though stocking out would signal a stochastically larger demand distribution. 2. It can be optimal to drop a product after a period of successful sales.

Slotting allowances-lump sum transfers from manufacturers to retailers for carrying new products-have become an important part of promotional agreements over the past decade. Hardly known before the mid-1980s, they now represent a significant cost to launching a new entry in a wide range of product categories. Despite being commonplace, slotting allowances have remained extremely controversial both with manufacturers and retailers. The controversy, in part, follows from a poor understanding of the role that slotting allowances actually play in new product introductions. We attempt to clarify the purpose slotting allowances serve by relating the payment of a slotting allowance to the retailer's cost structure and informational asymmetries within a channel. We consider a manufacturer introducing a new product into a retail channel. The retailer is independent of the manufacturer and only accepts the product if he expects to recover a positive fixed cost at the terms of trade offered by the manufacturer. Following acceptance, the retailer exerts merchandising effort and sets the retail price. We show that if the manufacturer and the retailer are equally informed of the product's demand, the terms of trade never include a slotting allowance. High retail costs are compensated through a lower wholesale price. Similarly, if the manufacturer is better informed of the product's demand, she prefers to convey that information through the wholesale price alone. That is, a high wholesale price, not a slotting allowance, is the manufacturer's preferred signaling instrument. Signaling with the wholesale price alone fails, however, when the retailer has high fixed costs. To convey information and assure retailer participation, the terms of trade must include a positive slotting allowance. A slotting allowance thus serves two purposes in launching a product: passing information down to the retailer and shifting costs up to the manufacturer. We show that the manufacturer prefers paying a slotting allowance to undertaking purely wasteful advertising. A principal virtue of a slotting allowance, then, is keeping money within the channel. Our work is novel along two important dimensions. First, others (e.g., Chu 1992) have assumed that slotting fees arise as manufacturers respond to retailer demands. Here, the manufacturer willingly offers an allowance. As a consequence, slotting allowances do not represent a windfall for the retailer; he merely breaks even on a product for which a slotting allowance is paid. Second, we tie the payment of a slotting allowance to the retailer's fixed cost and the overall terms of trade. This allows us to consider a number of comparative statics with interesting implications. For example, a retailer may receive a slotting allowance for some categories and not for others if his costs differ across categories. A "slotted" product is offered at a lower wholesale price which results in greater retailer effort than for a product on which no allowance is paid. Over a range of fixed costs, greater retailer effort should be correlated with a higher slotting allowance. Finally, for a specific functional form, we show that slotting allowances become more common (in the sense that they are paid over a greater range of retailer costs) as the retailer has greater merchandising ability.

We consider a contracting problem in which a firm outsources its call center operations to a service provider. The outsourcing firm (which we term the originator) has private information regarding the rate of incoming calls. The per-call revenue (or margin) earned by the firm and the service level depend on the staffing decisions by the service provider. Initially, we restrict attention to pay-per-call contracts under which the parties contract on a service level and a per-call fee. The service provider is modeled as a multi-server queue with a Poisson arrival process, exponentially distributed service times and customer abandonment. We assume that the service provider's queue is large enough such that the economically sensible mode of operation for staffing it is the Quality-and-Efficiency-Driven regime, which allows tractable approximations of various performance metrics. We first consider a screening scenario with the service provider offering a contract to the originator. Due to the statistical economies of scale phenomenon observed in queueing systems, the allocation of the originator with higher arrival rate is distorted, which reverses the typical "efficiency at top" result present in the literature on monopolist screening. We then consider the alternative scenario with the originator offering a contract to signal her information and show that the service level of the high volume firm is again distorted. The introduction of a fixed payment ameliorates distortions from first-best and may eliminate them.

We consider a service provider in a market with two segments. Members of the first request a reservation ahead of service and will not patronize the firm without one. Members of the second walk in and demand service immediately. These customers have a fixed cost of reaching the firm and may behave strategically. In equilibrium, they randomize between walking in and staying home. The service provider must decide how much of a limited capacity to make available to reservation customers. When the reservation segment offers a higher per customer margin, the firm may opt to decline some reservation requests in order to bolster walk-in demand. When walk-in customers are more valuable, we have a variation of Littlewood (1972). Where Littlewood would always save some capacity for valuable late arrivals, here it is possible that the optimal policy saves no capacity for walk-ins. Thus, it may be better to ignore rather than pamper walk-in customers.

We examine the role of reservations in capacity-constrained services with a focus on restaurants. Although customer value reservations, restaurants typically neither charge for them nor impose penalties for failing to honor them. However, reservations impose costs on firms offering them. We highlight ways in which reservations can increase a firm's sales by altering customer behavior. First, when demand is uncertain, reservations induce more customers to patronize the restaurant on slow nights. The firm must then trade off higher sales in a soft market with sales lost to no shows on busy nights. Competition makes reservations more attractive as long as enough customers will consider dining at either restaurant. When there are many firms in the market, it is rarely an equilibrium for none to offer reservations. Second, we show that reservations can increase sales by shifting demand from a popular peak period to a less desirable off-peak time. This is accomplished by informing diners that the peak is full. In this setting, competition may make offering reservations less attractive and a market with many firms may have no one offering reservations.

We consider a supply chain consisting of one supplier selling through one retailer who faces a newsvendor problem. There is a positive probability that the retailer is capable of gaining improved demand information through costly forecasting. The supplier would like to induce the retailer to forecast and share that information. Restricting the retailer's ability to return unsold product would intuitively appear to be a viable way by which to provide the desired incentives. However, it is well known that a generous returns policy increases the supplier's profit. We explore this tension between providing incentives to forecast and capturing channel profits. We examine both price-based returns mechanisms and quantity-based returns mechanisms. Thus, a second objective of this research is to compare the relative performance of these two schemes.

We consider a manufacturer introducing a new product into a distribution channel and examine what wholesale price should be charged. The setting in many ways is simple. The channel is abbreviated with the manufacturer selling directly to the retailer. The contract is also simple, merely a flat wholesale price. Demand is stochastic but independent and identically distributed in each period. Complications arise from two additional assumptions. First, neither party knows some parameter of the demand distribution. The system evolves informationally as the channel has more experience with, and information about, the product. Second, we assume unmet demand is both lost and unobserved, so only sales data are available. The autonomous retailer's stocking level consequently dictates the rate at which the channel acquires information. The manufacturer's pricing policy, in turn, influences the retailer's actions. We explore how the wholesale price evolves as beliefs are updated in a Bayesian fashion. Pricing is driven by the precision of information and not the size of the market. In particular, we show that the manufacturer charges a lower price following a stockout than after an exact observation. That is, she prices more aggressively following a signal of relatively weak demand (unsold stock) than after a signal of strong demand (empty shelves). The apparent anomaly is explained by relating the precision of information to the number of observed stockouts and the elasticity of retailer orders to the precision of information; stockouts are less informative, and an uncertain retailer is relatively price sensitive.

Bruce Alfred Technologies (BAT) has built a successful business selling packaged software. Its marketing has long promised free technical support to all customers, a key point of differentiation from BAT’s competitors. However, the call center providing tech support is now in crisis. Wait times for callers are unacceptably high, leading to low customer satisfaction and negative press. BAT managers are evaluating the Fast Track Proposal, which would create two classes of calls. Fast Track calls would be promised a one-minute wait but pay for service. Standard calls would still be free but be given lower priority and have no wait time guarantee. The case considers both the operational impact of this change as well as the strategic considerations of backing away from free tech support. This case has been used both in an elective course on service operations and a core operations management class. In the former setting, the intention is to emphasize the impact of priorities and alternative ways of managing capacity. It can also be used to discuss different ways of pricing services—i.e., pay-per-transaction vs. subscription. These can still be discussed in a core class, but the case can also serve to demonstrate the basics of the relation between utilization and delay.