Callable products for an implicit time model with dependent demands

Capacity providers such as airlines and hotels have traditionally increased revenues by practicing market segmentation and revenue management, enabling them to sell the same capacity pool to different consumers at different prices. Callable products can enhance profits and improve consumers' welfare by allowing the firm to broker capacity between consumers with different willingness to pay. A consumer who buys a callable product gives the capacity provider the right to recall capacity at a prespecified recall price. This article studies callable products in the context of the model most commonly used in industry, which handles time implicitly imposing fewer restrictions on the nature of randomness compared to the Poisson arrival process favored in academia. In the implicit time model, capacity providers set booking limits to protect capacity for future high-fare demand. Our numerical study identifies conditions where callable products result in significant gains in profits.     

Revenue management with aircraft reassignment flexibility

A well‐studied problem in airline revenue management is the optimal allocation of seat inventory among different fare‐classes, given a capacity for the flight and a demand distribution for each class. In practice, capacity on a flight does not have to be fixed; airlines can exercise some flexibility on the supply side by swapping aircraft of different capacities between flights as partial booking information is gathered. This provides the airline with the capability to more effectively match their supply and demand. In this paper, we study the seat inventory control problem considering the aircraft swapping option. For theoretical and practical purposes, we restrict our attention to the class of booking limit policies. Our analytical results demonstrate that booking limits considering the swapping option can be considerably different from those under fixed capacity. We also show that principles on the relationship between the optimal booking limits and demand characteristics (size and risk) developed for the fixed‐capacity problem no longer hold when swapping is an option. We develop new principles and insights on how demand characteristics affect the optimal booking limits under the swapping possibility. We also develop an easy to implement heuristic for determining the booking limits under the swapping option and show, through a numerical study, that the heuristic generates revenues close to those under the optimal booking limits. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

A note on “resource flexibility with responsive pricing”

We revisit the capacity investment decision problem studied in the article “Resource Flexibility with Responsive Pricing” by Chod and Rudi [Operations Research 53, (2005) 532–548]. A monopolist firm producing two dependent (substitutable or complementary) products needs to determine the capacity of one flexible resource under demand risk so as to maximize its expected profit. Product demands are linear functions of the prices of both products, and the market potentials are random and correlated. We perform a comparative statics analysis on how demand variability and correlation impact the optimal capacity and the resulting expected profit. In particular, C&R study this problem under the following assumptions/approximations: (i) demand intercepts follow a bivariate Normal distribution; (ii) demand uncertainty is of an additive form; (iii) and under approximate expressions for the optimal capacity and optimal expected profit. We revisit Propositions 2, 3, 4, 5, and 10 of C&R without these assumptions and approximations, and show that these results continue to hold (i) for the exact expressions for the optimal expected profit and optimal capacity, and (ii) under any arbitrary continuous distribution of demand intercepts. However, we also show that the additive demand uncertainty is a critical assumption for the C&R results to hold. In particular, we provide a case of multiplicative uncertainty under which the C&R results (Propositions 2 and 3) fail. © 2010 Wiley Periodicals, Inc. Naval Research Logistics 2010     

Optimal control of price through restricted production

Consider a regulated monopolist whose current profits would be maximized if they could charge a price p?, where p? exceeds the current market price. By reducing production below current consumer demand the monopolist can create an illusion of a shortage and induce the regulator to allow a price increase. Conditions are given for which the production rate that maximizes the monopolist's expected discounted profits over an infinite horizon will have the property that the amount of unsatisfied consumer demand will be a non-increasing function of current market price.     

Social benefits of government investment in enterprises

A critical issue for many governments is boosting the adoption rates of products or technologies that enhance consumer surplus or total social welfare. Governments may, for example, pay subsidies to producers or to consumers to stimulate the manufacture or consumption of specific products, for example, energy-efficient appliances or more effective drugs. This research proposes a strategic government investment policy, namely, share acquisition, and demonstrates its effectiveness in reaching societal objectives. We consider a Cournot quantities-choice market comprised of homogeneous firms where the government intervenes to buy shares, and turning private firms into state-owned enterprises. We recognize that purchasing a single private firm is the optimal policy for the government to reach its societal objectives. Additionally, taking into consideration financial constraints, we find that the optimal stake increases with the budget. Compared with the optimal output-based subsidy policy, when the budget is low, the optimal government investment policy induces a higher consumer surplus. In addition, in differentiated Cournot competition, under which firms compete in selling substitutable products, we find that when the budget is sufficient, the optimal stake purchased first decreases and then increases according to the substitutability level among products.     

Nonlinear pricing with consumer satiation

In various scenarios, consumers may become satiated with products, and the degree of satiation is directly associated with their prior experiences. Confronted with consumer satiation, the seller is unable to either identify consumers who have a higher likelihood of being satiated ex ante or distinguish satiated from non‐satiated consumers ex post. Therefore, the seller should address dynamic selling, valuation uncertainty, and quantity decisions, all of which are important operational issues. We consider a two‐period problem in which consumer types are influenced by their prior consumption experiences. Faced with these consumers, the seller intends to optimize quantities and adjust the prices of the products in each period to maximize revenue. We find that the seller may reduce ex ante production quantity as some consumers become satiated. Moreover, the ex ante quantity is first decreasing and then increasing with regard to the satiation rate. Furthermore, two‐period information asymmetries may provide a rationale for upward distortion in quantity when consumer preferences are highly sensitive to first‐period consumption. © 2016 Wiley Periodicals, Inc. Naval Research Logistics 63: 386–400, 2016     

A nonatomic‐game model for timing clearance sales under competition

We deal with dynamic revenue management (RM) under competition using the nonatomic‐game approach. Here, a continuum of heterogeneous sellers try to sell the same product over a given time horizon. Each seller can lower his price once at the time of his own choosing, and faces Poisson demand arrival with a rate that is the product of a price‐sensitive term and a market‐dependent term. Different types of sellers interact, and their respective prices help shape the overall market in which they operate, thereby influencing the behavior of all sellers. Using the infinite‐seller approximation, which deprives any individual seller of his influence over the entire market, we show the existence of a certain pattern of seller behaviors that collectively produce an environment to which the behavior pattern forms a best response. Such equilibrium behaviors point to the suitability of threshold‐like pricing policies. Our computational study yields insights to RM under competition, such as profound ways in which consumer and competitor types influence seller behaviors and market conditions. © 2014 Wiley Periodicals, Inc. Naval Research Logistics 61: 365–385, 2014     

Bayesian strategies for dynamic pricing in e‐commerce

E‐commerce platforms afford retailers unprecedented visibility into customer purchase behavior and provide an environment in which prices can be updated quickly and cheaply in response to changing market conditions. This study investigates dynamic pricing strategies for maximizing revenue in an Internet retail channel by actively learning customers' demand response to price. A general methodology is proposed for dynamically pricing information goods, as well as other nonperishable products for which inventory levels are not an essential consideration in pricing. A Bayesian model of demand uncertainty involving the Dirichlet distribution or a mixture of such distributions as a prior captures a wide range of beliefs about customer demand. We provide both analytic formulas and efficient approximation methods for updating these prior distributions after sales data have been observed. We then investigate several strategies for sequential pricing based on index functions that consider both the potential revenue and the information value of selecting prices. These strategies require a manageable amount of computation, are robust to many types of prior misspecification, and yield high revenues compared to static pricing and passive learning approaches. © 2006 Wiley Periodicals, Inc. Naval Research Logistics, 2007     

Pricing and capacity allocation strategies: Implications for manufacturers with product sharing

Emerging sharing modes, like the consumer-to-consumer (C2C) sharing of Uber and the business-to-consumer (B2C) sharing of GoFun, have considerably affected the retailing markets of traditional manufacturers, who are motivated to consider product sharing when making pricing and capacity decisions, particularly electric car manufacturers with limited capacity. In this paper, we examine the equilibrium pricing for a capacity-constrained manufacturer under various sharing modes and further analyze the impact of capacity constraint on the manufacturer's sharing mode selection as well as equilibrium outcomes. We find that manufacturers with low-cost products prefer B2C sharing while those with high-cost products prefer C2C sharing except when the sharing price is moderate. However, limited capacity motivates manufacturers to enter into the B2C sharing under a relatively low sharing price, and raise the total usage level by sharing high-cost products. We also show that the equilibrium capacity allocated to the sharing market with low-cost products first increases and then decreases. Finally, we find that sharing low-cost products with a high limited capacity leads to a lower retail price under B2C sharing, which creates a win-win situation for both the manufacturer and consumers. However, sharing high-cost products with a low limited capacity creates a win-lose situation for them.     

Newsvendor problems with sequentially revealed demand information

This article analyzes a capacity/inventory planning problem with a one‐time uncertain demand. There is a long procurement leadtime, but as some partial demand information is revealed, the firm is allowed to cancel some of the original capacity reservation at a certain fee or sell off some inventory at a lower price. The problem can be viewed as a generalization of the classic newsvendor problem and can be found in many applications. One key observation of the analysis is that the dynamic programming formulation of the problem is closely related to a recursion that arises in the study of a far more complex system, a series inventory system with stochastic demand over an infinite horizon. Using this equivalence, we characterize the optimal policy and assess the value of the additional demand information. We also extend the analysis to a richer model of information. Here, demand is driven by an underlying Markov process, representing economic conditions, weather, market competition, and other environmental factors. Interestingly, under this more general model, the connection to the series inventory system is different. © 2012 Wiley Periodicals, Inc. Naval Research Logistics 2012     

Spares stocking policies for repairable items with dependent repair times

This paper analyzes the problem of determining desirable spares inventory levels for repairable items with dependent repair times. The problem is important for repairable products such as aircraft engines which can have very large investment in spares inventory levels. While existing models can be used to determine optimal inventory spares levels when repair times are independent, the practical considerations of limited repair shop capacity and prioritized shop dispatching rules combine to make repair times not independent of one another. In this research a simulation model of a limited capacity repair facility with prioritized scheduling is used to explore a variety of heuristic approaches to the spares stocking decision. The heuristics are also compared with use of a model requiring independent repair times (even though that assumption is not valid here). The results show that even when repair time dependencies are present, the performance of a model which assumes independent repair times is quite good.     

Production and employment scheduling in multistage production systems

A model is developed for planning optimal production and employment levels in multi-product, multistage production systems. The market requirements for each product over the planning period are given. Backorders and/or shortages are permitted. Backorders and shortages must be considered in order to determine the amount of each product's demand that should be filled, backlogged, or go unsatisfied if the production capacity is insufficient to fill all market requirements. Backorders and shortages, on the other hand, are desirable under certain dynamic market conditions.     

Capacity games for partially complementary products under multivariate random demands

In this study, we consider n firms, each of which produces and sells a different product. The n firms face a common demand stream which requests all their products as a complete set. In addition to the common demand stream, each firm also faces a dedicated demand stream which requires only its own product. The common and dedicated demands are uncertain and follow a general, joint, continuous distribution. Before the demands are realized, each firm needs to determine its capacity or production quantity to maximize its own expected profit. We formulate the problem as a noncooperative game. The sales price per unit for the common demand could be higher or lower than the unit price for the dedicated demand, which affects the firm's inventory rationing policy. Hence, the outcome of the game varies. All of the prices are first assumed to be exogenous. We characterize Nash equilibrium(s) of the game. At the end of the article, we also provide some results for the endogenous pricing. © 2012 Wiley Periodicals, Inc. Naval Research Logistics, 59: 146–159, 2012     

How to deal with consumers who group to request a discount?

We investigate operations impacts of consumer‐initiated group buying (CGB), whereby consumers voluntarily form buying groups to negotiate bulk deals with retailers. This differs from regular purchasing whereby consumers visit retailers individually and pay posted prices. Upon the visit by group consumers, a retailer decides to forgo or satisfy their demand in its entirety. Turned down by a retailer, group consumers continue to visit other retailers. In the case where their group effort fails to conclude a deal, some group consumers switch to individual purchasing provided they receive a non‐negative utility by doing so. Even after a successful group event, the group consumers who forgo the event out of utility concern may switch to individual purchasing as well. Retailer competition, group size, and the chance that group consumers switch to individual purchasing upon unsatisfaction are crucial to how retailers adjust operations to deal with CGB. With retailer competition, the rise of CGB results in every consumer paying the same reduced price when group size is small but makes group consumers pay more than by purchasing individually when group size is large. This has mixed consequences on the profits for retailers in both absolute and relative terms.     

Dynamic pricing in a dual‐market environment

This article is concerned with the determination of pricing strategies for a firm that in each period of a finite horizon receives replenishment quantities of a single product which it sells in two markets, for example, a long‐distance market and an on‐site market. The key difference between the two markets is that the long‐distance market provides for a one period delay in demand fulfillment. In contrast, on‐site orders must be filled immediately as the customer is at the physical on‐site location. We model the demands in consecutive periods as independent random variables and their distributions depend on the item's price in accordance with two general stochastic demand functions: additive or multiplicative. The firm uses a single pool of inventory to fulfill demands from both markets. We investigate properties of the structure of the dynamic pricing strategy that maximizes the total expected discounted profit over the finite time horizon, under fixed or controlled replenishment conditions. Further, we provide conditions under which one market may be the preferred outlet to sale over the other. © 2015 Wiley Periodicals, Inc. Naval Research Logistics 62: 531–549, 2015     

Market entry strategy in the presence of market spillovers and efficiency differentiation

Firms form various alliances or use brand extensions to enter new markets in order to improve their operational efficiency and create a positive spillover. However, they do not always know the implications of these strategies for market entry and multimarket competition because the sale of products in one market can have negative spillover effects on product sales in other markets. We present an analytical framework to examine whether and how (i.e., by choosing alliance entry or independent entry) competing firms should enter a market in a situation where market spillovers occur when a firm enters a spillover-producing market to sell products that may increase or decrease the consumers' willingness to pay for products in the primary market. Our analysis shows that the operational efficiency (or quality differentiation ability) of firms in a spillover-producing market varies, and hence, the impact of market spillovers differs for firms. We identify the key factors, such as bargaining power, brand value difference in the primary market, and the extent of efficiencies and spillovers, that determine the firms benefitting from the different entry strategies. Specifically, we show that firms would be more willing to choose an alliance strategy to enter a spillover-producing market if the negative spillover is small and alliance efficiency is high. In contrast, if an alliance entry is not favored, the firms' relative operational efficiency is crucial for them to decide whether to enter the market independently under moderate spillover conditions. Finally, we show the implications of market entry strategies for managers.     

Monitoring the market or the salesperson? The value of information in a multilayer supply chain

We study a supply chain in which a manufacturer relies on a salesperson to sell the products to the consumers. The sales outcome is determined by a random market condition and the salesperson's service level, both of which are privately observed by the salesperson. Apart from them, there are two types of resellers: a knowledgeable reseller observes the market condition, whereas a diligent reseller can monitor the service level. While delegating to a reseller enhances information acquisition, it may also result in double marginalization and inefficiency. We identify several operating regimes in which double marginalization can be eliminated via simple contracts and establish the benefit of monitoring the salesperson over monitoring the market. Our dominance result is not prone to our model characteristics regarding the complementarity of market condition and sales effort, the relative importance of adverse selection and moral hazard, and the contract form. We then generalize our model and re‐establish the dominance result in the presence of reseller's risk aversion or private monitoring expertise. We also quantify the performance gaps among different selling schemes under various scenarios. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Inventory management with advance capacity information

An important aspect of supply chain management is dealing with demand and supply uncertainty. The uncertainty of future supply can be reduced if a company is able to obtain advance capacity information (ACI) about future supply/production capacity availability from its supplier. We address a periodic‐review inventory system under stochastic demand and stochastic limited supply, for which ACI is available. We show that the optimal ordering policy is a state‐dependent base‐stock policy characterized by a base‐stock level that is a function of ACI. We establish a link with inventory models that use advance demand information (ADI) by developing a capacitated inventory system with ADI, and we show that equivalence can only be set under a very specific and restrictive assumption, implying that ADI insights will not necessarily hold in the ACI environment. Our numerical results reveal several managerial insights. In particular, we show that ACI is most beneficial when there is sufficient flexibility to react to anticipated demand and supply capacity mismatches. Further, most of the benefits can be achieved with only limited future visibility. We also show that the system parameters affecting the value of ACI interact in a complex way and therefore need to be considered in an integrated manner. © 2011 Wiley Periodicals, Inc. Naval Research Logistics, 2011     

Designing and pricing menus of extended warranty contracts

Extended warranties provide “piece of mind” to a consumer in that product failures which occur after the base warranty expires are rectified at little or no cost. They also provide an additional source of revenue for manufacturers or third‐party providers, such as retailers or insurance providers, and help cultivate consumer loyalty. In this article, we analyze a number of extended warranty contracts which differ in design, including restrictions on deferrals and renewals. With the use of dynamic programming, we compute the optimal strategy for a consumer with perfect information and determine the optimal pricing policy for the provider given the consumer's risk characterization. We also provide insight into when different contracts should be issued. Finally, we illustrate how profits can be dramatically increased by offering menus of warranty contracts, as opposed to stand alone contracts, with the use of integer programming. Surprisingly, risk‐taking consumers provide the greatest benefit to offering menus. These insights can help a company develop a comprehensive warranty planning strategy for given products or product lines. © 2009 Wiley Periodicals, Inc. Naval Research Logistics 2009     

Nash bargaining over allocations in inventory pooling contracts

When facing uncertain demand, several firms may consider pooling their inventories leading to the emergence of two key contractual issues. How much should each produce or purchase for inventory purposes? How should inventory be allocated when shortages occur to some of the firms? Previously, if the allocations issue was considered, it was undertaken through evaluation of the consequences of an arbitrary priority scheme. We consider both these issues within a Nash bargaining solution (NBS) cooperative framework. The firms may not be risk neutral, hence a nontransferable utility bargaining game is defined. Thus the physical pooling mechanism itself must benefit the firms, even without any monetary transfers. The firms may be asymmetric in the sense of having different unit production costs and unit revenues. Our assumption with respect to shortage allocation is that a firm not suffering from a shortfall, will not be affected by any of the other firms' shortages. For two risk neutral firms, the NBS is shown to award priority on all inventory produced to the firm with higher ratio of unit revenue to unit production cost. Nevertheless, the arrangement is also beneficial for the other firm contributing to the total production. We provide examples of Uniform and Bernoulli demand distributions, for which the problem can be solved analytically. For firms with constant absolute risk aversion, the agreement may not award priority to any firm. Analytically solvable examples allow additional insights, e.g. that higher risk aversion can, for some problem parameters, cause an increase in the sum of quantities produced, which is not the case in a single newsvendor setting. © 2008 Wiley Periodicals, Inc. Naval Research Logistics, 2008