In the newsvendor problem, a decision maker facing random demand for a perishable product decides how much of it to stock for a single selling period. This simple problem with its intuitively appealing solution is a crucial building block of stochastic inventory theory, which comprises a vast literature focusing on operational efficiency. Typically in this literature, market parameters such as demand and selling price are exogenous. However, incorporating these factors into the model can provide an excellent vehicle for examining how operational problems interact with marketing issues to influence decision making at the firm level. In this paper we examine an extension of the newsvendor problem in which stocking quantity and selling price are set simultaneously. We provide a comprehensive review that synthesizes existing results for the single period problem and develop additional results to enrich the existing knowledge base. We also review and develop insight into a dynamic inventory extension of this problem, and motivate the applicability of such models.

W e consider the problem of a newsvendor that is served by multiple suppliers, where any given supplier is defined to be either perfectly reliable or unreliable. By perfectly reliable we mean a supplier that delivers an amount identically equal to the amount desired, as is the case in the most basic variant of the newsvendor problem. By unreliable, we mean a supplier that with some probability delivers an amount strictly less than the amount desired. Our results indicate the following effects of unreliability: From the perspective of the newsvendor, the aggregate quantity ordered is higher than otherwise would be ordered if the newsvendor's suppliers were completely reliable. From the perspective of end customers, however, the service level provided is lower than otherwise would be provided if the newsvendor's suppliers were completely reliable. From the perspective of the suppliers, although reliability affects how much is ordered from a selected supplier, cost generally takes precedence over reliability when it comes to selecting suppliers in the first place. Even perfect reliability is no guarantee for qualification since, in an optimal solution, a given supplier will be selected only if all less-expensive suppliers are selected, regardless of the given supplier's reliability level. Nevertheless, the relative size of a selected supplier's order depends on its reliability.

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T his article presents a comparative analysis of possible postponement strategies in a two-stage decision model where firms make three decisions: capacity investment, production (inventory) quantity, and price. Typically, investments are made while the demand curve is uncertain. The strategies differ in the timing of the operational decisions relative to the realization of uncertainty.We show how competition, uncertainty, and the timing of operational decisions influence the strategic investment decision of the firm and its value. In contrast to production postponement, price postponement makes the investment and production (inventory) decisions relatively insensitive to uncertainty. This suggests that managers can make optimal capacity decisions by deterministic reasoning if they have some price flexibility. Under price postponement, additional postponement of production has relatively small incremental value. Therefore, it may be worthwhile to consider flexible ex-post pricing before production postponement reengineering. While more postponement increases firm value, it is counterintuitive that this also makes the optimal capacity decision more sensitive to uncertainty. We highlight the different impact of more timely information, which leads to higher investment and inventories, and of reduced demand uncertainty, which decreases investment and inventories. Our analysis suggests appropriateness conditions for simple make-to-stock and make-to-order strategies. We also present technical sufficiency and uniqueness conditions. Under price postponement, these results extend to oligopolistic and perfect competition for which pure equilibria are derived. Interestingly, the relative value of operational postponement techniques seems to increase as the industry becomes more competitive.

Customers often have to wait during the process of acquiring and consuming many products and services. These waiting experiences are typically negative and have been known to affect customers' overall satisfaction with the product or service. To better manage these waiting experiences, many firms have instituted a variety of programs not only to reduce the actual duration of the wait but also to improve customers' perceptions of it. In this paper, we examine the impact of one such initiative, namely, the institution of a waiting time guarantee, on customers' waiting experiences. A waiting time guarantee is a commitment from a firm to serve its customers within a specified period of time. If the firm fails to meet this commitment for some customers then it compensates them for the delay. Today, a large number of firms in a variety of industries such as fast food, banking, industrial distribution, and healthcare offer such time guarantees to their customers. We develop a utility theory-based model of customers' satisfaction with waiting in line. The model is based upon the assumption that when a customer joins a queue he or she has some prior beliefs about the distribution of service times at the firm. The customer estimates the likely duration of the waiting time on the basis of these beliefs about the service times and the observed queue length. We further assume that as the customer observes the service times for other customers who are ahead in the queue, he or she successively updates these beliefs about the distribution of service times in a Bayesian manner. We then posit that the customer's satisfaction both during as well as the end of the wait is determined by the difference between the customer's updated and the prior estimates of the total waiting time. We apply the model to derive select hypotheses pertaining to the impact of a waiting time guarantee on customers' waiting experiences. These hypotheses are based upon the assumption that an offer of a time guarantee is a signal of reliability from the firm and reduces customers' perceived variance around the expected service times. We empirically test these hypotheses using data from a series of interactive, computer-based laboratory experiments. In these experiments, we used the computer to create animations of reallife waiting experiences. The computer display consisted of a queue of customers waiting for service at a counter. One of the customers represented the participant in the experiment. During the course of the experiment, each participant joined the queue, waited in line for service, and then exited the system. At several points during the wait, each participant reported his or her level of satisfaction with the waiting experience. Our results suggest that if customers observe the service times to be less than expected, their satisfaction increases monotonically during the wait. Further, under such circumstances, the explicit provision of a waiting time guarantee enhances satisfaction both during as well as at the end of the wait. However, if cu...

The occurrence of temporary stock-outs at retail is common in frequently purchased product categories. Available empirical evidence suggests that when faced with stock-outs, consumers are often willing to buy substitute items. An important implication of this consumer behavior is that observed sales of an item no longer provide a good measure of its core demand rate. Sales of items that stock-out are right-censored, while sales of other items are inflated because of substitutions. Knowledge of the true demand rates and substitution rates is important for the retailer for a variety of category management decisions such as the ideal assortment to carry, how much to stock of each item, and how often to replenish the stock. The estimated substitution rates can also be used to infer patterns of competition between items in the category. In this paper we propose methods to estimate demand rates and substitution rates in such contexts. We develop a model of customer arrivals and choice between goods that explicitly allows for possible product substitution and lost sales when a customer faces a stock-out. The model is developed in the context of retail vending, an industry that accounts for a sizable part of the retail sales of many consumer products. We consider the information set available from two kinds of inventory tracking systems. In the best case scenario of a perpetual inventory system in which times of stock-out occurrence and cumulative sales of all goods up to these times are observed, we derive Maximum Likelihood Estimates (MLEs) of the demand parameters and show that they are especially simple and intuitive. However, state-of-the-art inventory systems in retail vending provide only periodic data, i.e., data in which times of stock-out occurrence are unobserved or “missing.” For these data we show how the Expectation-Maximization (EM) algorithm can be employed to obtain the MLEs of the demand parameters by treating the stock-out times as missing data. We show an application of the model to daily sales and stocking data pooled across multiple beverage vending machines in a midwestern U.S. city. The vending machines in the application carry identical assortments of six brands. Since the number of parameters to be estimated is too large given the available data, we discuss possible restrictions of the consumer choice model to accomplish the estimation. Our results indicate that demand rates estimated naively by using observed sales rates are biased, even for items that have very few occurrences of stock-outs. We also find significant differences among the substitution rates of the six brands. The methods proposed in our paper can be modified to apply to many nonvending retail settings in which consumer choices are observed, not their preferences, and choices are constrained because of unavailability of items in the choice set. One such context is in-store grocery retailing, where similar issues of information availability arise. In this context an important issue that would need to be dealt with is changes in t...

By committing to long-term supply contracts, buyers seek to lower their purchasing costs, and have products delivered without interruption. When a long-term contract is available, suppliers are less pressured to ®nd new customers, and can aord to charge a price lower than the prevailing spot market price. We examine sourcing decisions of a ®rm in the presence of a capacity reservation contract that this ®rm makes with its long-term supplier in addition to the spot market alternative. This contract entails delivery of any desired portion of a reserved ®xed capacity in exchange for a guaranteed payment by the buyer. We investigate rational actions of the two parties under two dierent types of periodic review inventory control policies used by the buyer: the two-number policy, and the base stock policy. When typical demand probability distributions are considered, inclusion of the spot market source in the buyerÕs procurement plan signi®cantly reduces the capacity commitments from the long-term supplier. Ó

T his article presents a comparative analysis of possible postponement strategies in a two-stage decision model where firms make three decisions: capacity investment, production (inventory) quantity, and price. Typically, investments are made while the demand curve is uncertain. The strategies differ in the timing of the operational decisions relative to the realization of uncertainty.We show how competition, uncertainty, and the timing of operational decisions influence the strategic investment decision of the firm and its value. In contrast to production postponement, price postponement makes the investment and production (inventory) decisions relatively insensitive to uncertainty. This suggests that managers can make optimal capacity decisions by deterministic reasoning if they have some price flexibility. Under price postponement, additional postponement of production has relatively small incremental value. Therefore, it may be worthwhile to consider flexible ex-post pricing before production postponement reengineering. While more postponement increases firm value, it is counterintuitive that this also makes the optimal capacity decision more sensitive to uncertainty. We highlight the different impact of more timely information, which leads to higher investment and inventories, and of reduced demand uncertainty, which decreases investment and inventories. Our analysis suggests appropriateness conditions for simple make-to-stock and make-to-order strategies. We also present technical sufficiency and uniqueness conditions. Under price postponement, these results extend to oligopolistic and perfect competition for which pure equilibria are derived. Interestingly, the relative value of operational postponement techniques seems to increase as the industry becomes more competitive.